Joint Sensing Matrix Design And Recovery Based On Normalized Iterative Hard Thesholding for Sparse Systems

Abstract

In this work, we present a joint sensing matrix design and recovery algorithm based on the normalized iterative hard thresholding (NIHT) algorithm for cost-effectively solving the problem of sparse recovery. In particular, we consider both the Gram of the sensing matrix and a gradient-based algorithm based on the real mutual coherence (RMC) to compute the sensing matrix, so that the Gram of the matrix can closely approach the relaxed equiangular tight frame (ETF. By optimizing the sensing matrix together with its column normalization, a better recovery performance can be achieved. Simulations assess the performance of the proposed approach versus other iterative hard thresholding-based algorithms and show that the proposed approach achieves the best recovery performance.