Nonadaptive lossy encoding of sparse signals

Abstract

At high rate, a sparse signal is optimally encoded through an adaptive strategy that finds and encodes the signal's representation in the sparsity-inducing basis. This thesis examines how much the distortion rate (D(R)) performance of a nonadaptive encoder, one that is not allowed to explicitly specify the sparsity pattern, can approach that of an adaptive encoder. Two methods are studied: first, optimizing the number of nonadaptive measurements that must be encoded and second, using a binned quantization strategy. Both methods are applicable to a setting in which the decoder knows the sparsity basis and the sparsity level. Through small problem size simulations, it is shown that a considerable performance gain can be achieved and that the number of measurements controls a tradeoff between decoding complexity and achievable D(R).