Theoretical and empirical results for recovery from multiple measurements

E. van den Berg and M. P. Friedlander
IEEE Trans. Info. Theory, 56(5):2516-2527, 2010 PDF
doi:10.1109/TIT.2010.2043876

Abstract

The joint-sparse recovery problem aims to recover, from sets of compressed measurements, unknown sparse matrices with nonzero entries restricted to a subset of rows. This is an extension of the single-measurement-vector (SMV) problem widely studied in compressed sensing. We analyze the recovery properties for two types of recovery algorithms. First, we show that recovery using sum-of-norm minimization cannot exceed the uniform recovery rate of sequential SMV using L1 minimization, and that there are problems that can be solved with one approach but not with the other. Second, we analyze the performance of the ReMBo algorithm [M. Mishali and Y. Eldar, IEEE Trans. Sig. Proc., 56 (2008)] in combination with L1 minimization, and show how recovery improves as more measurements are taken. From this analysis it follows that having more measurements than number of nonzero rows does not improve the potential theoretical recovery rate.

Reproducible research

To reproduce the experiments in this paper, download one of the following files:

To unpack the archive and run the experiments, execute the following commands from the Matlab commandline:

>> !unzip xxxx.zip
>> cd scripts
>> ScriptsSetup
>> GenerateFigure(...)

Note that you will need to have CVX installed. Our experiments are based on using Matlab 7.x and CVX v1.2m (and the included version of SDTP3).

BibTeX

@Article{BergFriedlander:2010,
  author =       {Ewout {van den} Berg and Michael P. Friedlander},
  Title =        {Theoretical and empirical results for recovery from
                  multiple measurements},
  journal =      "IEEE Trans. Inf. Theory",
  year =         2010,
  volume =       56,
  number =       5,
  pages =        {2516-2527},
  DOI =          {10.1109/TIT.2010.2043876}
}