# PolMERLIN: Self-Supervised Polarimetric Complex SAR Image Despeckling with
Masked Networks

Shunya Kato, Masaki Saito, Katsuhiko Ishiguro, and Sol Cummings Shunya Kato is
with the Graduate School of Informatics, Kyoto University, Kyoto 606-8501,
Japan (e-mail: s-kato@nlp.ist.i.kyoto-u.ac.jp).Masaki Saito, Katsuhiko
Ishiguro, and Sol Cummings are with Preferred Networks Inc., Tokyo 100-0004,
Japan (e-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>scummings@preferred.jp).

###### Abstract

Despeckling is a crucial noise reduction task in improving the quality of
synthetic aperture radar (SAR) images. Directly obtaining noise-free SAR
images is a challenging task that has hindered the development of accurate
despeckling algorithms. The advent of deep learning has facilitated the study
of denoising models that learn from only noisy SAR images. However, existing
methods deal solely with single-polarization images and cannot handle the
multi-polarization images captured by modern satellites. In this work, we
present an extension of the existing model for generating single-polarization
SAR images to handle multi-polarization SAR images. Specifically, we propose a
novel self-supervised despeckling approach called channel masking, which
exploits the relationship between polarizations. Additionally, we utilize a
spatial masking method that addresses pixel-to-pixel correlations to further
enhance the performance of our approach. By effectively incorporating multiple
polarization information, our method surpasses current state-of-the-art
methods in quantitative evaluation in both synthetic and real-world scenarios.

###### Index Terms:

Polarimetric SAR image, despeckling

##  I Introduction

Figure 1:  Comparison of self-supervised despeckling methods. Blue pixels
indicate the range of receptive fields. (a) Speckle2Void uses blind-spotting
(spatial information). (b) MERLIN predicts a Re/Im component from the
counterpart component in a single polarization signal. (c) The proposed
PolMERLIN predicts Re/Im components from the counterpart components of multi-
polarization signals. To use spatial information as well, PolMERLIN
intentionally removes some pixels from the receptive field.

SAR images suffer from signal-dependent and spatially correlated noise, which
is commonly referred to as speckle noise. This noise arises due to the
interference of scattered waves, which are randomly phased, from numerous
scattering surfaces. Due to the pronounced degradation of image quality by the
speckle noise, despeckling of SAR images is crucial to preserve image fidelity
and prevent performance degradation in downstream tasks, such as semantic
segmentation [4].

The tremendous strides made in deep learning have spurred the development of
numerous despeckling techniques. These approaches generally fall into two
categories of training methods: supervised and self-supervised. In the former
[2, 14, 13], a network is trained from a set of paired noisy and noise-free
images of the same subject, with the benefit of leveraging well-established
denoising networks like CNN and Transformer. However, obtaining noise-free SAR
images directly from satellites or aircraft remains a challenge [11, 12].
These studies circumvent this by calculating the mean of multi-temporal SAR
images, which requires avoiding areas that have undergone changes, or by
adding pseudo-speckle noise in non-remote sensing optical images, which
creates a gap between training and testing conditions. [14, 13].

On the other hand, self-supervised training can bypass this challenge, as it
does not require noise-free SAR images. Speckle2Void [9] addresses despeckling
of SAR amplitude images using a self-supervised denoising method [6].
Additionally, MERLIN [3] presents a self-supervised despeckling technique
designed for two channels, based on the statistical property that the real and
imaginary components of a complex SAR image are uncorrelated. However, this
method is still limited to single polarization SAR images, thus constraining
the available speckle noise data.

In this study, we present PolMERLIN, a novel self-supervised despeckling
method that leverages “multi-polarization complex SAR images” to achieve
superior performance. As depicted in Figure 1, PolMERLIN exploits the spatial
correlation among multiple polarization complex images, in contrast to MERLIN,
which can only handle single polarization complex SAR images. Specifically, we
extend the statistical model of speckle noise from single-polarization complex
SAR images to multi-polarization complex SAR images.

According to this model, we reveal that the same components between different
polarizations are correlated, while different components are independent.
Based on these findings concerning the (in)dependencies, we propose a novel
self-supervised learning method, called channel masking, which masks the same
component in a multi-polarization complex SAR image and predicts it from the
other component.

