Rice University, L1-Related Optimization Project

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RecPF: Reconstruction from Partial Fourier data

RecPF solved the following model

-- u is the signal/image to be reconstructed
-- TV(u) is the total variation regularization term
-- Ψ is a sparsifying basis
-- Fp is a partial Fourier matrix
-- fp is a vector of partial Fourier coefficients

Matlab Code and Demo

[Version 2.2 (zip file)] --- Released: Nov 23rd, 2010. Copyright (c) 2010. Bugs (Z was incorrectedly writen as z) fixed.
[Version 2.1 (zip file)] --- Released: Oct 11th, 2009. Copyright (c) 2009. Bugs fixed.
[Version 2.0 (zip file)] --- Released: May 25th, 2009. Copyright (c) 2009.
New features:
  • Switched to complex computation, fully compatible with complex data;
  • Replaced penalty parameter continuation by R. Glowinski and P.L. Tallec's alternating direction method (ADM or ADMM);
  • New parameter/data normalization was added to make parameters rather independent of the image size, pixel intensity range, and number of CS measurements. To find the parameters aTV and aL1 for version 2.0 corresponding to those used in versions 1.1 or 1.0, see Lines 60, 66, and 67 of RecPF.m.
[Version 1.1 (zip file)] --- Released: Febuary 4th, 2009. Copyright (c) 2009.
[Version 1.0 (zip file)] --- Released: January 9th, 2009. Copyright (c) 2009.


The work of W. Yin has been supported in part by NSF CAREER Award DMS-0748839, ONR Grant N00014-08-1-1101, AFOSR STTR Grant FA9550-09-C-0121, the U. S. Army Research Laboratory and the U. S. Army Research Office grant W911NF-09-1-0383, and an Alfred P. Sloan Research Fellowship.

The work of Y. Zhang has been supported in part by NSF Grant DMS-0811188 and ONR Grant N00014-08-1-1101.

RecPF Related Papers

The code above uses the alternating direction method (ADM or ADMM), and it is newer than the papers.
  • J. Yang, Y. Zhang and W. Yin,
    "A Fast Alternating Direction Method for TVL1-L2 signal reconstruction from Partial Fourier Data",
    To appear in IEEE Journal of Selected Topics in Signal Processing Special Issue on Compressed Sensing.
    Technical Report, TR08-27, CAAM, Rice University. [PDF file]
  • Y. Wang, J. Yang, W. Yin and Y. Zhang,
    "A New Alternating Minimization Algorithm for Total Variation Image Reconstruction",
    SIAM Journal on Imaging Sciences 1(3), 248-272. [PDF file]

Related Codes

  • YALL1 - a MATLAB package for various L1-minimization problems, using a dual alternating direction method. [link]
  • RecPC - 1D/2D compressive sensing with Toeplitz and circulant matrices using ADM. [link]
  • FTVd - Total variation based Deconvolution, Deblurring, and Denoising. [link]
  • TVAL3 - General total variation minimization by augmented Lagrangian and ADM. [link]
  • ISD - Iterative support detection for compressive sensing. Fast and better recovery than L1. [link]
  • FPC - iterative shrinkage with continuation for L_1-miminization. [link]
  • FPC_AS - the active-set acceleration of FPC. Works better than FPC. [link]