Alternative optimization of sensing matrix and sparsifying dictionary for compressed sensing systems

Compressive sensing theory shows that sparse signals can be reconstructed from far less samples than those required by the classical Shannon-Nyquist Theorem. An optimized sensing matrix for a certain class of signals can further reduce the necessary number of samples. Additionally, in order to make the signals represented as sparse as possible, a dictionary can be optimized. In this paper, we introduce a framework for joint design of the sensing matrix and dictionary. A new design procedure is proposed, which is based on an alternative optimization of the sparsifying dictionary and the sensing matrix. Simulation results show that this alternate optimization yields a better performance in terms of signal recovery than that by those existing algorithms.