While channel masking effectively despeckles by taking into account the
independent relation between components, it overlooks the pixel-to-pixel
relationship that is employed in [9]. To enhance the despeckling performance
further, we incorporate the idea of spatial masking that masks a portion of
the unmasked component [9, 6]. By integrating these two techniques, PolMERLIN
outperforms MERLIN, a state-of-the-art self-supervised despeckling method, in
both simulated and real datasets.

##  II Statistical Model of Complex SAR

This section summarizes the generation process of single-polarization complex
SAR images formulated in MERLIN [3] as a basis of our generation model of
multi-polarization complex SAR images. It is based on the Speckle model of
Goodman et al. [5], which states that radar reflection is much more sensitive
to the roughness of the ground surface than the radar wavelength. Let us
denote a pixel value observed by the sensor as $z\in\mathbb{C}$. Then we can
describe $z$ as the sum of independent reflected waves:
$z_{n}\equiv\rho_{n}\exp(j\phi_{n})$. That is, we can also represent
$z=\sum_{n}\rho_{n}\exp(j\phi_{n})$. Assuming that (i) the number of reflected
waves is sufficiently large, (ii) amplitudes and phases are independent, and
(iii) the phases distribute uniformly within ($-\pi$, $\pi$), then the
distribution $p(z)$ of $z$ follows the following circularly symmetric complex
Gaussian distribution:

$p(z)=\frac{1}{\pi r}\exp\left(-\frac{|z|^{2}}{r}\right),$ (1)

where $r>0$ represents the reflectance of the SAR. That is, the variance of
the noise observed by the sensor is determined by the magnitude of the SAR
reflectance. Decomposing $z$ into its real and imaginary components as
$z=a+jb$, the distribution $p(z)$ can be expressed as
$p(z)\propto\exp\left(-a^{2}/r\right)\exp\left(-b^{2}/r\right)$. It shows that
in $p(z)$ the distributions of the real and imaginary components are
independent.

In the above equation, the joint distribution of the image, consisting of the
array of values observed by the sensor, is assumed to be pixel-independent.
However, the actual observed values are known to be spatially correlated due
to small deformations originating from the sensor. To represent this, MERLIN
uses a linear transformation of $z$ to represent the process of observing the
actual SAR image. Specifically, when we define the SAR image with $N$ pixels
before the linear transformation as $\bm{z}\in\mathbb{C}^{N}$ and the linear
transformation matrix as $\bm{T}\in\mathbb{R}^{N\times N}$, the spatially
uncorrelated signal $\bm{z}$ can be transformed into a spatially correlated
signal $\tilde{\bm{z}}$ represented as $\tilde{\bm{z}}=\bm{Tz}$. The real and
imaginary components of z are similarly transformed and can be expressed as
$\tilde{\bm{a}}\equiv\bm{Ta}$ and $\tilde{\bm{b}}\equiv\bm{Tb}$, respectively.
This transformation implies that although there is spatial correlation with
respect to the real and imaginary component images of the actual complex SAR
image, these distributions are independent as long as $\bm{T}$ is a real
matrix, i.e., $p(\tilde{\bm{z}})=p(\tilde{\bm{a}})p(\tilde{\bm{b}})$.

Using the above generation process, MERLIN performs self-supervised
despeckling using the so-called masked training. Specifically, MERLIN performs
masking on the complex input ($[\bm{a},\bm{b}]$), for example, masking the
real component ($\bm{a}$) and not masking the imaginary component ($\bm{b}$).
It then trains a neural network to predict the real image from the imaginary
image. Dalsasso et. al. [3] have demonstrated that accurate despeckling can be
achieved with these procedures.

##  III Proposed Method

Figure 2:  Overview of PolMERLIN. After channel masking and spatial masking
are performed on the input, the model is trained by restoring the masked
components using a despeckling network. For the despeckling network
architecture we used the U-Net model [15].

###  III-A Statistical Model of Polarimetric Complex SAR

To clarify the relationship between pixels in multi-polarization SAR images
studied in this paper, we extend the statistical model of MERLIN (Sec. II) to
multi-polarization images. The complex amplitude $z$ is once defined as a
scalar value in MERLIN. In our model, $z$ is extended as a vector,
$\bm{\zeta}$, to capture multi-polarization. In this section, we assume
$\bm{\zeta}$ as $\bm{\zeta}\equiv[z_{\mathrm{hh}}\
z_{\mathrm{vv}}]^{T}\in\mathbb{C}^{2}$ since the TerraSAR-X dataset used in
our experiments is dual polarization data (HH, VV). Using the stochastic model
for the multi-polarization SAR [8], the joint distribution $p(\bm{\zeta})$ is
an extension of Equation 1 as follows:

