Reconstruction of Complex Sparse Signals in Compressed Sensing with Real Sensing Matrices

The existing greedy algorithms for the reconstruction in compressed sensing were designed no matter which type the original sparse signals and sensing matrices have, real or complex. The reconstruction algorithms definitely apply to real sensing matrices and complex sparse signals, but they are not customized to this situation so that we could improve those algorithms further. In this paper, we elaborate on the compressed sensing with real sensing matrices when the original sparse signals are complex. We propose two reconstruction algorithms by modifying the orthogonal matching pursuit to include some procedures specialized to this setting. It is shown via analysis and simulation that the proposed algorithms have better reconstruction success probability than conventional reconstruction algorithms.