Typical Performance of Sparse Signal Recovery from a Linear Measurement with Large Coherence

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We discuss typical ‘potential’ performance of sparse signal recovery in the case where iterative recovery algorithms fail to converge. We especially focus on sparse signal recovery from a linear measurement whose measurement matrix has large coherence and evaluate the mean square error of the estimate in such a case by using the statistical mechanical method. It can be considered that this kind of analysis gives a theoretical limit for iterative sparse recovery algorithms. When coherence of the measurement matrix is large, the mean square error between an original signal to be estimated and its estimate tends not to depend on the compression rate.