A feedback-based construction of multilayer measurement matrix for compressive sensing

Abstract

A feedback-based multilayer measurement matrix (FBMM) within compressive sensing (CS) framework is introduced. In CS, the restricted isometry property (RIP) condition of measurement matrix determines the reconstruction precision. The smaller coherence between measurement matrix and sparse dictionary, the better signal reconstruction performs. However, the construction of a small coherence measurement matrix with large size (e.g., Gaussian matrix) consumes numerous of storage and calculation. Therefore, we introduce a FBMM algorithm where small measurement matrix is applied by feedback method for multilayer to reduce the consumption of resource. Finally, we prove that the FBMM algorithm satisfies the RIP conditionally and provides several selectable measurement matrix with different measuring dimensions. In addition, we established several experiment to test the performance of the proposed algorithm and compare with the traditional algorithm. we conclude that the FBMM algorithm can reduce the consumption of resource for hardware implementation with acceptable reconstruction precision.