Statistical mechanical assessment of a reconstruction limit of compressed sensing: Toward theoretical analysis of correlated signals
Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology Yokohama 226-8502, Japan
Accepted: 23 May 2011
We provide a scheme for exploring the reconstruction limits 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.
PACS: 89.70.-a – Information and communication theory / 75.10.Nr – Spin-glass and other random models / 05.70.Fh – Phase transitions: general studies
© EPLA, 2011