Permutation enhanced parallel reconstruction for compressive sampling

Hao Fang, Sergiy A. Vorobyov, Hai Jiang

Abstract: In this paper, a simple but efficient permutation enhanced parallel reconstruction architecture for compressive sampling (CS) is proposed. In this architecture, a measurement matrix is constructed from a block-diagonal sensing matrix, the sparsifying basis of the target signal, and a pre-defined permutation matrix. In this way, the projection of the signal onto the sparsifying basis can be divided into several segments and all segments can be reconstructed in parallel. Thus, the computational complexity and the time for reconstruction can be reduced significantly. With a good permutation matrix, the error performance of the proposed method can be improved compared with the option without permutation. The proposed method can be used in applications where the computational complexity and time for reconstruction are crucial evaluation criteria and centralized sampling is acceptable. Simulation results show that the proposed method can achieve comparable results to the centralized reconstruction methods (i.e., standard CS and distributed CS), while requiring much less reconstruction time.