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.



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.