APPROXIMATE MESSAGE PASSING ALGORITHMS FOR COMPRESSIVE SENSING

Abstract

C oulpressive Sensing is a novel sampling technique in which we sample very few samples (onlpare(I to traditional Nyquist Sampling theorem. The reconstruction is more complex in compressive sensing, where as it is linear in Nyquist Sampling methodology. A variety of Reconstruction algorithms are proposed in the literature from Convex Opitmization foriiiiilations to greedy algorithms. Approximate Message Passing algorithms have attracted a lot of attention because they provide good recovery guarantees similar to Optimization based alternatives at the same time being more computationally efficient. Another important aspect of Message Passing algorithms is that they involve a probabilistic fornuilatiou. wInch provides for a way to incorporate additional structure to augment sparsity resulting iiiore robust reconstruction algorithms. The present effort is devoted to Compressive Sensing in the form of a survey of various Sparse Recovery algorithms. Then we study a message passing algorithm for recovery of block sparse signals. This is followed by a discussion of Message Passing algorithms where turboAMP algorithm for recovery of images is studied. The turboAMP algorithm takes advantage of structure in wavelet coefficients of an imliage in addition to sparsity for recovery. We propose two message schedules as modifications to turboAMP algorithm to ol )t.aimm improved results.