Perturbation analysis of simultaneous orthogonal matching pursuit

• We analyze the performance of simultaneous orthogonal matching pursuit (SOMP) based on restricted isometry property (RIP).
• For an almost sparse signal ensemble, the results reveal that the set of these locations can be recovered exactly under some RIP-based conditions.
• We prove that the derived conditions are rather tight for a special scenario.
• We extend the analysis to strong-decaying signal ensemble, where the decay of entries in each signal is sufficiently strong.

The theory of compressed sensing (CS) indicates that a sparse vector lying in a high dimensional space can be accurately recovered from only a small set of linear measurements, under appropriate conditions on the measurement matrix. For multiple sparse signals that share common locations of the nonzero entries, simultaneous orthogonal matching pursuit (SOMP) is a widely used algorithm for joint recovery. In this paper, when both the measurements and the measurement matrix are perturbed by some errors, we analyze the performance of SOMP based on restricted isometry property (RIP). For an almost sparse signal ensemble {xj∈RN}{xj∈RN}, where the locations of the K   (K≪NK≪N) largest magnitude entries in each xjxj are identical and the differences among each signal are not very large, the results reveal that the set of these locations can be recovered exactly under some RIP-based conditions. We prove that the derived conditions are rather tight for a special scenario. Furthermore, we extend the analysis to strong-decaying signal ensemble, where the decay of entries in each signal is sufficiently strong. The results show that the corresponding RIP-based conditions are relaxed when compared with arbitrary sparse signal ensemble.