An achievable measurement rate-MSE tradeoff in compressive sensing through partial support recovery

Abstract

For compressive sensing, we derive achievable performance guarantees for recovering partial support sets of sparse vectors. The guarantees are determined in terms of the fraction of signal power to be detected and the measurement rate, defined as a relation between the dimensions of the measurement matrix. Based on this result we derive a tradeoff between the measurement rate and the mean square error, and illustrate it by a numerical example.

Methods for Distributed Compressed Sensing

“…Information theory provides sufficient conditions for information exchange, while we, for compressed sensing in networks, are still searching for necessary conditions on the CS part of the problem; therefore, a common assumption is often that the transmission links are perfect (but maybe costly). There has been some attempts at bringing information theory and compressed sensing together [16][17][18]. In our understanding, if information theory is brought into DCS, it is also necessary to consider the effects of source and channel coding errors [19][20][21][22][23][24].…”