Statistical mechanical assessment of a reconstruction limit of compressed sensing: Toward theoretical analysis of correlated signals

Details Statistical mechanical assessment of a reconstruction limit of compressed sensing: Toward theoretical analysis of correlated signals Statistical mechanical assessment of a reconstruction limit of compressed sensing: Toward theoretical analysis of correlated signals

2010-08-31

arxiv.org/abs/1008.5274v2

Europhys. Lett. 95 (2011) 18006

Computer Science

Information Theory

6 pages, 3 figures

Scientific paper

10.1209/0295-5075/95/18006

We provide a scheme for exploring the reconstruction limit of compressed sensing by minimizing the general cost function under the random measurement constraints for generic correlated signal sources. Our scheme is based on the statistical mechanical replica method for dealing with random systems. As a simple but non-trivial example, we apply the scheme to a sparse autoregressive model, where the first differences in the input signals of the correlated time series are sparse, and evaluate the critical compression rate for a perfect reconstruction. The results are in good agreement with a numerical experiment for a signal reconstruction.

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