This project contains scripts to reproduce experiments from the paper AMP-Inspired Deep Networks for Sparse Linear Inverse Problems by Mark Borgerding , Phil Schniter , and Sundeep Rangan. To appear in IEEE Transactions on Signal Processing. See also the related preprint

Briefly, the Sparse Linear Inverse Problem is the estimation of an unknown signal from indirect, noisy, underdetermined measurements by exploiting the knowledge that the signal has many zeros. We compare various iterative algorithmic approaches to this problem and explore how they benefit from loop-unrolling and deep learning.

The included scripts

• are generally written in python and require TensorFlow,
• work best with a GPU,
• generate synthetic data as needed,
• are known to work with CentOS 7 Linux and TensorfFlow 1.1,
• are sometimes be written in octave/matlab .m files.

You might prefer the Matlab code in GAMP/code/VAMP/ or the python code in Vampyre.

Creates numpy archives (.npz) and matlab (.mat) files with (y,x,A) for the sparse linear problem y=Ax+w. These files are not really necessary for any of the deep-learning scripts, which generate the problem on demand. They are merely provided for better understanding the specific realizations used in the experiments.

Using the .mat files created by save_problem.py, this octave/matlab script tests the performance of non-learned algorithms ISTA, FISTA, and AMP.

e.g.

octave:1> ista_fista_amp
loaded Gaussian A problem
AMP reached NMSE=-35dB at iteration 25
AMP terminal NMSE=-36.7304 dB
FISTA reached NMSE=-35dB at iteration 202
FISTA terminal NMSE=-36.7415 dB
ISTA reached NMSE=-35dB at iteration 3420
ISTA terminal NMSE=-36.7419 dB

This is an example implementation of LISTA Learned Iterative Soft Thresholding Algorithm by (Gregor&LeCun, 2010 ICML).

Example of Learned AMP (LAMP) with a variety of shrinkage functions.

Example of Learned Vector AMP (LVAMP).