Generalized fusion algorithm for compressive sampling reconstruction and RIP-based analysis

We design a Generalized Fusion Algorithm for Compressive Sampling (gFACS) reconstruction. In the gFACS algorithm, several individual compressive sampling (CS) reconstruction algorithms participate to achieve a better performance than the individual algorithms. The gFACS algorithm is iterative in nature and its convergence is proved under certain conditions using Restricted Isometry Property (RIP) based theoretical analysis. The theoretical analysis allows for the participation of any off-the-shelf or new CS reconstruction algorithm with simple modifications, and still guarantees convergence. We show modifications of some well-known CS reconstruction algorithms for their seamless use in the gFACS algorithm. Simulation results show that the proposed gFACS algorithm indeed provides better performance than the participating individual algorithms.