New Bayesian Compressive Sensing Algorithms for Sparse Signal Recovery

Proposed Bayesian Model and Defining Priors Basic MMV Model: Solve for Xsp in Y = AXsp + E , where Y ∈ RM×N, A ∈ RM×P, Xsp ∈ RP×N, and (M P) Promoting sparsity: Gaussian-Bernoulli prior by defining Xsp := s ◦ X , where s ∈ {0,1}P×1 I s accounts for the supports of the solution and “◦” denotes Hadamard product Promoting clustering pattern: Incorporating total variation like prior on the support learning vector s using measure of clumpiness (Σ∆)s := ∑P i=2 |si − si−1| I There exist few transitions for the clustered pattern supports Examples: