Statistical mechanical analysis of compressed sensing utilizing correlated compression matrix

We investigate a reconstruction limit of compressed sensing for a reconstruction scheme based on the L
₁
-norm minimization utilizing a correlated compression matrix with a statistical mechanics method. We focus on the compression matrix modeled as the Kronecker-type random matrix studied in research on multiple-input multiple-output wireless communication systems. We found that strong one-dimensional correlations between expansion bases of original information slightly degrade reconstruction performance.