11institutetext: Technical University of Munich, Munich, Germany 11email:
<EMAIL_ADDRESS>22institutetext: Institute of Computational
Biology, Helmholtz Munich, Munich, Germany 33institutetext: Institute of AI
for Health, Helmholtz Munich, Munich, Germany 44institutetext: Department of
Ophthalmology, Ludwig-Maximilians-University, Munich, Germany 55institutetext:
Munich School for Data Science, Munich, Germany

# Noise transfer for unsupervised domain adaptation of retinal OCT images

Valentin Koch 113355 Olle Holmberg 1122 Hannah Spitzer 22 Johannes
Schiefelbein 44 Ben Asani 44 Michael Hafner 44 Fabian J Theis 1122

###### Abstract

Optical coherence tomography (OCT) imaging from different camera devices
causes challenging domain shifts and can cause a severe drop in accuracy for
machine learning models. In this work, we introduce a minimal noise adaptation
method based on a singular value decomposition (SVDNA) to overcome the domain
gap between target domains from three different device manufacturers in
retinal OCT imaging. Our method utilizes the difference in noise structure to
successfully bridge the domain gap between different OCT devices and transfer
the style from unlabeled target domain images to source images for which
manual annotations are available. We demonstrate how this method, despite its
simplicity, compares or even outperforms state-of-the-art unsupervised domain
adaptation methods for semantic segmentation on a public OCT dataset. SVDNA
can be integrated with just a few lines of code into the augmentation pipeline
of any network which is in contrast to many state-of-the-art domain adaptation
methods which often need to change the underlying model architecture or train
a separate style transfer model. The full code implementation for SVDNA will
be made available at https://github.com/ValentinKoch/SVDNA.

###### Keywords:

Style-transfer Unsupervised Domain Adaptation Semantic Segmentation.

##  1 Introduction

Diseases in the Human retina are among the leading reasons for reduced vision
and blindness globally. Estimates are that currently roughly 170 million
people are affected by Age-related Macular Degeneration [1], while Diabetic
Retinopathy is recognized as a global epidemic with the numbers increasing at
ever higher rates [2]. Optical coherence tomography (OCT) is a powerful
technique used in many medical applications to generate real time and non-
invasive cross-sectional images of live biological tissues [3]. In the field
of Ophthalmology, OCT images help doctors to make therapy decisions and
monitor the treatment outcome. As eye diseases are becoming more and more
prevalent due to the increased age of populations [4], the need for research
in automating diagnosis and aiding doctors is increasing.

Recently, deep learning methods are showing promising results in areas such as
disease prediction [5, 6], semantic segmentation [7, 8] or improving quality
[9] of retinal OCT images. Although a lot of progress has been made,
challenges remain in applying artificial intelligence methods on real-world
OCT data, where image characteristics such as signal-to-noise ratio,
brightness, and contrast can vary and cause changes in data distribution, so-
called domain shifts. For OCT images, a particular domain shift is introduced
from different OCT imaging devices being used, which have different image-
quality properties. While for a medical doctor those differences are only a
mild annoyance, machine learning models can quickly fail when faced with only
small disturbances in the underlying data distribution. One solution is to
label images from all possible devices, but as manually labeling images is
very costly and needs highly skilled specialists, other methods need to be
developed.

Domain adaptation methods offer a solution to the reduced performance of AI
algorithms that are caused by the difference in data distribution [10, 11].
Domain adaptation has also been used for shifting domains between different
device manufacturers for OCT imaging devices. Yang et al. [12] detect lesions
in OCT images from different camera devices using an adversarial approach,
several recent works use CycleGAN approaches to transfer style between domains
[13, 14, 15]. In particular, Romo-Bucheli et al. train a CycleGAN and measure
the improved performance on a segmentation task, which makes it the most
comparable work to ours [13]. While GAN architectures are performant when
dealing with domain shifts where the structural difference between the domains
is much larger than between OCT camera devices [16], we argue that for domain
adaptation between retinal OCT devices these models are unnecessarily complex
and can through small changes to image content even be decremental to the
performance.

In this work, we present a novel method for unsupervised domain adaptation
(UDA) for semantic segmentation of retinal OCT images from multiple devices.
The underlying observation motivating our approach is twofold. First, we
observe that the noise structure is a key difference between images from
different OCT cameras and needs to be specifically modeled. Second, we observe
that many UDA methods are often developed for unsupervised domain adaptation
between synthetic and real-world data and are not necessarily optimal for
retinal OCT images. We therefore develop and evaluate a simple but effective
unsupervised domain adaptation method using a singular value decomposition-
based noise adaptation approach (SVDNA). We train a semantic segmentation
model by using SVDNA and show that the model generalizes to unseen OCT devices
and even performs on par with supervised methods trained with manual labels.
Further, we show that the SVDNA method is comparable or even outperforms other
state-of-the-art UDA methods that often require more complex training schemes
or implementation and usage of separate style transfer models. Further, to the
best of our knowledge previous work evaluated on private datasets, making
comparisons difficult, whereas we benchmark SVDNA on publicly available OCT
datasets from multiple devices.

####  1.0.1 Contributions

We make the following contributions to OCT imaging analysis and biomedical
unsupervised domain adaptation:

  * •

We present SVDNA, a minimal method for unsupervised domain adaptation method
that transfers style between images by using a singular value decomposition-
based noise transfer model.

  * •

We demonstrate that our method performs on par or even outperforms more
complex state-of-the-art UDA methods as well as models trained with supervised
labels, while considerably reducing training complexity.

##  2 Proposed method

First we introduce our Singular Value Decomposition-based noise adaptation
method. In the second part, we describe how we trained our segmentation
network with the help of the SVDNA restyled images.

Figure 1:  (a):We train a segmentation network with images from the Spectralis
device which are randomly restyled to the style of the Cirrus, Topcon or
Bioptigen OCT device using SVDNA, thereby enabling unsupervised adaptation to
multiple domains. (b) Comparisons between segmentations before and after SVDNA
domain adaptation.

###  2.1 Singular value decomposition-based noise adaptation (SVDNA)

SVDNA achieves style transfer between a source and target domain image by
decomposing both images of size $n\times n$ into their respective singular
value decompositions $U\Sigma V^{T}$, where $U$ corresponds to the left
singular vectors, $V$ to the right singular vectors and $\Sigma$ to the
singular values. Then, the reconstructed noise from the target domain image is
added to the reconstructed content of the source image. Therefore, we use the
first $k$ singular values and their corresponding right and left singular
vectors from the source image, where the content is encoded, and add the noise
that is encoded in the $k+1,...,n$ singular values and their corresponding
vectors from the target image. The resulting image can be expressed as a
matrix multiplication as can be seen in algorithm 1. The parameter $k$ must be
chosen by hand but is in our experience not very sensitive to variation. In
practice, values between $k=20$ and $k=50$ were used to train our network with
images of $256\times 256$ pixels. For more details on the feasibility of the
used values of $k$ see supplementary figure 2.

Algorithm 1 SVDNA

Let $U\Sigma V^{T}$ be the singular value decomposition of the respective
images imsource, im${}_{target}\in\mathbb{R}^{n\times n}$ and $k$ the noise
transfer threshold.

im${}_{source}=U_{s}\Sigma_{s}V_{s}^{T},\quad$im${}_{target}=U_{t}\Sigma_{t}V_{t}^{T}$,

$U_{r}\leftarrow u_{s}^{1},...,u_{s}^{k},u_{t}^{k+1},...,u_{t}^{n}$

$\Sigma_{r}\leftarrow$diag$(\sigma_{s}^{1},...,\sigma_{s}^{k},\sigma_{t}^{k+1},...,\sigma_{t}^{n})$

$V_{r}^{T}\leftarrow
v_{s}^{1^{T}},...,v_{s}^{k^{T}},v_{t}^{{k+1}^{T}},...,v_{t}^{n^{T}}$

Im${}_{noised}\leftarrow U_{r}\Sigma_{r}V_{r}^{T}$

Im${}_{clipped}\leftarrow$clip_values_to_interval$($Imnoised,$[0,255])$

Im${}_{restyled\\_final}\leftarrow$histogram_matching$($source$=$Imclipped,
target$=$im${}_{target})$

To account for possible out of bound pixel values that can occur after this
noise transfer operation, values are clipped to the interval $[0,255]$. In
addition, a histogram matching [17] step is done after the noise adaptation to
match pixel intensity distribution. This step is motivated by the fact that
after the addition of target image noise and source image content, the pixel
values of the resulting restyled image and target image are still differently
distributed. The effect of this step can be seen in the ablation study in
table 1 of the supplementary material.

