  In this paper, a communication-efficient multi-processor compressed sensing
framework based on the approximate message passing algorithm is proposed. We
perform lossy compression on the data being communicated between processors,
resulting in a reduction in communication costs with a minor degradation in
recovery quality. In the proposed framework, a new state evolution formulation
takes the quantization error into account, and analytically determines the
coding rate required in each iteration. Two approaches for allocating the
coding rate, an online back-tracking heuristic and an optimal allocation scheme
based on dynamic programming, provide significant reductions in communication
costs.
