Compressive color imaging with group-sparsity on analysis prior

Compressed sensing (CS) of color images can be formulated as a group-sparsity promoting inverse problem. In the past, group-sparsity constraint was imposed on the CS synthesis prior formulation with an orthogonal transform to solve the inverse problem. The objective of this work is to empirically show that better results can be obtained if a group-sparsity constraint is imposed on the CS analysis prior formulation with a redundant transform. This problem requires solving a group-sparsity promoting inverse problem which has not been addressed earlier. Therefore we derive a new algorithm for solving it based on the Majorization-Minimization approach. Experimental results corroborate that analysis prior with a redundant transform gives far superior (about 1.5dB) improvement compared to synthesis prior with orthogonal transform.