Combined, this does not only achieve a visually good style transfer, but we
are also able to match different noise-related metrics of the target domain
well as seen in figure 2. We evaluate the noise transfer from our private
source domain dataset, where images were taken with a Spectralis device, on
three different datasets: Two datasets from the RETOUCH challenge [18]
111Access can be requested at https://retouch.grand-challenge.org/ who use
Cirrus and Topcon devices as well as a dataset with images taken with a
Bioptigen device [19] 222https://www.kaggle.com/paultimothymooney/farsiu-2014.

###  2.2 Training the segmentation network with SVDNA

SVDNA can be used to train any segmentation network and is applied before
augmenting the training images. When loading an image, either no style
transfer (probability $p=1/n$), or an SVDNA style transfer to a randomly
chosen target domain ($p=1-1/n$) is applied, where $n$ is the total number of
domains, including the source domain. When a target domain is chosen, one
image is randomly selected and used as a style target for the input image.
When the source domain is chosen, no style transfer is applied. To maximize
style variability, the hyperparameter $k$, determining the amount of noise to
be transferred, is randomly sampled for each style transfer individually
within range $[20,50]$. As the content of the source image is combined with
the style of the target image, the annotated labels of the source dataset can
be used as ground truth to train the network.

##  3 Results

Figure 2: (a): Sample SVDNA restyling to Topcon, Cirrus, and the Bioptigen
device from a single source domain image (bottom row) for $k=30$. (b): Noise
statistics UMAP [20] between datasets of different domains and SVDNA adapted
datasets.

We compare our SVDNA against state-of-the-art domain adaptation approaches
that we trained with the same segmentation model architecture, data processing
pipeline, and augmentations. As the baseline, we use a network without any
domain adaptation, which we compare to Fourier Domain Adaptation (FDA) [21],
Confidence regularized self-training (CRST) [22], the CycleGAN approach [13]
and an SVDNA trained model. For each method, the main hyperparameters were
individually optimized to include each models best possible results in the
comparison. Training details of all methods can be seen in the supplementary
material.

###  3.1 Data

Our source domain training set consists of 462 OCT scans of the macula, taken
with a Spectralis device (Spectralis; Heidelberg Engineering GmbH, Heidelberg,
Germany) from different patients suffering from age-related macular
degeneration. It is a private dataset annotated by three retinal experts of
the Department of Ophthalmology, Ludwig-Maximilians-University, Munich (B.A.,
J.S. and M.H.), where each pixel of an OCT scan is labeled with one of 14
classes following the Consensus Nomenclature for Reporting Neovascular Age-
Related Macular Degeneration Data of the AAO (American Academy of
Ophthalmology) [23]: Intraretinal Fluid, Subretinal Fluid, Pigment Epithelium
Detachments, Fibrosis, Epiretinal Membrane, Posterior Hyaloid Membrane,
Subretinal Hyper Reflective Material, Neurosensory Retina, Choroid layers,
Choroid Border, Vitreous and Subhyaloid Space, Retinal Pigment Epithelium,
imaging artifacts, image padding. For the quantitative evaluation, the RETOUCH
challenge dataset is used, where images are taken from the Topcon ($2688$
images) and Cirrus ($3072$ images) device and are annotated with Subretinal
Fluid, Intraretinal Fluid, Pigment Epithelium Detachments. The OCT images
annotations were not used in training any algorithms but only for evaluating
performance.

###  3.2 Evaluation

Figure 3: 5-fold cross-validation comparison of different state-of-the-art
methods, the SVDNA method, and the baseline network on the RETOUCH challenge
datasets Cirrus (left) and Topcon (right). The SVDNA trained model outperforms
the baseline and compares or outperforms all other tried methods across all
datasets and classes.

For all experiments a Unet++ [24] with a ResNet18 [25] encoder is used as the
segmentation model. In figure 2a, SVDNA is applied to images of three
different domains, showing how one image can be fitted to the style
characteristics of different target domain images. Figure 2b shows a noise
representation UMAP [20] embedding. For the embedding, three different noise
statistics (signal-to-noise ratio [26], noise variance estimator [27], and
wavelet noise standard deviation estimator [28]) are used. After SVDNA, the
noise embeddings of the restyled Spectralis images align closely with those of
the target domains Topcon and Cirrus. Only with Bioptigen, a domain with a
very high noise level, there is still a gap between the respective embeddings.
Additionally, we compare SVDNA against state-of-the-art domain adaptation
approaches for the task of semantic segmentation on two datasets consisting of
images of a Topcon or Cirrus device respectively in figure 3. As the baseline,
a network without any domain adaptation is used, which is compared to Fourier
Domain Adaptation (FDA) [21], Confidence regularized self-training (CRST)
[22], the CycleGAN approach of Romo-Bucheli et al. [13] as well as our SVDNA
trained model. For each method, the individual hyperparameter were optimized
to include each models best possible results in the comparison. For further
training details of all methods, we refer to the supplementary material. The
evaluation is done on a 5-fold cross-validation over both datasets, using 80%
of the target domain images as style targets for SVDNA or the Fourier Domain
Adaptation or as training images for Self-Training and evaluate on the 20%
remaining images and iterate this until the algorithm has been evaluated on
all data samples. The CycleGAN method was, due to its complicated proposed
evaluation scheme, trained on all of the images. As done in the RETOUCH
challenge, we measure the performance with the dice score. The largest
performance gain over the baseline can be seen for images from the Topcon
device, where the SVDNA model consistently outperformed all other methods
segmenting subretinal fluid and PED and is on par with the CycleGAN method for
intraretinal fluid. When considering the mean performance difference across
all classes, the SVDNA model performs better than all other methods.

Table 1: SVDNA and baseline model compared to the best supervised trained
models from 8 teams in the RETOUCH challenge [18] on a non-public testset of
Topcon (left) and Cirrus (right).

Name | SRF | IRF | PED | mean | rank
---|---|---|---|---|---
SFU [29] | 0.80 | 0.72 | 0.74 | 0.75 | 1
SVDNA | 0.80 | 0.61 | 0.72 | 0.710 | 2
Baseline | 0.42 | 0.17 | 0.66 | 0.42 | 10

Name | SRF | IRF | PED | mean | rank
---|---|---|---|---|---
SFU [29] | 0.72 | 0.83 | 0.73 | 0.76 | 1
SVDNA | 0.66 | 0.61 | 0.74 | 0.67 | 7
Baseline | 0.42 | 0.39 | 0.71 | 0.51 | 10

We also benchmark SVDNA on the separate hold-off non-public test datasets,
where we compare our domain adaptation method to results achieved by fully
supervised trained networks submitted in the RETOUCH challenge. We handed in
predictions of the naive baseline as well as from our SVDNA trained model,
again on the three classes Subretinal Fluid (SRF), Intraretinal Fluid (IRF)
and Pigment Epithelium Detachements (PED). With SVDNA we achieved the second-
best result of 10 submitted segmentation methods on the Topcon dataset and the
sixth-best on the Cirrus dataset. SVDNA achieved a large improvement over the
baseline, as well as a very competitive performance compared to fully
supervised trained models as can be seen in table 1. A qualitative analysis
between methods can be seen in supplementary figure 1, where the three retinal
experts (B.A., J.S. and M.H.) annotated all 14 classes on images from the two
domains Topcon and Cirrus, as well as on the dataset of the manufacturer
Bioptigen. There, accurate segmentations of the SVDNA model can be seen,
whereas other methods often struggle to segment correctly.