$p(\bm{\zeta})=\frac{1}{\pi^{2}|\sum|}\exp(-\bm{\zeta}^{H}\Sigma^{-1}\bm{\zeta}),$
(2)

where $\Sigma$ is the Hermitian and covariance matrix defined as
$\Sigma=\mathbb{E}[\bm{\zeta}\bm{\zeta}^{H}]$, where H represents the
Hermitian operator. Since $p(a_{\mathrm{hh}})=p(b_{\mathrm{hh}})$ and
$p(a_{\mathrm{vv}})=p(b_{\mathrm{vv}})$ from the discussion in Sec. II, one of
the off-diagonal components of the above matrix can be written as
$\mathrm{Im}(\mathbb{E}[z_{\mathrm{hh}}\overline{z_{\mathrm{vv}}}])=\mathbb{E}[-a_{\mathrm{hh}}b_{\mathrm{vv}}+b_{\mathrm{hh}}a_{\mathrm{vv}}]=0$.
Similarly, we can write
$\mathrm{Im}(\mathbb{E}[\overline{z_{\mathrm{hh}}}z_{\mathrm{vv}}])=0$.
Therefore, $\Sigma$ can be redefined by the following real matrix:
$\begin{bmatrix}r_{\mathrm{hh}}&r_{\mathrm{hv}}\\\
r_{\mathrm{hv}}&r_{\mathrm{vv}}\end{bmatrix}$. Note that from Equation 1,
$r_{\mathrm{hh}}$ and $r_{\mathrm{vv}}$ are the components of the SAR image we
wish to predict.

From the above, the exponential component of Equation 2 can be decomposed as

$\displaystyle\bm{\zeta}^{H}\Sigma^{-1}\bm{\zeta}$
$\displaystyle=(r_{\mathrm{vv}}a_{\mathrm{hh}}{}^{2}-2r_{\mathrm{hv}}a_{\mathrm{hh}}a_{\mathrm{vv}}+r_{\mathrm{hh}}a_{\mathrm{vv}}{}^{2})$
$\displaystyle+(r_{\mathrm{vv}}b_{\mathrm{hh}}{}^{2}-2r_{\mathrm{hv}}b_{\mathrm{hh}}b_{\mathrm{vv}}+r_{\mathrm{hh}}b_{\mathrm{vv}}{}^{2}).$
(3)

Hence, if we represent $\bm{\alpha}$ and $\bm{\beta}$ by
$\bm{\alpha}=[a_{\mathrm{hh}}\ a_{\mathrm{vv}}]^{T}$ and
$\bm{\beta}=[b_{\mathrm{hh}}\ b_{\mathrm{vv}}]^{T}$, then
$p(\bm{\zeta})=p(\bm{\alpha})p(\bm{\beta})$ holds. Similarly,
$p(\bm{\alpha})\neq p(a_{\mathrm{hh}})p(a_{\mathrm{vv}})$ and
$p(\bm{\beta})\neq p(b_{\mathrm{hh}})p(b_{\mathrm{vv}})$ hold except in the
obvious case of $r_{\mathrm{hv}}=0$. That is, $\bm{\alpha}$ and $\bm{\beta}$
are independent, but $a_{\mathrm{hh}}$ and $a_{\mathrm{vv}}$ are non-
independent (the same applies to $b_{\mathrm{hh}}$ and $b_{\mathrm{vv}}$).

This means that not only is there independence between the real and imaginary
parts of the same polarized image (e.g., $a_{\mathrm{vv}}$ and
$a_{\mathrm{hh}}$) as assumed in MERLIN, but there is also similar
independence between the real and imaginary parts of different polarized
images (e.g., $a_{\mathrm{hh}}$ and $b_{\mathrm{vv}}$). It also means that
assuming $\bm{T}$ is real, the real and imaginary components of any
polarization images are still independent after the linear transformation. On
the other hand, since the real and imaginary components of different
polarizations are not independent of each other, a simple extension of MERLIN
(Noise2Noise [7] between arbitrary components) does not satisfy the above
condition.

###  III-B Channel Masking

Noise2Noise [7] enables denoising by training to recover another independent
noisy image from an input, without explicitly defining ground truth or noise
models. MERLIN’s approach [3] is based on Noise2Noise.

