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README - Phase Retrieval code v20150728

https://github.com/JeffFessler/PhaseRetrievalWithOutliers

Created by Daniel Weller, University of Virginia, and Jeffrey Fessler, University of Michigan

Please direct questions and comments to Daniel Weller at [email protected].

The contents of this program are subject to copyright as set forth in the file LICENSE.TXT accompanying this software. If you did not receive a copy of LICENSE.TXT, please email [email protected].

The enclosed program includes implementations of the phase retrieval algorithm proposed in the paper

D. S. Weller, A. Pnueli, G. Divon, O. Radzyner, Y. C. Eldar, and J. A. Fessler, "Undersampled Phase Retrieval with Outliers," IEEE Transactions on Computational Imaging, 1(4):247-58, Dec. 2015.

A draft version of the manuscript appeared on arXiv: 1411.2183 [stat.AP].

We ask that any user please cite this work in any publications that present results based on this software.

This code has been tested with MATLAB (The Mathworks, Inc.) versions R2014a and R2015a. Please note that some major changes in the graphics subsystem between R2014a and R2015a means that some of the plotting code no longer functions equivalently across platforms. In addition, other changes in more recent releases may no longer be compatible with this code.

To use this code, you need to install the Michigan Image Reconstruction Toolbox (MIRT) provided from http://web.eecs.umich.edu/~fessler/code/index.html.

Installation instructions for that toolbox can be found on the website or in the readme file included with the toolbox. Once the toolbox is installed, you should either include the toolbox directories on your MATLAB path at startup, or be sure to call the setup_IRT.m function in this software before running the included scripts.

Once MIRT is installed, you should be almost ready to go. Clone this repo and redirect the MATLAB working directory to the src/ folder. You should now be able to run any of the run_*.m or plot_*.m scripts therein after following the directions in that script file. Note that some scripts require that you have run others first.

A quick note about the "results" directory: the scripts will not attempt to create a results directory to store simulation data. You must create a readable/writable directory and update the path "outfolder" in your scripts to point to this folder.

A number of scripts are included with this software, mainly with the goal of recreating figures from the paper above. To generate figures, run in order:

• surrogate_examples.m
• run_phase_retrieval_padmm_mus.m
• run_phase_retrieval_betas.m
• plot_phase_retrieval_betas.m
• run_phase_retrieval_MC.m
• run_sparse_fienup_MC.m
• plot_phase_retrieval_MC.m
• run_phase_retrieval_MC_noise.m (with settings varying outliers)
• run_sparse_fienup_MC_noise.m (with settings varying outliers)
• plot_phase_retrieval_MC_outliers.m
• run_phase_retrieval_MC_noise.m (with settings varying noise levels)
• run_sparse_fienup_MC_noise.m (with settings varying noise levels)
• plot_phase_retrieval_MC_noise.m
• run_phase_retrieval_SOD.m
• run_sparse_fienup_SOD.m
• plot_phase_retrieval_SOD.m

Each script contains a description of its purpose and which figures it can help recreate. Note that many of the figures in the paper contain results from competing methods such as GESPAR and PR-GAMP that are not included with this code. Please contact the authors of those methods to obtain software to test them directly.

The main functionality for the proposed method requires these files:

• phase_retrieval_p1_q2.m
• ox_fessler_p1_q2.m
• PADMM_1split_p1_q2.m
• surrogate_p1_q2.m
• shrink.m
• compute_beta_normalization.m

The first three files contain the three levels of the algorithm (initializations, MM, and ADMM). The last three are utility functions used to evaluate the majorizer, perform soft-thresholding, and compute the normalization factor for beta, respectively. We hope the scripts described in Part III above provide adequate examples of how to use these functions for your own code.

Experimental code for the quadratic data fit case is also included. Those files have p2_q2 in their names.

Enjoy!

Daniel Weller Assistant Professor University of Virginia [email protected]

July 30, 2015

This github version created by Jeff Fessler on 2022-08-16, using code previously downloaded on 2016-05-03 from http://people.virginia.edu/~dsw8c/sw.html.