##  4 Discussions and Limitations

We demonstrate that the minimal SVDNA method outperforms or performs on par
with state-of-the-art UDA methods and allows for accurate cross-device
segmentation of OCT Images without using any additional labeled data. The
other main benefit of the SVDNA method is that it integrates directly to the
regular training pipeline of semantic segmentation networks and does not need
any modifications to the models architecture or training of a separate style
transfer model as done in the CycleGAN approach [13], which can influence the
feasibility of applying a method in practice. One possible limitation of the
SVDNA method could be that it does not necessarily denoise images well. This
would mean that domain adaptation from Spectralis, a less noisy domain, to
Topcon, Cirrus, or Bioptigen works well but the opposite direction might not
be as successful. One possible solution would then be to do test time SVDNA
style transfer, meaning that when predicting low noise images on a high noise
image trained model, one could add noise to the images before feeding it into
the model, similar to the idea used by the CycleGAN approach where they
restyle images from the target to the source domain at test time. The other
benchmarked state-of-the-art domain adaptation methods did not consistently
perform well for all devices. In our experiments with the CycleGAN model, we
sometimes found it can slightly alter the content of the image or sometimes
even fail completely to produce images similar to the input OCT image. As OCT
biomarkers such as intraretinal cysts and PEDs are often represented by
ambiguous and hard to detect textual features, even the slightest distortion
to the morphology of the tissue can cause incorrect segmentation results, for
examples of content distortions achieved by an optimized CycleGAN see
supplementary figure 4. It is worth noting that in other domains such as on
natural images, small context distortions might have a smaller effect on the
segmentation performance. The features distinguish objects such as cars,
houses, and trees or are considerably different from those representing OCT
biomarkers. The FDA method [21] does not directly distort the content of the
source image, however, we were not able to improve meaningfully over the
baseline. Depending on the hyperparameter settings, either little to no style
transfer was achieved for small beta values or image distorting artifacts got
introduced into images for higher beta values, as can be seen in supplementary
figure 3. Finally using a self-training-based domain adaptation method did not
work well in our experiments which might be due to the limited size of the
datasets.

## Acknowledgements

The present contribution is supported by the Helmholtz Association under the
joint research school “Munich School for Data Science - MUDS“. H.S. and F.J.T.
acknowledge support by the BMBF (grant number: 031L0210A) and by the Helmholtz
Association’s Initiative and Networking Fund through Helmholtz AI (grant
number: ZT-I-PF-5-01). We want to thank Dr. Carsten Marr for his support and
Dr. Hrvoje Bogunović for his help in evaluating our results on the non-public
testset.

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11institutetext: Jet Propulsion Laboratory, California Institute of
Technology, Pasadena, CA, 91109, USA
22institutetext: Montana State University, Bozeman, MT, 59717 ,USA
33institutetext: The Johns Hopkins University Applied Physics Laboratory,
Laurel, MD 20723, USA

# Evolution of a Streamer-Blowout CME as Observed by Imagers on Parker Solar
Probe and the Solar Terrestrial Relations Observatory

P. C. Liewer 11 J. Qiu 22 A. Vourlidas 33 J. R. Hall 11 P. Penteado 11

(Received 00000000; accepted 00000000, 2020)

###### Abstract

Context. On 26-27 January 2020, the wide-field imager WISPR on Parker Solar
Probe (PSP) observed a coronal mass ejection (CME) from a distance of
approximately 30 R⊙ as it passed through the instrument’s $95^{\circ}$ field-
of-view, providing an unprecedented view of the flux rope morphology of the
CME’s internal structure. The same CME was seen by STEREO, beginning on 25
January.

Aims. Our goal was to understand the origin and determine the trajectory of
this CME.

Methods. We analyzed data from three well-placed spacecraft: Parker Solar
Probe (PSP), Solar Terrestrial Relations Observatory-Ahead (STEREO-A), and
Solar Dynamics Observatory (SDO). The CME trajectory was determined using the
method described in Liewer et al. (2020) and verified using simultaneous
images of the CME propagation from STEREO-A. The fortuitous alignment with
STEREO-A also provided views of coronal activity leading up to the eruption.
Observations from SDO, in conjunction with potential magnetic field models of
the corona, were used to analyze the coronal magnetic evolution for the three
days leading up to the flux rope ejection from the corona on 25 January.

Results. We found that the 25 January CME is likely the end result of a slow
magnetic flux rope eruption that began on 23 January and was observed by
STEREO-A/Extreme Ultraviolet Imager (EUVI). Analysis of these observations
suggest that the flux rope was apparently constrained in the corona for more
than a day before its final ejection on 25 January. STEREO-A/COR2 observations
of swelling and brightening of the overlying streamer for several hours prior
to eruption on January 25 led us to classify this as a streamer-blowout CME.
The analysis of the SDO data suggests that restructuring of the coronal
magnetic fields caused by an emerging active region led to the final ejection
of the flux rope.

###### Key Words.:

Sun: corona – Sun: coronal mass ejections

###### Key Words.:

Sun: coronal mass ejections (CMEs); Sun: corona

Figure 1:  Polar plot showing the locations of the three spacecraft (PSP, STA
and SDO(Earth)) on 27 January 2020 at 0 UT. The fields-of-view of the WISPR-I
and WISPR-O telescopes on PSP and COR2 and HI-1 on STA are indicated by solid
lines. The plot is in the Heliocentric Earth Ecliptic (HEE) coordinate frame
and distances are in AU. Figure 2: The CME at two times, 26 January 2020 at 7
UT (left) and 10 UT (right), as seen in WISPR Inner telescope. The inner edge
(left side) is $13.5^{\circ}$ from the Sun center. The cavity, as well as
striations along the length of the flux rope, are evident. The back of the
cavity is indicated by black arrows. Denser material at the back of the flux
rope is also evident. The images are Level-3 data with the background removed
(see text). The white streaks are caused by sunlight reflecting off debris
created by dust striking the spacecraft. The triangular feature near the inner
edge of  the images is an artifact resulting from pixel saturation.

##  1 Introduction

Streamer-blowout CMEs (SBO-CMEs) are typically slow CMEs which originate in
the streamer belt, taking streamer material along as they exit the corona, and
leaving an evacuated streamer behind. The streamer itself is generally seen to
brighten and swell prior to the CME eruption, with considerable coronal
outflow following in its wake (Sheeley et al., 1982; Illing & Hundhausen,
1986; Howard et al., 1986). From a study of 909 LASCO SBO-CMEs, Vourlidas &
Webb (2018) found that SBO-CMEs are associated with polarity inversion lines
away from active regions and are often accompanied by a prominence eruption.
The observed position angle in coronagraph images is generally that of the
streamer belt and heliospheric current sheet.

On 26-27 January 2020, the Wide-field Imager for Solar Probe (WISPR; Vourlidas
et al., 2016) on Parker Solar Probe (PSP; Fox et al., 2016) observed a CME
closely as it passed through the telescope’s 95∘ wide field-of-view. The WISPR
instrument has two white-light telescopes, WISPR-I (inner; covering
approximately $13.5^{\circ}-53.0^{\circ}$ elongation from Sun center) and
WISPR-O (outer; covering approximately $50.5^{\circ}-108.5^{\circ}$ elongation
from Sun center). The transverse extent is approximately $50^{\circ}$; the
inner edge points a fixed $13.5^{\circ}$ from Sun center.

The fortuitous alignment with the Solar Terrestrial Relations Observatory
(STEREO) Ahead spacecraft (STA; Kaiser et al., 2008) at this time provided
views of coronal activity leading up to the eruption, and, based on the
STA/COR2 observations of swelling and brightening of the streamer for several
hours prior to eruption, we classify this as a SBO-CME. PSP was approximately
30 solar radii from the Sun during the observation, providing an unprecedented
view of the flux rope morphology of the CME’s internal structure. We used the
WISPR data to determine the trajectory of the CME by means of the tracking and
fitting technique introduced in Liewer et al. (2020). The CME eruption itself
was observed by the STA/Sun Earth Connection Coronal and Heliospheric
Investigation (SECCHI; Howard et al., 2008) coronagraphs as a near-limb CME on
25 January and the propagation was seen in both COR2 and HI-1 images. The
STA’s second view-point was also used to verify the trajectory determined from
the WISPR data using a novel triangulation technique.

The CME ejection seemed to be associated with the newly emerged active region,
National Oceanic and Atmospheric Administration (NOAA) active region AR 12757.
However, data from the Extreme Ultraviolet Imager (EUVI; Wuelser et al., 2004)
on-board STA suggest that the flux rope may have been sitting high in the
corona for more than a day before the ejection. AR 12757 may have altered the
coronal magnetic structure in a manner that allowed the existing flux rope to
escape. To investigate this scenario, we analyzed data from the Solar Dynamics
Observatory (SDO; Pesnell et al., 2012), which, during this period, was
separated by about 80∘ from STA, and provided disk observations of the solar
activity underlying the CME source region. These observations were compared
with potential-field source-surface (PFSS) models of the corona to help
understand the source region and the sequence of events. The trajectory
determined from the WISPR data suggests that the source region was located
significantly west of AR 12757. To provide context for the analysis presented
below, the positions of the three spacecraft whose data were used – PSP, STA
and SDO (at Earth)– are shown in the polar plot of Fig. 1. The fields-of-view
of the WISPR-I and WISPR-O telescopes on PSP and COR2 and HI-1 on STA are
indicated by solid lines emanating from their spacecraft. These are the
positions on 27 January at 0 UT. The dashed blue line shows PSP’s orbit for
this time period.