Specifically, as shown in Sec. II, according to the Goodman’s speckle model,
as long as $\bm{T}$ is a real square matrix, a single-polarization complex SAR
image is considered to consist of two independent noisy images, one with a
real component and the other with an imaginary component. MERLIN uses them to
generate noise-reduced SAR images from noisy SAR images by training the
network to recover one element from the other.

The despeckling method for multi-polarization complex SAR images also follows
Noise2Noise. As shown in Sec. III-A, the real components of different
polarizations are correlated with each other, and the real and imaginary
components of different polarizations can be considered independent. Based on
this statistical model, the real and imaginary components of multiple
polarizations can be regarded as a pair of images collapsed according to the
same noise distribution. Thus, we propose a method called channel masking,
which masks one component of the multi-polarization complex SAR image and
predicts the other component. Figure 2 shows the procedure of the channel
masking. By defining multi-polarization complex SAR images and an input tensor
after channel masking as $\bm{x}=[\bm{a}_{\mathrm{hh}}\ \bm{b}_{\mathrm{hh}}\
\bm{a}_{\mathrm{vv}}\ \bm{b}_{\mathrm{vv}}]\in\mathbb{R}^{N\times 4}$ and
$\bm{x}_{c}$, respectively, we have $\bm{x}_{c}=\mathrm{M_{c}}\circ\bm{x}$,
where $\circ$ is a Hadamard product and $\mathrm{M_{c}}\in\\{0,1\\}^{N\times
4}$ is a binary matrix with zero for the channel to be masked and one for all
other channels.

###  III-C PolMERLIN

Channel masking allows despeckling using only noisy SAR images when the data
provided are multi-complex polarization images. For further improvement, we
introduce spatial masking: a training scheme that extends masking in the
channel direction, as proposed in Noise2Void [6], to the spatial direction.
Since speckle noise is spatially correlated, simply using only spatial masking
violates the assumption of Noise2Void where noise is spatially independent.
Inspired by Noise2Void, Speckle2Void [9] uses several tricks to mitigate
spatial correlation. However, this method does not solve the fundamental
problem of spatial correlation because it is a pseudo-relaxation of spatial
correlation and makes the network more complex. Thus, we have introduced a
trick to mitigate the negative effects of spatial correlation by using two
orthogonal pieces of information together: spatial masking and channel
masking. Specifically, the image $\bm{x}_{s}$ after spatial masking can be
expressed as $\bm{x}_{s}=\mathrm{M_{s}}\circ\bm{x}$, where
$\mathrm{M_{s}}\in\\{0,1\\}^{N\times 4}$ is a binary matrix whose masked
elements are zero and the rest are one, randomly determined with a certain
probability.

Figure 2 shows an overview. PolMERLIN uses channel masking to mask the
channels representing either real or imaginary components to be predicted in a
multi-polarization complex SAR image, and spatial masking to mask pixels in
the channels that are not to be predicted. The despeckling network recovers
the elements masked by channel masking from the given tensor, i.e.,
$\bm{r}=f_{\theta}(\mathrm{M_{c}}\circ\mathrm{M_{s}}\circ\bm{x})$.
$f_{\theta}$ is the despeckling network and $\bm{r}=[\bm{r}_{\mathrm{hh}}\
\bm{r}_{\mathrm{vv}}]\in\mathbb{R}^{N\times 2}$.

At training time, the reconstructed components are compared with the original
SAR image to evaluate how similar they are. The loss function
$\mathcal{L}^{\prime}$ is defined as an extension to that of MERLIN [3] to
multiple polarizations:

$\mathcal{L}^{\prime}=\mathcal{L}(\bm{r}_{\mathrm{Re}},\bm{x}_{\mathrm{Im}})+\mathcal{L}(\bm{r}_{\mathrm{Im}},\bm{x}_{\mathrm{Re}}),$
(4)
$\mathcal{L}(\bm{r},\bm{\gamma})=\sum_{k=1}^{N}\sum_{p\in\\{\mathrm{hh},\mathrm{vv}\\}}\left({\frac{1}{2}\mathrm{log}(r_{kp})+\frac{\gamma_{kp}^{2}}{r_{kp}}}\right),$
(5)

where $\bm{r}_{\mathrm{Re}}$ and $\bm{r}_{\mathrm{Im}}$ are real and imaginary
matrices of $\bm{r}$ in which the real or imaginary component of $\bm{x}$ is
masked and the other is predicted for by $f_{\theta}$. $\bm{x}_{\mathrm{Re}}$
and $\bm{x}_{\mathrm{Im}}$ are the matrices from which the real and imaginary
components of $\bm{x}$ are extracted.

