Density Compensated Unrolled Networks for Non-Cartesian MRI Reconstruction

Deep neural networks have recently been thoroughly investigated as a powerful tool for MRI reconstruction. There is a lack of research, however, regarding their use for a specific setting of MRI, namely non-Cartesian acquisitions. In this work, we introduce a novel kind of deep neural networks to tackle this problem, namely density compensated unrolled neural networks, which rely on Density Compensation to correct the uneven weighting of the k-space. We assess their efficiency on the publicly available fastMRI dataset, and perform a small ablation study. Our results show that the density-compensated unrolled neural networks outperform the different baselines, and that all parts of the design are needed. We also open source our code, in particular a Non-Uniform Fast Fourier transform for TensorFlow.

Reference: Z. Ramzi,  J.-L. Starck and P. Ciuciu “Density Compensated Unrolled Networks for Non-Cartesian MRI Reconstruction.

This conference paper presents an adaptation of unrolled networks to the challenging setup of Non-Cartesian MRI Reconstruction. It also introduces the implementation of the Non-Uniform Fast Fourier Transform in TensorFlow: tfkbnufft.
It has been accepted at ISBI 2021.

shear bias


Authors:  M. Kilbinger, A. Pujol
Language: Python
Download: GitHub
Description: shear_bias is a package that contains tools and scripts for shear bias estimation for weak gravitational lensing analysis.


Download the code from the github repository.

git clone

A directory shear_bias is created. There, call the setup script to install the package.

cd shear_bias
python install



Authors: M. Jiang
Language: Python
Download: Python
Description: A toolbox for solving joint multichannel Deconvolution and Blind Source Separation (DBSS)



DecGMCA (Deconvolution Generalized Morphological Component Analysis) is a sparsity-based algorithm aiming at solving joint multichannel Deconvolution and Blind Source Separation (DBSS) problem.

For more details, please refer to the paper Joint Multichannel Deconvolution and Blind Source Separation (



Authors:  S. Farrens, Z. Ramzi, Contributors
Language: Python
Download: GitHub
Description: ModOpt is a series of Modular Optimisation tools for solving inverse problems.

API documentation


$ pip install modopt


If you want to contribute to ModOpt, be sure to review the contribution guidelines and follow to the code of conduct.



Authors:  S. Farrens, A. Grigis, L. El Gueddari, Z. Ramzi, Chaithya G. R., S. Starck, B. Sarthou, H. Cherkaoui, P.Ciuciu, J-L. Starck
Language: Python
Download: GitHub
Description: PySAP (Python Sparse data Analysis Package) is a Python module for sparse data analysis.

PySAP paper


The installation of PySAP has been extensively tested on Ubuntu and macOS, however we cannot guarantee it will work on every operating system (e.g. Windows).

If you encounter any installation issues be sure to go through the following steps before opening a new issue:

  1. Check that that all of the installed all the dependencies listed above have been installed.
  2. Read through all of the documentation provided, including the troubleshooting suggestions.
  3. Check if you problem has already been addressed in a previous issue.

Further instructions are available here.

From PyPi

To install PySAP simply run:

$ pip install python-pysap

Depending on your Python setup you may need to provide the --user option.

$ pip install --user python-pysap


To build PySAP locally, clone the repository:

$ git clone

and run:

$ python install


$ python develop

As before, use the --user option if needed.


Help with installation on macOS is available here.


Please refer to the PyQtGraph homepage for issues regarding the installation of pyqtgraph.


If you want to contribute to pySAP, be sure to review the contribution guidelines and follow to the code of conduct.

Space test of the Equivalence Principle: first results of the MICROSCOPE mission

Space test of the Equivalence Principle: first results of the MICROSCOPE mission

Authors: P. Touboul, G. Metris, M. Rodrigues, Y. André, Q. Baghi, J. Bergé, D. Boulanger, S. Bremer, R. Chhun, B. Christophe, V. Cipolla, T. Damour, P. Danto, H. Dittus, P. Fayet, B. Foulon, P.-Y. Guidotti, E. Hardy, P.-A. Huynh, C. Lämmerzahl, V. Lebat, F. Liorzou, M. List, I. Panel, S. Pires, B. Pouilloux, P. Prieur, S. Reynaud, B. Rievers, A. Robert, H. Selig, L. Serron, T. Sumner, P. Viesser
Journal: Classical and Quantum Gravity
Year: 2019
Download: ADS | arXivFait Marquant


The Weak Equivalence Principle (WEP), stating that two bodies of different compositions and/or mass fall at the same rate in a gravitational field (universality of free fall), is at the very foundation of General Relativity. The MICROSCOPE mission aims to test its validity to a precision of 10^-15, two orders of magnitude better than current on-ground tests, by using two masses of different compositions (titanium and platinum alloys) on a quasi-circular trajectory around the Earth. This is realised by measuring the accelerations inferred from the forces required to maintain the two masses exactly in the same orbit. Any significant difference between the measured accelerations, occurring at a defined frequency, would correspond to the detection of a violation of the WEP, or to the discovery of a tiny new type of force added to gravity. MICROSCOPE's first results show no hint for such a difference, expressed in terms of Eötvös parameter δ =  [-1 +/- 9(stat) +/- 9 (syst)] x 10^-15 (both 1σ uncertainties) for a titanium and platinum pair of materials. This result was obtained on a session with 120 orbital revolutions representing 7% of the current available data acquired during the whole mission. The quadratic combination of 1σ uncertainties leads to a current limit on δ of about 1.3 x 10^-14.



Authors: F. Lalande, A. Peel
Language: Python 3
Download: mgcnn.tar.gz
Description: A Convolutional Neural Network (CNN) architecture for classifying standard and modified gravity (MG) cosmological models based on the weak-lensing convergence maps they produce.


This repository contains the code and data used to produce the results in A. Peel et al. (2018), arXiv:1810.11030.

The Convolutional Neural Network (CNN) is implemented in Keras using TensorFlow as backend. Since the DUSTGRAIN-pathfinder simulations are not yet public, we are not able to include the original convergence maps obtained from the various cosmological runs. We do provide, however, the wavelet PDF datacubes derived for the four models as described in the paper: one standard LCDM and three modified gravity f(R) models.


  • Python 3
  • numpy
  • Keras with Tensorflow as backend
  • scikit-learn


$ python3 -n0

The three options for the noise flag "-n" are (0, 1, 2), which correspond to noise standard deviations of sigma = (0, 0.35, 0.70) added to the original convergence maps. Additional options are "-i" and "-e" for the number of training iterations and epochs, respectively.

Confusion matrices and evaluation metrics (loss function and validation accuracy) are saved as numpy arrays in the generated output/ directory after each iteration.