The organization of the paper is as follows: In Section 2, we present the
WISPR observations of the CME on 25-26 January, 2020 and the trajectory of the
CME determined from these data. The observation of the CME eruption and
propagation by STA/COR2 and HI-1 are also presented in Section 2. In Section
3, we present observations and analysis chronicling the formation and partial
eruption and final ejection of the CME, the analysis of the corresponding SDO
observations, and the comparison with the PFSS models. In Section 4 we present
the results for determination of the CME location using triangulation between
STA and WISPR and compare these with the trajectory of the CME determined from
the WISPR data alone. Section 5 contains a summary and discussion of the
results.

##  2 White Light Observations of the CME Propagation

###  2.1 WISPR Observations of the CME 26-27 January and Determination of the
Trajectory

The CME, as seen in the WISPR-I telescope, is shown at two times on 26 January
2020 in Fig. 2. These are Level-3 images that have been calibrated in units of
Mean Solar Brightness (MSB), with bias, stray light and vignetting corrections
applied, and a background subtracted. (The publicly released data, and the
descriptions of the data products, can be found at
https://wispr.nrl.navy.mil/wisprdata.) The white streaks in the WISPR images,
here and the images below, are caused by sunlight reflecting off debris
created by dust striking the spacecraft. The images show several features of
the CME flux rope morphology. The cavity is visible, but no bright leading
edge or shock is seen, presumably because of the low speed of the CME (e.g.
Vourlidas et al., 2013). The fact that the cavity is visible suggests that the
axis of the CME is more or less perpendicular to the image plane, and the rib-
like striations surrounding the cavity suggest that the flux rope is at a
slight yaw to this plane, allowing us to see structure along the flux rope
axis. The cavity is followed by considerable bright dense material that
presumably lies at the bottom of the flux rope cavity and is distributed along
the axis. At this time, the CME must be near the location in the sky where the
Thomson-scattered signal into the telescope is maximum to allow such details
to be seen; the region of maximum scattering, along a given line of sight, is
an extended region around the position where the ray intersects the surface a
sphere, called the Thomson sphere (Vourlidas & Howard, 2006; Vourlidas et al.,
2016), which has a diameter extending from the Sun to WISPR.

Fig. 3 shows the CME at a later time on 26 January as it extends across the
fields-of-view of both telescopes. In this figure, the two images have been
reprojected into a coordinate system that we call the PSP orbital coordinate
system (see Liewer et al., 2020). This observer-centric projective cartesian
system is defined by two vectors: the Sun-spacecraft vector and the PSP
velocity vector; together they define the PSP orbit plane. One angle is
measured out of the PSP orbit plane and the other angle parallel to the plane;
the angles are referenced to the midpoint of the inner telescope FOV. This
frame is similar to the HelioProjective Cartesian (HPC) coordinate system in
that both are cartesian, observer-centric and projective. The HPC system uses
the Sun – spacecraft vector and a vector perpendicular to this in the plane
containing both the Sun-spacecraft vector and the solar north axis (Thompson,
2006). In both systems, the coordinates of the solar north vector vary. In
this image and the movie, the Sun is at (0,0). In this system density
structures that might pass over the PSP spacecraft can be seen traveling in
the PSP orbit plane.

In both images of Fig. 3, the CME cavity and dense material are still visible
and, in addition, streamer material, which has been pushed aside, is visible
above the CME structure. In the lower image, the reformed streamer can be seen
behind the CME, and a diffuse V-shaped feature is visible at the back of the
cavity (white circle) that may represent the reconnection site behind the CME.
A movie of the CME in PSP orbital frame covering 26-27 January, 2020 is
available online.

Figure 3: The CME at two times (26 January at 16 and 20 UT) seen in a
projection combining the inner and outer telescope images. Visible in the top
panel, above the CME cavity, is streamer material that has been pushed up by
the CME. In the lower panel, the re-formed streamer behind the CME is visible,
and a diffuse V-shape feature is visible behind the cavity that may mark the
reconnection site (white circle). The position of Mars is labeled in red. The
coordinate system used here is the observer-centric PSP orbital frame,
described in the text. The PSP orbit plane is labeled $0^{\circ}$N and the Sun
(yellow circle, shown to scale) is located at (0,0). A movie of the CME in
this projection is available online.

Using the WISPR images, we determined the trajectory of the CME using the
method described in Liewer et al. (2020). Briefly, a CME “feature” is tracked
in a time sequence of images and the track is fit to analytic expressions
relating the feature’s position in the image as a function of time to its
trajectory in the Heliocentric Inertial (HCI) coordinate system. The analytic
expressions are derived assuming the feature moves radially at a constant
velocity. The HCI coordinate system is an inertial system, centered on the
Sun, with the $z$-axis aligned with solar north axis; latitude is measured
from the $z$-axis and longitude is measured in the the solar equatorial plane
(Thompson, 2006). In this system, the two trajectory angles remain constant
for radial motion. The four trajectory parameters determined using this
technique are the velocity, the two angles, and the radial distance from the
Sun at the time tracking begins. This technique is related to methods used to
determine feature’s trajectories using J-maps (Sheeley et al., 1999, 2008;
Rouillard et al., 2008; Conlon et al., 2014), but extended to include the
effects on the WISPR images caused by PSP’s rapid, highly elliptical orbit
(Liewer et al., 2019, 2020).

Figure 4: Two distinct features that were tracked in a series of images to determine the trajectory of the CME using the technique of Liewer et al. (2020); both images are Level-3 running-differenced images. Left: A WISPR-I image on 26 January 11 UT with the tracked feature (bright V at back of the cavity) circled in red. Right: A WISPR-O differenced image on 27 January 0 UT with the feature (dark spot below bright V-shape) circled. The resulting trajectories are summarized in Table 1.  Table 1: Trajectory Results from Tracking and Fitting Feature Tracked | Bright V at back of Cavity WISPR-I | Dark Spot by V WISPR-O
---|---|---
Parameter | mean | uncertainty | mean | uncertainty
tracking start time $t_{0}$ | 2020-01-26 T03:33 | 2020-01-26 T20:04
distance from Sun (R⊙) | 14 | 0.1 | 30.3 | 0.3
velocity (km s-1) | 278 | 6 | 248 | 16
HCI longitude (degree) | 57 | 2 | 65 | 2
HCI latitude (degree) | 1 | 2 | 2 | 2
HEE longitude (degrees) at 2020-01-26T00:00 | 7.4 |  | 15.7 |
HEE latitude (degrees) at 2020-01-26T00:00 | 7 |  | 9 |

Fig. 4 shows two features that were tracked, one in WISPR-I and one in
WISPR-O, and their trajectories determined. No feature was found that could be
accurately tracked in the FOVs of both telescopes. These images, and the
sequence used in the tracking, are Level-3 running difference images. We use
running-difference images because it makes it possible to track features over
a longer period of time. The circled feature in the WISPR-I image on the left
corresponds to a bright feature at the back of the cavity seen in the upper
panel of Fig. 2. The WISPR-I feature, the bright V at the back of the cavity,
was tracked in 12 images covering 10.5 hours. The results of the tracking and
fitting for this feature gave a velocity of 278$\pm$6 km/s and HCI longitude
and latitude of 57${}^{\circ}\pm 2^{\circ}$ and $1^{\circ}\pm 2^{\circ}$,
respectively. Note that the HCI angles are constant since radial motion has
been assumed in obtaining this trajectory. These HCI angles correspond to
Heliocentric Earth Ecliptic (HEE) angles of (7.4∘, 7.0∘) for the date 26
January 2020 at 12:00 UT. The HEE system uses the Earth Ecliptic plane as the
$x-y$ plane ($0^{\circ}$ latitude), with the $x$-axis ($0^{\circ}$ longitude)
pointing to Earth. Thus, the CME flank could have impacted Earth. The feature
in the WISPR-O image on the right is a dark spot just below the bright
V-shaped figure in the WISPR-O image on the lower panel of Fig. 3. This
feature was tracked in 13 images covering 10 hours.The results of the tracking
and fitting gave HCI longitude and latitude = (65${}^{\circ}\pm$2∘,
2${}^{\circ}\pm 2^{\circ}$) which corresponds to Heliocentric Earth Ecliptic
(HEE) angles of (15.7∘, 9.0∘) for the date 26 January 2020 at 12:00 UT. These
tracking and fitting results (velocity, angles, and radius at time tracking
starts) are summarized in Table 1. Averaging the velocities and angles of
these two solutions gives v=263$\pm$20 km/s and HCI longitude and latitude =
($61^{\circ}\pm 5^{\circ},1^{\circ}\pm 2^{\circ}$).