The model’s inference is carried out by feeding both the real and imaginary
parts of the given noisy image into the Despeckling Network. Note that the
computational cost of the proposed method is nearly the same as existing
methods since there is almost no difference between the architectures of
MERLIN and PolMERLIN. Actually, when the images were $4\times 256\times 256$
px, the costs for MERLIN and PolMERLIN were 36.96 GFlops and 37.51 GFlops,
respectively.

##  IV Experiments

In our experiments, we evaluated our method on two datasets: synthetic speckle
noise images and real SAR images.

###  IV-A Procedure

During testing, channel masking was applied to the real and imaginary
components, respectively, and the average of the restored results was used as
the final despeckling result defined by $\bm{r}^{\prime}$, i.e.,
$\bm{r}^{\prime}\equiv(\bm{r}_{\mathrm{Re}}+\bm{r}_{\mathrm{Im}})/2$.

#### Synthetic Speckle Noise

In this experiment, 400 training and validation images of BSDS500 [1] were
used for training, and 100 test images were used for evaluation. As for the
synthetic speckle noise, we used noise that follows a gamma distribution with
mean and variance of 1 as the equivalent of single-look speckle noise. We
assume the image before applying the synthetic speckle noise as the ground
truth. Then we can evaluate the performance of the model by comparing the GT
with the image after denoising. In this experiment, we adopt PSNR and SSIM as
image quality evaluation metrics. Since optical images do not possess the
concept of polarization, RGB channels were regarded as separate polarizations
instead. As there is also no complex component in optical images, the channels
were replicated and considered as the real and imaginary components of each
channel instead.

We chose two baseline methods: (i) a supervised method using the original
“clean” images as the ground truth, and (ii) MERLIN, a self-supervised method
relying only on noisy images corrupted by the synthetic speckle noise.

#### Real SAR Images

Following previous studies [9, 3], we used TerraSAR-X imagery111https://tpm-
ds.eo.esa.int/oads/access/collection/TerraSAR-X/tree captured in StripMap mode
with a spatial resolution of 3m as the dataset. Since PolMERLIN handles multi-
polarization complex SAR images, only 8 SAR images with HH and VV polarization
information and complex components were used in our experiments. Because of
the huge size of the SAR images (average 16,000 $\times$ 16,000 px per image),
we divided each image into $256\times 256$ patches without overlap. Finally,
we used 30,654 patches for training and 2,640 patches for evaluation. Since
there is no ground truth in this dataset, we used the Equivalent Number of
Looks (ENL) [10] as an evaluation metric, which is a statistical property of
speckle noise commonly used in the despeckling domain. The higher the ENL
value, the more successful the despeckle is. As a baseline for the comparison
method, we used MERLIN [3], which is also a self-supervised training method.

#### Training Details

For fair comparisons, all models used the same U-Net-like architecture [15].
We employed the AdamW optimizer with a learning rate of $10^{-5}$ and a batch
size of 16. All models were trained for 100 epochs in the experiments of the
TerraSAR-X. In the BSD-500, our model was trained for 2400 epochs, while
existing methods were trained for 800 epochs. This is due to the different
number of epochs at which PSNR and SSIM converged. To narrow the range of
values, the inputs and outputs of all models were set to log scale, as in
previous studies [3]. 2% of pixels were set to be masked in the spatial mask.
Equation 4 was used for the loss of MERLIN and PolMERLIN, and an MSE loss was
used for the supervised method. All models were trained on 8 Tesla V100 GPUs
and PyTorch was used for implementation.

