Information-Theoretically Optimal Compressed Sensing via Spatial Coupling and Approximate Message Passing
Information-Theoretically Optimal Compressed Sensing via Spatial Coupling and Approximate Message Passing
We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and numerically by Krzakala [30], message passing algorithms can effectively solve the reconstruction problem for spatially coupled measurements …