The polar plot in Fig. 5 shows the predicted trajectory (Table 1) for the
bright feature at the back of the cavity of the CME (*) and the trajectory of
PSP(o) in the HCI coordinate frame with distances in solar radii and HCI
longitude measured from the x-axis. Their locations are plotted every 6 hours
from 26 January at 0 UT to 27 January at 6 UT, the approximate time interval
the CME was observed by WISPR. From this, we see that, according to our
predicted trajectory, PSP is approaching the CME, starting about 35 R⊙ away
and decreasing to about 30 R⊙. The CME is predicted to be very close to
WISPR’s Thomson surface at the beginning, which explains the detailed
observation of the internal structure, but it moves beyond the surface towards
the end of the time interval. The trajectory solution predicts the separation
between STA and the CME to be about 90∘ on 26 January at 0 UT, consistent with
the CME’s appearance as a limb CME for STA. The arrows on the plot point in
the direction to STA (blue, HCI longitude =$-28^{\circ}$) and to Earth (green,
HCI longitude = 49∘) at this same time. Using the velocities and distances
from these trajectories to propagate the CME back to the Sun indicates the CME
left the Sun before 17 UT on 25 January. How much before would depend on the
CME’s unknown acceleration profile.

Figure 5:  Polar plot showing the locations (HCI longitudes and distances from
the Sun in solar radii) at several times for PSP (o) and the predicted
locations of the CME (*) using the trajectory found from the feature tracked
in the WISPR-I images. The locations of each are plotted at the same six
times: every 6 hours from 26 January at 0 UT to 27 January at 6 UT, the
approximate time interval that the CME was observed by WISPR. PSP, heading
toward perihelion, is approaching the path of the CME. The blue arrow shows
the direction to STEREO-A and the green arrow the direction to Earth at the
start of the time interval, 26 January at 0 UT.

###  2.2 STEREO-A COR2 and HI-1 Observations of the CME

The positions of STA and PSP on 27 January at 0 UT can be seen in Fig. 1. The
first indication of the final CME eruption was seen in STA/COR2 on 25 January
2020 at $\sim$ 13 UT on STA’s west limb. For about 8-10 hrs prior to this,
swelling and brightening of the streamer could be seen, indicating that this
was a SBO-CME. Thus, the timing of the CME is consistent with the CME
trajectories determined from the WISPR data, which place the final ejection no
later than mid-day January 25. The COR2 images in Fig. 6 show, on the left,
the streamer before the eruption on 25 January at 0:2:39 UT and, on the right,
the streamer-blowout CME on 26 January at 00:36 UT. In the image on the right,
streamer material is evident both above and below the cavity region as the CME
pushes the streamer open during its escape. No bright front is seen,
indicating a slow CME, consistent with the average velocity of 263 km/s for
the trajectories in Section 2.1 (Table 1). By 26 January at $\sim$ 3-4 UT, the
CME is near the edge of the COR2 FOV, just as the CME enters the WISPR-I FOV.
Unfortunately, STA has a data gap on 26 January from 4 UT until 20 UT, by
which time the CME is in the WISPR-O FOV.

Figure 6: STEREO-A/COR2 images of the streamer before the eruption on 25
January at 0:2:39 UT (left) and of the streamer-blowout CME on 26 January at
00:36 UT (right) . The CME has pushed the streamer material aside as it
escapes the corona. No bright leading edge is seen.

Fig. 7 shows the CME as seen in a HI-1 cropped running-difference image on 26
January at 20:49 UT. This is close to the time of the WISPR images in the
lower panel of Fig. 3. The overall similarity of the structures is evident,
e.g., a cavity region trailed by a large V-shaped structure, displaced
streamer material, and no evidence of a bright leading edge or shock. A movie
of the running-difference images covering 26-27 January is available online.
The movie shows considerable outflow with blobs in the wake of the CME well
after the CME leaves the FOV. This outflow was likely sampled in situ by PSP
instruments a few days later when PSP encountered streamer plasma. There was
no useful data from either COR1 or HI-2 for this event.

Figure 7: A STEREO-A/ HI-1 cropped running-difference image of the CME on 26
January at 20:49 UT. This is close to the time of the WISPR image in Figure 2,
lower panel and similar morphology is seen. An animation of the of CME as seen
by HI-1 is available online. Figure 8: Snapshots of the low coronal evolution
of the MFR associated with the 25 January, 2020 CME, as seen by STA/EUVI 171 Å
. The off-limb emission has been enhanced by removing the background stray
light using a wavelet technique (Stenborg et al., 2008). The dashed arrows
mark the direction of motion. The full movie is available online.

##  3 Evolution of Source Region Leading to Flux Rope Formation, Rise, and
Eruption

During this period, STA and SDO, in Earth orbit, were observing the Sun from
vantage points separated by 79∘ (Fig. 1). They were positioned well to observe
both the source region and the low corona evolution of the CME. In the
following, we use off-limb observations from EUVI and on-disk observations by
the Atmospheric Imaging Assembly (AIA; Lemen et al., 2012) and Helioseismic
and Magnetic Imager (HMI; Schou et al., 2012) onboard SDO to identify the
source region and probe the mechanisms leading to the eruption of the magnetic
flux rope (MFR). As we will see in the following, our data analysis suggests a
highly unusual eruption sequence.

###  3.1 STEREO-A EUVI Observations

The most likely candidate for the source of the 25 January CME seen in COR2
(and WISPR) is a magnetic flux rope structure that began to erupt a full two
days earlier. On 23 January, an MFR-like structure rises from around 12:00 UT
to at least 23:58 UT from a location in the northeast, as seen in EUVI 171Å
images (Fig. 8 and online). The structure moves towards the equator as it
rises, in a ‘tumbling’ manner, common for slow eruptions during solar minimum
(e.g. Panasenco et al., 2013). Unfortunately, no SECCHI data is available from
23 January 23:58 UT through 24 January due to a data gap. The next available
time series, on 25 January, from 00:07 UT on, shows the bottom part of a
structure at the same location as the 23 January MFR (Fig. 8 ). This structure
can be seen to leave the EUVI field of view by about 6 UT on 25 January,
several hours before the CME was detected in COR2. The motions on 23 and 25
January, indicated by dotted arrows on Fig. 8, can be best seen in the online
movie. An inspection of the online movie suggests that the 23 and 25 January
structures are likely the same, but the lack of continuous observation due to
the 24 January data gap, makes this interpretation somewhat uncertain. We did
an exhaustive search of the available imaging data from LASCO and WISPR but
found no evidence of eruptions between 23 January and our CME on the 25th.
STA/COR2 and HI-1 suffer from the same data gap as EUVI. However, there should
be some evidence in HI-1 of any events prior to our target CME due to the
large HI-1 FOV (15 to 96 R⊙, approximately). We found none. So we infer that
the flux rope that started erupting slowly on 23 January at 11 UT in EUVI 171Å
was constrained by the overlying coronal fields until 25 January, probably
rising slowly throughout. The first clear signature of the CME (the opening up
of the steamer) is seen at $\sim$ 13 UT in the COR2 FOV. Such a slow evolution
in the inner corona is not as unusual as it seems. Hess et al. (2020) reported
a similarly slow rising MFR structure for the first CME captured by WISPR on 1
November 2018. These events are usually associated with streamer-blowout CMEs
(SBO-CMEs), named after the almost complete evacuation of the streamer during
the ejection. In an extensive analysis of these events, Vourlidas & Webb
(2018) found that the average SBO-CME duration is 40.5 hours. Therefore, our
CME is fully consistent with a typical SBO-CME.