###  IV-B Experiments on Synthetic Speckle Noise

(a) BSDS500 |  (b) Noisy |  (c) MERLIN
---|---|---
(d) Ours (c) |  (e) Ours (c+s) |
Figure 3:  Qualitative results for the R channel of the BSDS500 image
despeckled with pseudo-noise.  (a) TerraSAR-X (b) MERLIN (c) Ours (c+s)
---
Figure 4:  Qualitative despeckling results of MERLIN and Ours(c+s) in TerraSAR-X. Noisy bright (white) spots are found in the lower-left part of the MERLIN result. Ours(c+s)’ result is not suffered from such artifacts.  Method | R | G | B
---|---|---|---
Input | $16.88/0.408$ | $16.69/0.367$ | $18.17/0.432$
Supervised | $23.33/0.616$ | $23.69/0.634$ | $23.83/0.624$
MERLIN | $23.30/0.617$ | $23.57/0.609$ | $23.51/0.610$
Ours (c) | $23.61/0.668$ | $23.39/0.667$ | $23.30/0.620$
Ours (c+s) | $\mathbf{24.14/0.687}$ | $\mathbf{24.50/0.696}$ | $\mathbf{24.01/0.646}$
TABLE I: Comparison of Despeckling results in terms of PSNR (left) and SSIM
(right) on synthetic noise. “Ours (c)” is our model adapting only channel
masking, whereas “Ours (c+s)” is our model adapting the both methods.

Table I shows the quantitative results for synthetic noise. Compared to the
input images, both despeckling methods show an improvement in PSNR and SSIM.
Comparing the MERLIN and the supervised method, we found that their PSNR and
SSIM are almost the same. This indicates that the self-supervised, single-
polarized MERLIN can perform as well as the supervised model. Next, we
compared Ours(c) with these two methods and found the Ours(c) model is
evidently better than the other two in SSIM and is marginally better in PSNR.
It implies that our method performs better despeckling than the existing
methods. We also compared Ours(c+s) with the other methods, and confirmed that
it outperforms the others in both PSNR and SSIM, indicating that spatial
masking contributes to despeckling improvement. Figure 3 shows the qualitative
results of despeckling in synthetic noise. The results suggest that the image
despeckled by MERLIN is blurred because only one channel is used, whereas our
method uses the RGB channel and thus preserves the image detail relatively
well.

###  IV-C Experiments on Real SAR

Method | HH | VV | Method | HH | VV
---|---|---|---|---|---
Input | $2.9$ | $2.9$ | Ours (c) | $173.6$ | $191.8$
MERLIN | $148.8$ | $186.3$ | Ours (c+s) | $\bm{274.0}$ | $\bm{301.3}$
|  |  | mask HH/VV chs. | 38.0 | 134.4
TABLE II: Comparison of Despeckling Results in terms of ENL on Real SAR
Images.

Table II shows the quantitative results for real speckle noise in terms of
ENL. It shows that all self-supervised despeckle methods significantly
outperform the input images in both HH and VV, indicating that they are also
capable of improving image quality by despeckling real SAR images. A
comparison with Ours(c) and MERLIN shows that our HH and VV results exceed
those of MERLIN. This indicates that the use of multiple polarization images
significantly improves despeckling performance in real SAR images. In
addition, Ours(c+s) outperforms Ours(c) by large margins in both HH and VV. It
implies that adding spatial masking improves despeckling performance in real
SAR images. To check the validity of the probabilistic model discussed in
Section III, we also measured the ENL using a model (“mask HH/VV chs”) that
predicts other images after masking either HH or VV images. The results are
shown in Table II. These values are lower than MERLIN. This suggests a
performance degradation due to information leakage, and at the same time, it
indicates that our probabilistic model has a certain degree of validity.

Since the ENL only covers an aspect of the speckle noises, we cannot judge the
quality of the despeckling based solely on the ENL values. Therefore, we
analyzed the qualitative results as well to determine the performance. Figure
4 shows the qualitative results of despeckling on real SAR images. We found
that the proposed PolMERLIN successfully reduces noise while preserving
semantic context without excessive smoothing, compared to MERLIN. These
results illustrate the qualitative and quantitative performance improvements
of our method over MERLIN.

##  V Conclusion

We studied an efficient despeckling of multi-polarization complex SAR images.
We first extended a known generative model of single-polarization complex SAR
images to complex multi-polarization ones. Based on this model, we proposed a
channel masking and a spatial masking method for self-supervised despeckling
of multi-polarization complex SAR images. Experiments showed that our method
outperforms the despeckling method for single-polarization complex SAR images
both quantitatively and qualitatively. We are currently planning to test
whether our proposed method is effective with other SAR wavelengths and
airborne SAR as well. Additionally, since the training takes a long time to
converge, establishing a method to shorten this duration is our future
challenge.

## Acknowledgment

We would like to thank Shin-ichi Maeda and Tsukasa Takagi for helpful
discussions. This research work was financially supported by the Ministry of
Internal Affairs and Communications of Japan with a scheme of “Research and
development of advanced technologies for a user-adaptive remote sensing data
platform” (JPMI00316).

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