RecPF: Reconstruction from Partial Fourier data

RecPF solved the following model

where
-- u is the signal/image to be reconstructed
-- TV(u) is the total variation regularization term
-- &Psi is a sparsifying basis
-- F_p is a partial Fourier matrix
-- f_p is a vector of partial Fourier coefficients

Matlab Code

[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;
• 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.

Authors

Junfeng Yang (Nanjing University, China), Wotao Yin [web], Yin Zhang [web] (Rice University)

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, 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

• J. Yang, Y. Zhang and W. Yin,
  "A Fast TVL1-L2 Minimization Algorithm for Signal Reconstruction from Partial Fourier Data",
  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, to appear. [PDF file]