Slow rising CMEs leave very little trace of activity on disk. An SBO-CME was
the archetypical ‘stealth’ CME (Robbrecht et al., 2009). The EUVI images show
no connection to AR 12757, clearly seen on the disk by EUVI on 25 January,
which suggests that the event originates behind the visible (from STA) western
limb. We, hence, turn to the AIA and HMI observations to search for the source
region.

Figure 9: (a)-(c): Full disk SDO/AIA images in 171 Å passband on 23, 24 and 25
January, overlaid with contours ($\pm 200$ G, red and blue) of line-of-sight
magnetic flux density obtained by HMI at around the same times of the AIA
images. (d): signed total magnetic flux integrated over the full disk. (e):
total EUV flux in 171 Å integrated over the full disk. (f): EUV flux in 171 Å
integrated in several Regions Of Interest (ROIs), as indicated by circles or
ovals in panels (a) - (c). Note that the EUV flux is derived by integrating
data counts in each of these ROIs with a fixed angular extent, and the
changing projected area in the plane of sky due to solar rotation is not
corrected. For clarity of display, these light curves are normalized to the
flux at 0 UT on 23 January. Vertical dashed lines in panels (d-f) indicate the
three stages of the radiation and magnetic activities, and the solid arrows
indicate the times when the MFR was seen rising on 23 January and then erupted
on 25 January, as observed in the STA images.An animation of the AIA/HMI
overlays is available online.

###  3.2 HMI and AIA Observations

We have analyzed full-disk EUV 171 Å images obtained by SDO/AIA, and full-
disk, line-of-sight magnetograms obtained by SDO/HMI from 23 January through
25 January. These observations reveal surface activities that are likely
related to the evolution of the corona and flux rope during its eruption. HMI
shows emergence and cancellation of magnetic flux, including the birth of AR
12757 prior to the CME. Prominent radiation signatures in the AIA 171 Å
passband are brightenings, indicative of reconnection heating, and dimmings
which indicate evacuation of coronal material due to expansion of the coronal
structure (Sterling & Hudson, 1997; Thompson et al., 2000; Reinard &
Biesecker, 2009) or by interchange reconnection between low-lying and high-
lying magnetic fields (e.g. Attrill et al., 2006; Downs et al., 2016). Such
signatures were observed at the times when the flux rope was seen by STA/EUVI
to rise on the morning of 23 January and when the flux rope escaped two days
later on 25 January (Section 2.2). These signatures are likely related to
changes in the corona during the partial eruption and final escape of the flux
rope.

The top panel of Fig. 9 shows a series of 171 Å full-disk images during the
three days, superimposed with the contours of the longitudinal magnetic field
at $\pm 200$ G in red and blue, respectively. Also shown in Fig. 9d and 9e are
the signed total magnetic flux (in units of Mx) and the total 171 Å flux (in
units of counts per second), both integrated over the entire disk, over the
three days. Brightenings and dimmings were prevalent in various regions within
$\pm$30∘ in latitude from the equator. We identify several of these regions as
Regions of Interest (ROIs), which are denoted by color-coded circles or ovals
in Fig. 9a-c. The 171 Å light curves for these ROIs are given in Fig. 9f with
the same colors. The movie shows more clearly radiation and magnetic
activities in these regions during the three days, which may be described in
three stages, as marked by the vertical dashed lines in Fig. 9d-f. We discuss
each stage in detail below.

Formation and Rise of the Flux Rope:  Throughout 23 January, the total
magnetic flux does not vary significantly, but the total 171 Å flux increases
from the start of the day until 10 UT, and then decreases. Specifically,
sudden brightenings with small ejecta occurred before 3 UT on 23 January in a
bipolar region (referred to as Region of Interest-A, or ROI-A hereafter) in
the northwest, shown in Fig. 9a. Subsequently, from 8 UT, significant dimming
was observed in ROI-A. From 6 to 12 UT, a couple of bipolar regions to the
south-east of ROI-A, near the equator and central meridian, also exhibit
brightenings. Finally, a sequence of brightenings and dimmings, although not
as prominent, was observed in extended areas across the disk along the similar
latitude, or the northern region ROI-N, shown in Fig. 9a. The lightcurves in
171 Å in ROI-A and ROI-N are given in Fig. 9f. This series of events coincided
with the appearance of the rising flux rope in the field of view of EUVI (Fig.
8), and are therefore likely the on-disk manifestations of the partial
eruption of the MFR see on the limb by EUVI.

Emergence of AR 12757:  Early on 24 January, emerging flux was observed near
the east limb as seen from Earth (and near the west limb as seen from STA).
The flux emergence region is referred to as ROI-B and denoted in Fig. 9b and
c. In twelve hours, the magnetic flux in ROI-B has increased by 4$\times
10^{20}$ Mx in both the positive and negative polarities (Fig. 9d), associated
with prominent alternating brightenings and dimmings in this area as shown in
Fig. 9f. The flux emergence paused at 12 UT on 24 January for the remainder of
the day, although brightenings and dimmings continue to occur. This region was
officially identified as AR 12757 on 25 January.

Ejection of the Flux Rope: Early on 25 January, rapid flux emergence took
place again in AR 12757 (ROI-B), as shown in Fig. 9d. This was accompanied by
brightenings due to formation and heating of new loops in the emerging active
region. Subsequently, dimmings occurred around these new loops and are visible
in the included movie. These signatures suggest reconnection between emerging
flux and adjacent or overlying fields, leading to a restructuring of the
corona (e.g., Shibata et al., 1992; Moreno-Insertis & Galsgaard, 2013). Weak
coronal dimmings were also observed in an extended area, denoted as the
middle-southern region, ROI-M, in Fig. 9c and f, which proceeded from the
start of the day till 6 UT on 25 January. These events coincided with the
final eruption of the flux rope, seen leaving the EUVI field of view by 6 UT
on 25 January near the solar equator (Fig. 8, and accompanying movie). These
signatures are likely related to the final eruption of the CME by
restructuring global coronal magnetic fields constraining the CME. On the
other hand, they are not direct signatures of an ejection from the low corona,
which should usually produce significant and expanding dimmings, waves, or
cool ejecta, not evident in the disk observations. This is consistent with the
release and acceleration of the CME high in the corona and lends further
support to our eruption scenario. The lack of association between AR 12757 and
the rising coronal structure can also be seen in the EUVI movie on 25 January;
AR 12757 is the small bright region approaching the west limb.

Figure 10: PFSS reconstructions of the coronal magnetic fields at three times
showing the evolution of the global magnetic field from the SDO view (top
panels) and from the STA view (lower panels). The three times, 23 January at
12 UT, 24 January at 18 UT, and 25 January at 0 UT, show the global magnetic
field during the three stages described in the previous text. The green and
magnetic lines show the open field lines of two polarities.

###  3.3 Comparison with PFSS modeling

The combined STEREO and SDO observations provide a comprehensive view of CME-
associated activities, which occur over a large range of heliolongitudes. To
probe the connection between the evolution of the flux rope and brightening
and dimming signatures on the disk, we reconstruct the global magnetic field
using the PFSS model available in SolarSoft. This model uses synoptic
magnetograms which include the effects of magnetic flux transport as described
in (Schrijver & De Rosa, 2003), updated to use HMI magnetograms. New active
regions are not incorporated into the synoptic magnetograms until reaching the
HMI FOV which covers about $\pm 30^{\circ}$ from the central meridian. Thus AR
12757, which emerged on 24 January, is not in the synoptic magnetograms until
25 January .

Fig. 10 shows the global magnetic field from the SDO view (upper row) and from
the STA view (lower row), during the three stages described in the previous
section. Before the emergence of AR 12757, the maps reveal a magnetic arcade
extending from the north-west toward the center of the Sun with multiple
smaller arcades underneath. These arcades indicate polarity inversion lines
over which flux ropes could form. After 24 January, the arcade is further
elongated toward the east. The ROI-A exhibiting prominent brightenings and
dimmings at the time of the partial eruption of the flux rope on 23 January is
located at the western end of the arcade, whereas the emerging AR 12757
(ROI-B) is located at the eastern end of the elongated arcade.

These observations suggest that the flux rope was likely confined in the
corona, and its partial eruption on 23 January and final ejection on 25
January were related to activities in these two ROIs. It is plausible that,
during the initial eruption on 23 January, the rise of the flux rope was held
back by overlying coronal magnetic fields. The brightening and dimming
signatures in the northern band (ROI-N) probably reflect the impact of the
rising flux rope on the overlying coronal fields. Two days later, interaction
between the emerging active region and magnetic field of the flux rope or the
large scale coronal fields overlying the flux rope probably played a role in
the final MFR ejection.

