Compressed image sensing with components regularization based on Bregman iteration

Compressed sensing (CS) is a new theory of signal processing for simultaneous signal sampling and compression. The optimization methods with components regularization have been proposed to perform CS reconstruction of the natural images which always contain various morphological components. In this paper, in order to solve the components regularized optimization problem more accurately, an iterative algorithm is proposed based on the Bregman iteration. The proposed algorithm is an inner-outer iterative procedure, with the two-variable Bregman iteration as its outer iteration and the alternating minimization as its inner iteration. Experimental results show the superiority of the proposed algorithm to other recently developed algorithms in terms of the visual quality improvement and the detail feature preserving capability.