A new approach to sensing matrix optimization using steepest descent algorithm

In this paper, we discuss the design of optimal sensing matrix Φ for compressed sensing system, where the dictionary Ψ is assumed to be given. A new measure is proposed to obtain the sensing matrix, which unlike the traditional approaches, takes the sparse representation error of measurements into account, and leads to a more robust CS system. A gradient-based algorithm is derived to attack the optimization problem. Simulations are performed and the results illustrate the reconstruction accuracy performance of our novel approach outperforms the existing ones.