Interestingly, the PFSS reconstruction on 25 January, one day after the
emergence of AR 12757, shows significant changes in the global configuration
with a large amount of magnetic flux opening up in the northern hemisphere
(Fig. 10, top panel, right). This change also agrees with the hypothesis that
the flux rope was lying somewhere along the east-west direction north of the
equator, and its eruption opened up the magnetic field there.

To summarize, although the newly emerging AR 12757 has probably played an
important role in the final ejection of the CME on 25 January, joint STA and
SDO observations reveal that the flux rope has started to rise two days
earlier, before the birth of AR 12757. Based on the tracking and fitting
trajectories in Table 1, the CME is displaced by at least 30∘ to the west of
AR 12757. The trajectories were determined from the WISPR data using a
tracking and fitting technique which assumes a constant radial motion. To
further examine the location of the CME, we also apply triangulation using CME
observations from multiple views.

Figure 11: Left: WISPR-O image of 26 January at 20:49 UT with the selected
feature circled in red. Selecting this feature defines a line-of-sight from
PSP to the feature. Right: Simultaneous HI-1 image with points along the line
sight from PSP to the selected feature for three distances along this line-of-
sight, projected onto the image (red +’s). The points correspond to distances
of 10, 27 and 44 R⊙; the point corresponding to 27 R⊙ falls on the feature
selected in the WISPR-O image, which determines the feature’s coordinates (see
text). The Sun (yellow globe) in the panel on the right is shown to scale. The
HI-1 image is projected in the Helioprojective Cartesian (HPC) system (red and
blue grid lines) with the Sun (yellow globe) drawn to scale.

##  4 Determining CME’s Position by Triangulation using WISPR and STEREO-A

When an object or feature is observed simultaneously from two spacecraft, it
may be possible to use triangulation to determine the 3D location of the
feature at that time. Unlike the tracking and fitting technique used to
determine the CME trajectory (position vs. time) presented in Section 2,
triangulation makes no assumption about the motion of the feature. It does
assume that the same “feature” can be seen from both viewpoints, which works
best for localized features. Usually, because of the diffuse nature of CMEs
and the line-of-sight integration of coronagraphs, the CME may look quite
different from the two viewpoints and the application of this technique to
coronagraph images is limited (Liewer et al., 2009; Colaninno et al., 2013).
However, in this event, both WISPR and STA images resolve structure within the
CME and thus several features can be identified in simultaneous image pairs.
Because of the STA data gap on 26 January from 4 to 20 UT, simultaneous images
exist only for a few hours.

We use a novel triangulation technique to determine the location of the CME
using simultaneous FITS images from STA and WISPR that relies on the SolarSoft
package SUNSPICE. This technique can be used to determine the 3D location of
any feature in a WISPR image that is seen simultaneously in an image from a
white-light telescope on another spacecraft provided the FITS images have both
proper World Coordinate System (WCS; Thompson, 2006) and camera model
information in their headers. To start, the user selects the feature in the
WISPR image. The pixel location in the image defines a particular line-of-
sight through space; the WCS and camera model information in the header allow
that line-of-sight to be traced in, e.g., the Heliospheric Inertial frame. The
feature could lie anywhere along that line-of-sight. Any point along that line
is specified by its distance $d$ from PSP. Next, an array of possible
distances of the feature from PSP is chosen, which then specifies an array of
points along the line-of-sight, here, in HCI coordinates. These points are
then projected onto the simultaneous image from the second spacecraft using
WCS and camera model information in its FITS header. When one of these points
projects onto the same feature in the second image, the HCI coordinates of
this feature have been found. Trial and error are used to find the proper
distance of the feature from the spacecraft. If none of the projected points
falls on the feature in the second image, the process is repeated with a new
array of distances until one of the projected points “hits” the feature in the
second image. Once the proper distance to the feature has been determined, the
HCI coordinates of this point represent the 3D location of the feature.

This technique is illustrated in Fig. 11, using images from STA/HI-1 and
WISPR-O. The left image is the WISPR-O FITS image on 26 January at 20:49 UT.
We use the same WISPR-O feature used in the trajectory determination: the dark
spot behind the diffuse V. The position in the image of the selected feature
(red circle) specifies WISPR-O’s line of sight to the feature. The right image
is the HI-1 image at the same time, showing the projected locations of three
points along the WISPR line-of-sight, as viewed from STA, for three assumed
distances $d$ from PSP. The projected locations (red +’s) were specified by
the three distances from PSP of $d$ = 10, 27 and 44 R⊙. The middle red +,
corresponding to the distance of $d$=27 R⊙, falls on the selected feature,
and, thus the distance to this feature from PSP is determined. The uncertainty
in this distance is 2 R⊙, found by varying the distance as much as possible
while the red + still appeared to “hit” the feature. The coordinates of the
feature found in this manner are distance from the Sun r/R⊙ = 31 $\pm$ 2 , HCI
longitude and latitude = ( $66^{\circ}\pm 3^{\circ}$, $-2^{\circ}\pm
2^{\circ}$). These angles are in excellent agreement with the angles found by
tracking and fitting this feature in Table 1 (average angles: HCI longitude
and latitude = ($61^{\circ}\pm 5^{\circ},1^{\circ}\pm 2^{\circ}$). The
distance from the Sun is also in excellent agreement with the predicted
distance at this time of r/R⊙= $31.2\pm 0.3$, validating our trajectory
solution.

Figure 12: Left: WISPR-I running differenced image at 03:56 UT with the
feature used in tracking (bright spot at the back of the cavity) circled in
red. Center: nearly simultaneous STA/COR2 running differenced image (03:54 UT)
with the common feature use for triangulation labeled v1/yellow arrow. Also
shown are three predicted locations (red +’s) of the WISPR feature projected
onto the COR2 image for three possible distances of the feature from PSP. The
middle red + falls on the feature and thus determines the 3D location of the
common feature (see text). Right: COR2 image at an earlier time (01:39 UT)
when the full CME cavity structure was visible, allowing identification of the
feature (marked v1/yellow arrow). The COR2 image is projected in the
Helioprojective Cartesian (HPC) system (red and blue grid lines) with the Sun
(yellow globe) drawn to scale.

We also used the above triangulation technique to determine the location of
the CME at an earlier time (26 January at 03:54 UT) using WISPR-I and STA/COR2
images. The only simultaneous WISPR-COR2 image pairs occur when the CME was
just entering the WISRP-I FOV and just leaving the COR2 FOV. The two
simultaneous images used in the triangulation are shown in Fig. 12a (WISPR-I
at 03:56 UT) and Fig. 12b (COR2 at 03:54). Both are running difference images.
The CME feature used in the triangulation is the same bright V at the back of
the cavity (Fig. 4) used for trajectory determinations (Table 1); it is
circled in red in Fig. 12a. At this time, the full structure of the cavity was
no longer visible in the COR2 image (Fig. 12b), but several bright V-shaped
features are visible. It was only possible to determine which bright V
corresponded to the circled bright V feature in the WISPR-I image by using the
sequence of COR2 images leading up to this time. We started at a time more
than two hours earlier (01:39 UT) when the cavity structure was still visible
(Fig. 12c). In this image it is clear which bright feature marks the back of
the cavity: Note the similarity in the relation of this feature, labeled
V1/yellow arrow) to the CME cavity to that of the circled feature and cavity
in the WISPR image at 03:56 UT (Fig. 12a). Once the common feature was
identified at this earlier time, we followed it in the sequence of five COR2
images to the time of the simultaneous pair (03:54 UT, Fig. 12b) where the
feature (V1, yellow arrow) has now moved towards the edge of the COR2 FOV. In
addition, we then verified that we had identified the correct feature in the
COR2 image by using the trajectory determined for this feature in Sec. 2.1
(Table 1) to predict the HCI coordinates of this feature at the time of the
earlier image, before it was visible in WISPR, and projecting this location on
to the earlier COR2 image at 01:39 UT. The predicted location of this feature
is shown as the red + in Fig. 12c. It can be seen that it falls quite close to
the bright feature (V1/yellow arrow). Considering that this image is at a time
2 hrs before the tracking in WISPR began, we consider our feature
identification to be reliable.

