Sparse sequence recovery via a maximum a posteriori estimation

A maximum a posteriori (MAP) estimation algorithm is given for reconstructing sparse signals, where a part of the support, and an approximate estimate of the sparse signal are known. This method is useful, e.g., in magnetic resonance image (MRI) sequence, natural video sequences, etc, where it is required to recursively reconstruct a sequence of mutually correlated sparse signals or images. Here we use the last signal as an a priori estimate of the current signal. The priori information is often inaccurate, and we adopt MAP estimation framework to deal with this issue. Simulation studies are performed, and the algorithm is applied to reconstruct MRI image sequences.