Compressive sensing with un-trained neural networks: Gradient descent finds the smoothest approximation

This repository provides code for reproducing the figures in the paper:

``Compressive sensing with un-trained neural networks: Gradient descent finds the smoothest approximation'' by Reinhard Heckel and Mahdi Soltanolkotabi. Contact: reinhard.heckel@gmail.com

Organization

• Figure 1: compressive_sensing_example_convergence.ipynb
• Figure 5: MRI_multicoil_deep_decoder_accelerate.ipynb

Installation

The code is written in python and relies on pytorch. The following libraries are required:

• python 3
• pytorch
• numpy
• skimage
• matplotlib
• scikit-image
• jupyter

The libraries can be installed via:

conda install jupyter

The code to reproduce the MRI experiment uses a few function from the fastMRI repository to load the k-space data, those can be obtained by copying the data and common folders from the repository https://github.com/facebookresearch/fastMRI. In particular, download the code from the fastMRI repository, and copy the folder fastMRI/data into the cs_deep_decoder repository.

Citation

@inproceedings{heckel_compressive_2020,
    author    = {Reinhard Heckel and Mahdi Soltanolkotabi},
    title     = {Compressive sensing with un-trained neural networks: {Gradient} descent finds the smoothest approximation},
    booktitle = { {International} {Conference} on {Machine} {Learning} },
    year      = {2020},
}

Licence

All files are provided under the terms of the Apache License, Version 2.0