With a common feature identified in the simultaneous image pair, we now apply
the triangulation technique used for the HI-1 triangulation described above.
We projected potential locations for the WISPR feature V1(Fig. 12a, inside red
circle) at 03:56 UT onto the nearly simultaneous COR2 image (03:54 UT) for an
array of distances $d$ from PSP. Fig. 12b shows the projected location for
three assumed distances of the feature from PSP: $d$/R⊙ = 28, 33, and 38. As
for the HI-1 triangulation, the uncertainty was determined by varying the
choice of distances over which the projected point appeared to fall on the
feature. The end result for the location of this feature was distance from the
Sun r/R⊙ = $14.0\pm 0.1$, HCI longitude and latitude = ($67^{\circ}\pm
5^{\circ},-2^{\circ}\pm 1^{\circ}$). Recall that the trajectory determined for
this feature in Sec. 2.1 had a smaller HCI longitude ($57^{\circ}\pm
2^{\circ}$). The trajectory predicts that this feature should be at r/R⊙ =
$14.5\pm 0.1$ at this time. The agreement between the triangulated location
and the predicted location from the trajectory for this COR2 case is good, but
not as good as in the HI-1 case and not within the error bars due to the
techniques used. This may be due to the line-of-sight integration problem for
coronagraph images discussed above. Also, as discussed in Liewer et al.
(2020), there are additional sources of errors in the tracking and fitting
technique itself, most obviously from the possible violation of the assumption
of radial propagation at a constant velocity. We conclude that the two
techniques, tracking and fitting versus triangulation, are complementary and
help establish the overall limits on both techniques and help improve the
usefulness of both.

##  5 Summary and Discussion

In this paper, we have presented a detailed analysis of the evolution of a
streamer-blowout CME on 25 January 2020 using data from three spacecraft: PSP,
STEREO-A and SDO. WISPR on PSP provided images of the propagation of the CME
and its internal structure from a distance of about 30 R⊙, revealing a complex
flux rope morphology. The WISPR data were also used to determine the
trajectory of the CME using the technique of Liewer et al. (2020). STA/EUVI
provided data that suggested that the magnetic flux rope partially erupted two
days before the final ejection of the CME on January 25, 2020. Unfortunately,
there was a STA data gap on 24 January, so we are unable to follow the flux
rope continuously. However, a thorough search of available data (STEREO, SOHO,
PSP) did not show any eruptions on 23-24 January. On 25 January, STA/COR2 data
showed both the swelling of the streamer beforehand and the final ejection of
the CME, which led us to classify the event as a streamer-blowout CME. STA
provided images of the CME’s propagation, including simultaneous images with
WISPR at several times. These simultaneous images allowed us to use a novel
triangulation technique to determine the CME’s positions at the times of the
image pairs, confirming the trajectory determination using the WISPR data
alone. The technique can be used to locate features seen in simultaneous FITS
images from WISPR and any second spacecraft, provided the images have the
proper World Coordinate System (Thompson, 2006) and camera model information
in their headers.

The CME was near STA’s west limb and, fortuitously, SDO was about 80∘ to the
west of STA and provided excellent coverage of the underlying solar surface
activity. SDO/HMI data was used to track magnetic flux emergence and
disappearance for the three days 23-25 January, 2020. SDO/AIA 171 Å data was
used to track brightenings and dimmings, proxies for coronal heating by
reconnection and the opening and/or rising of coronal loops (leading to
evacuation or cooling), respectively. Three stages of activity were analyzed:
the confined eruption on 23 January, the emergence of new active region AR
12757 on 24-25 January, and the final ejection of the magnetic flux rope early
on January 25. The SDO analysis was supplemented by PFSS modeling of the
corona corresponding to each of the three stages.

The analysis supports the following scenario: A magnetic flux rope partially
erupted on 23 January. The prominent brightening and dimming observed in a
bipolar regions in the NW quadrant by SDO were possibly related to the initial
eruption. The flux rope deflected southward (cf. (Fig. 8), guided toward the
heliospheric current sheet near the solar equator by the overlying magnetic
fields (Liewer et al., 2015), which also confined the eruption (Figure 10). On
24 January, a new active region, later NOAA AR 12757, started emerging in the
NE quadrant as seen from SDO. This led to a major restructuring of the solar
magnetic field according to the PFSS models. Apparently, this reduced the
constraints on the flux rope, leading to the brightening and swelling of the
overlying streamer and final eruption of the flux rope. This scenario is
supported by the trajectory determined from the WISPR data using the tracking
and fitting technique of Liewer et al. (2020): The CME’s HCI latitude was
found to be $2^{\circ}\pm 2^{\circ}$ and is consistent with the latitude of
the very flat heliospheric current sheet essentially at the solar equator
during this time period. The longitude of about $61^{\circ}\pm 4^{\circ}$ puts
the trajectory about $13^{\circ}$ west of Earth and about $35^{\circ}$ west of
the location of AR 12757 on 25 January. The HCI latitude of $1^{\circ}\pm
2^{\circ}$ converts to an HEE latitude of $8^{\circ}\pm 2^{\circ}$. The CME
could have given Earth a glancing blow, but no ICME signatures were observed
in situ (Q. Hu, private communication). The average velocity of the CME was
found to be v=263$\pm$20 km/s. Nindos et al. (2020) (this issue) also made a
determination of the velocity of this CME as part of their work on tracking
WISPR-I features. They found v = 258 km/s (their Fig. 6, track Number 4), in
excellent agreement with our result.

A prolonged initiation phase for slow CMEs is not uncommon. As noted above,
Vourlidas & Webb (2018) derived an average duration for SBOs of 40.5 hours.
Many polar crown filaments exhibit the characteristic shape of a flux rope and
can exist for days before erupting (Gibson, 2015). For example Howard &
DeForest (2014) analyzed such a case and found that the slow ( 400km/s), CME
launched about 5 days after the formation of the flux rope.

We note that the DONKI data base also gave a prediction for the 25 January
2020 CME to deliver Earth a glancing blow. The CME speed in the database is
higher (v=362 km/s), the start time later, and the source region is identified
as the active region AR 12757. As we discussed above, this AR was in the FOVs
of both SDO and STA and analysis of AIA and EUVI data showed little connection
between the CME and this AR. The most likely reason for the misidentification
is the extremely slow evolution of this CME. It is not customary to search for
CME eruptions days before a CME while it is customary (and human nature) to
tend to associate CMEs with the nearest on-disk activity. As we show here (and
in the past, e.g. Nieves-Chinchilla et al., 2013; Patsourakos et al., 2013;
Colaninno & Vourlidas, 2015), the easiest approach is not necessarily the
correct one. This is particularly true for solar minimum CMEs that tend to
have weak or even no obvious low surface manifestations. Our event falls under
the ‘stealth’ CME category. As for the original ‘stealth’ CME (Robbrecht et
al., 2009), the event itself and its source region were identified only thanks
to the off-”Sun-Earth” Line (SEL) EUVI and coronagraphic observations from
STA. The 26 January CME event demonstrates two important space weather aspects
of slow CMEs: the formation/initial eruption phases of such events can be
long-lived, lasting for more than a day, below the traditional FOVs of
coronagraphs. Care must be exercised in the identification of the source
regions with the search extending at least a day or two prior to the
identification of the eruption in the middle corona. Although slow CMEs are
less likely to be geo-effective on their own, they carry magnetic fields and
will interact with other CMEs or stream interface regions (SIR), altering
their magnetic and plasma configuration. A slow CME, for example, could be
trapped and compressed at the leading edge of an SIR (Rouillard et al., 2011),
increasing the potential impact on geospace. So it is important to include
such events in the operational modeling of the inner heliosphere. The most
efficient way to detect them are the off-SEL observations, say, from Lagrange
L4 or L5 vantage points.

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###### Acknowledgements.

We gratefully acknowledge the help and support of the WISPR team and William
Thompson, Adnet System, Inc., throughout this work. The work of P. C. Liewer,
J. R. Hall, and P. Penteado was conducted at the Jet Propulsion Laboratory,
California Institute of Technology under a contract from NASA. A. Vourlidas is
supported by the WISPR Phase-E funding and NASA grant 80NSSC19K1261. J. Qiu is
partly supported by NASA’s HGI program (80NSSC18K0622). Parker Solar Probe was
designed, built, and is now operated by the Johns Hopkins Applied Physics
Laboratory as part of NASA’s Living with a Star (LWS) program (contract
NNN06AA01C). Support from the LWS management and technical team has played a
critical role in the success of the Parker Solar Probe mission.