One-dimensional piecewise-constant signal recovery via spike-and-slab approximate message-passing

This paper proposes a novel AMP solver for problems of 1-D piecewise-constant signals recovery under the compressed sensing framework. The proposed solver is named ssAMP-1D. The proposed solver is based on a factor graph consisting of two types of the factor nodes: one is for handling sparsity in finite differences X_i - X_i-1, and another is related to the measurement generation Y = HX + W. We construct the ssAMP-1D iteration from a sum-product rule based on the factor graph, where we use a spike-and-slab prior to encourage sparsity in the 1-D finite differences. We provide a summary of the algorithm construction, discussing the several aspects of ssAMP-1D through empirical comparison to the state-of-the-art solvers, GrAMPA, TV-AMP, EFLA and TV-CP.