Theory and Practice of Compressed Sensing in Communications and Airborne Networking

摘要

We consider the problem of compressed sensing and propose new deterministic constructions of compressive sampling matrices based on finite- geometry generalized polygons. For the noiseless measurements case, we develop a novel recovery algorithm for strictly sparse signals that utilizes the geometry properties of generalized polygons and exhibits complexity linear in the sparsity value. In the presence of measurement noise, recovery of the generalized-polygon sampled signals can be carried out most effectively using a belief propagation algorithm. Experimental studies included in this report illustrate our theoretical developments.