Sublinear compressive sensing reconstruction via belief propagation decoding

We propose a new compressive sensing scheme, based on codes of graphs, that allows for joint design of sensing matrices and low complexity reconstruction algorithms. The compressive sensing matrices can be shown to offer asymptotically optimal performance when used in combination with OMP methods. For more elaborate greedy reconstruction schemes, we propose a new family of list decoding and multiple-basis belief propagation algorithms. Our simulation results indicate that the proposed CS scheme offers good complexity-performance tradeoffs for several classes of sparse signals.