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Multi-Channel Logarithm with Gaussian Denoiser - A (Pol/In)SAR image speckle reduction algorithm.

Project description

This is a Python 3.10 implementation of MuLoG as described in reference [2].

MuLoG is a plug-and-play ADMM approach for (Pol/In)SAR image speckle reduction using an off-the-shelf Gaussian denoiser and matrix logarithm transform to stabilized noise and simplify the optimization.


Synthetic aperture radar (SAR) images are widely used for Earth observation to complement optical imaging. By combining information on the polarization and the phase shift of the radar echos, SAR images offer high sensitivity to the geometry and materials that compose a scene. This information richness comes with a drawback inherent to all coherent imaging modalities: a strong signal-dependent noise called "speckle". MuLoG algorithm addresses the mathematical issues of performing speckle reduction in a transformed domain: the matrix-log domain. Rather than directly estimating noiseless covariance matrices, recasting the denoising problem in terms of the matrix-log of the covariance matrices stabilizes noise fluctuations and makes it possible to apply off-the-shelf denoising algorithms.

While a large diversity of speckle reduction methods exist for intensity images, only few can be extended to process multi-channel SAR images. In particular, extension of variational methods lead to challenging optimization problems due to the non-convexity of the neg-log-likelihood and the positive definiteness constraint on the covariance matrices. Furthermore, signal and channel dependent variance lead to restoration results with an uneven suppression of speckle. This algorithm introduced a general scheme based on a matrix logarithm transform to approximately stabilize speckle variance and produce close to independent channels. Each channel can then be processed with the user-defined Gaussian denoiser. Upon re-iterating, a good fit of the restored multi-channel image with the Wishart distribution of input covariance matrices is enforced.


Unless you have Python 3.10 installed and enabled as default, we recommend installing MuLoG in a virtual environment as described in the following section.

Set up a virtual environment (optional)

We recommend installing MuLoG in a virtual environment such as venv. You can install venv for Python 3.10 on Debian/Ubuntu as follows:

sudo apt install python3.10-venv

If your system does not have Python 3.10, please refer to the "Troubleshooting" section below.

Create and activate your virtual environment by running the following either directly in the directory in which you will execute or clone MuLoG or in a parent directory, as

python3 -m venv venv
source venv/bin/activate

Alternatively, you can use other environment systems such as conda.

Latest stable version

We recommend installing the latest stable version of MuLoG by running

pip3 install mulog

in a system or environment with Python 3.10.

Development version

Alternatively, you can install the development version from git as

pip3 install -e git+

or, directly from the sources as

git clone
cd mulog2022-python
python3 sdist
python3 install

Run MuLoG

Examples on how to run mulog are provided in two scripts that you can execute as:

# Run MuLoG on a multlooked synthetic PolSAR image with 5 looks
python3 -m mulog.mulog_synthetic_example -l 5

# Run MuLoG on PolSAR images from a small PolSAR image
python3 -m mulog.mulog_examples -e sanfrancisco

If the execution stops with the warning "UserWarning: Matplotlib is currently using agg [...]", please refer to the "Troubleshooting" section below.

For more details on how to execute these examples, see:

python3 -m mulog.mulog_synthetic_example --help
python3 -m mulog.mulog_examples --help

To run MuLoG on your own data, you need to execute from Python the function called run_mulog that you can import as:

from mulog.mulog_algorithm import run_mulog

This function takes your data as input through the argument sar_image which has the format of a covariance matrix field (an image of non negative definite complex Hermitian matrices). It's your responsibility to load and format your data in Python to make it compatible with this input. SAR, InSAR, PolSAR, DualPolSAR PolInSAR images can be formatted as such a matrix field. For more details, please read [1-2].

List of the files in this folder


The code in this file, corresponding to Algorithm 5 of the paper, rescales the range of the eigenvalues of each matrix of a bi-dimensional field into a potentially smaller range to make sure that their condition number doesn't exceed the chosen threshold. It is applied on MuLoG input to compute the bi-dimensional field that will be used in the definition of the proximal operator of the data fidelity.


This file contains an implementation of Algorithm 4 of the paper which describes the process of correcting the coherence of MuLoG input in order to lessen the bias that will be introduced in the following steps. The result will serve as a starting point for the PnP-ADMM and helps to speed up the convergence.


Contains the function used in ADMM iterations to apply independently bm3d (a Gaussian denoiser) or TV on each channel of its input. The computational speed can be improved by parallelizing the process (which is not done here).

  • hermitian_matrix_field/
  • hermitian_matrix_field/
  • hermitian_matrix_field/
  • hermitian_matrix_field/

These files group the functions for the different transforms (and their inverse) to be performed on bi-dimensional fields of matrices including the multiplication transform, the matrix exponential transform, and the transform that decomposes 3x3 complex covariance matrices into 9 real-valued.


Implementation of Midal (mono channel version of MuLoG). This is the algorithm that MuLoG extend to multichannel SAR images.


Implementation of MuLoG as described in [2].


