Parallel matching pursuit algorithm and analysis

Abstract

For the existing compressed sensing greedy reconstruction algorithm, it is easy to fall into local optimum and overfitting problems. In this paper, we propose a new sparse recovery algorithm, called Parallel Matching pursuit (PMP), which searches the signal support set in both depth and breadth dimensions. PMP simultaneously examines multiple estimates of candidate support set in each iteration, and finally chooses the estimate that minimizes the reconstruction residual. Based on the restricted isometry property (RIP), sufficient conditions for PMP to reconstruct the signal are given to ensure that we can accurately recover any K-sparse signal from the measured value. Moreover, the recovery guarantee of the PMP algorithm is also provided for the case of noisy measurements. The performance of the PMP algorithm is evaluated by the signal reconstruction ability. Finally, numerical experiments verify the effectiveness of the algorithm.