Approximate lower bounds for rate-distortion in compressive sensing systems

We attempt to quantify the possible gains that can be achieved by examining a rate-distortion competition between a conventional and a compressive sampling solution to data rate reduction. Simple approximate expression are developed for the minimum bit rate required to obtain the best achievable average performance from the compressive sensing system and the performance that would be achieved if that rate requirement was met. An example of a signal that contains a small number of phasors in Gaussian white noise is used to validate these results and to compare the degradation in performance of the 2 systems when lower bit rates than those required by the theory are employed.