A cli tool to run MuLoG on a PolSAR example from a small dataset.


A cli tool to run MuLoG on a synthetic example.


Contains the code for PnP-ADMM iterations.


Implementations of proximal operators used by MuLoG, Midal and for the sake of unit tests.


Tools to generate synthetic mono-channel and multichannel SAR images.


Tools to render mono-channel and multichannel SAR images with proper adjustments (range clipping, gamma correction...).


Add infinitesimal variations in any Hermitian matrix this such that the matrix does not have true zeros, exact equal eigenvalues, or low rank. Recall that the space of such matrices is dense in the space of Hermitian matrices.


This file mostly contains various functions that MuLoG depends on.


Set up

Clone the git repository on your machine:

git clone
cd mulog2022-python

Set up a Python 3.10 virtual environment as described in the Installation section above. Once your virtual environment is set up and activated, install dependencies as

pip3 install -r requirements.txt


Any contributions must be submitted through peer reviews. Ask for an author account on the bitbucket repository, create your own branch and raise a pull-request. All additional code must be cover by a unit test. Any pull request needs to pass the following commands before approval:

black .
ruff --fix .
pyright .
python3 -m pytest -cov

If the last one does not have a 100% test coverage, run:

python3 -m pytest --cov --cov-report=html

and inspect the report.

Make sure to update requirements.txt to include any extra dependencies.


To distribute the project make sure to uptick the version number in and merge that upticked version on the master branch. Once the master branch is ready, run the following

git checkout master
cd $(git rev-parse --show-toplevel)
rm -rf dist/ build/ mulog.egg-info/
git status --porcelain

and make sure the last command did not print anything. After that, generate the distribution files by running

python3 sdist bdist_wheel
python3 -m twine check dist/*
python3 -m twine upload -r testpypi dist/*

Test in a different environment

mkdir /tmp/test
cd /tmp/test
python3 -m venv venv
source venv/bin/activate
pip3 install -i --extra-index-url mulog
python3 -m mulog.mulog_synthetic_example -l 5

Finally, publish the final version

python3 -m twine upload dist/*

Once done, tag the master branch with the new version number on Git.


How to fix "Unable to locate package python3.10-venv" on Debian/Ubuntu?

In case Python 3.10 is not available for your Debian/Ubuntu distribution, we recommend you to install pyenv ( At the time this documentation has been written, you can install pyenv as follow:

git clone ~/.pyenv

Once pyenv is installed, you can install Python 3.10 inside pyenv as:

sudo apt install python3-tk tk-dev libsqlite3-dev libbz2-dev libncurses-dev libreadline-dev
CONFIGURE_OPTS="--enable-shared" ~/.pyenv/bin/pyenv install 3.10

After this, you can call Python 3.10 as


Note that we do not encourage you to add that path in your PATH environment. Instead, as recommended above, use venv as follows

~/.pyenv/versions/3.10.*/bin/python3 -m venv venv
source venv/bin/activate

After your virtual environment is activated, you can proceed with the installation of MuLoG either by following the "Latest stable version" or "Development version" instructions.

How to fix "UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure"?

You need to activate a GUI default backend for Matplotlib compatible with your system. For more information see

If you are using Debian/Ubuntu, we recommend you using tk as backend, that you can install as

sudo apt install python3-tk


This software is governed by the CeCILL license under French law and abiding by the rules of distribution of free software. You can use, modify and/ or redistribute the software under the terms of the CeCILL license as circulated by CEA, CNRS and INRIA at the following URL "".

As a counterpart to the access to the source code and rights to copy, modify and redistribute granted by the license, users are provided only with a limited warranty and the software's author, the holder of the economic rights, and the successive licensors have only limited liability.

In this respect, the user's attention is drawn to the risks associated with loading, using, modifying and/or developing or reproducing the software by the user in light of its specific status of free software, that may mean that it is complicated to manipulate, and that also therefore means that it is reserved for developers and experienced professionals having in-depth computer knowledge. Users are therefore encouraged to load and test the software's suitability as regards their requirements in conditions enabling the security of their systems and/or data to be ensured and, more generally, to use and operate it in the same conditions as regards security.

The fact that you are presently reading this means that you have had knowledge of the CeCILL license and that you accept its terms.


  • Charles Deledalle (original version in Matlab)
  • Sébastien Mounier (translation in Python)
  • Cristiano Ulondu Mendes (bug fixes and improvements from MuLoG2022)

Scientific articles describing the method

Any published materials derived from MuLoG must cite [1-2].

[1] Deledalle, C. A., Denis, L., Tabti, S., & Tupin, F. (2017). MuLoG, or how to apply Gaussian denoisers to multi-channel SAR speckle reduction?. IEEE Transactions on Image Processing, 26(9), 4389-4403.

[2] Deledalle, C. A., Denis, L., & Tupin, F. (2022). Speckle reduction in matrix-log domain for synthetic aperture radar imaging. Journal of Mathematical Imaging and Vision, 64(3), 298-320.

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