Improved AMP (IAMP) for non-ideal measurement matrices

This paper studies the sparse recovery problem. Of particular interest is the well known approximate message passing (AMP) algorithm. AMP enjoys low computational complexity and good performance guarantees. However, the algorithm and performance analysis heavily rely on the assumption that the measurement matrix is a standard Gaussian random matrix. The main contribution of this paper is an improved AMP (IAMP) algorithm that works better for non-ideal measurement matrices. The algorithm is equivalent to AMP for standard Gaussian random matrices but provides better recovery when the correlations between columns of the measurement matrix deviate from those of the standard Gaussian random matrices. The derivation is based on a modification of the message passing mechanism that removes the conditional independence assumption. Examples are provided to demonstrate the performance improvement of IAMP where both a particularly designed matrix and a matrix from real applications are used.