On joint optimization of sensing matrix and sparsifying dictionary for robust compressed sensing systems

This paper deals with joint design of sensing matrix and sparsifying dictionary for compressed sensing (CS) systems. Based on the maximum likelihood estimation (MLE) principle, a preconditioned signal recovery (PSR) scheme and a novel measure are proposed. Such a measure allows us to optimize the sensing matrix and dictionary jointly. An alternating minimization-based iterative algorithm is derived for solving the corresponding optimal design problem. Simulation and experiments, carried with synthetic data and real image signals, show that the PSR scheme and the CS system, obtained using the proposed approaches, outperform the prevailing ones in terms of reducing the effect of sparse representation errors.