Multiple Description Coding for Distributed Compressed Sensing

The following thesis is devoted to the study of a multiple description framework for compressed sensing, with particular focus on a distributed application of compressed sensing. Compressed sensing is a novel theory for signal acquisition, that enables to directly acquire a compressed representation of a sparse or compressible signal, regardless of what is the basis in which the signal is actually sparse (compressible). The low complexity of an acquisition stage adopting compressed sensing raised interests about adopting it in sensor networks. In this distributed scenario compressed sensing is also able to exploit inter-correlation, in the form of joint sparsity, among different signals to improve coding efficiency without demanding any complex operation. Our work proposes the CS-SPLIT scheme to generate two or more descriptions from measurements acquired through compressed sensing. This scheme proved experimentally superior to another classic method of obtaining multiple descriptions, that is using a multiple description scalar quantizer on the measurements (CS-MDSQ). An analytic treatment of the two methods in terms of rate-distortion performance has also been given, using the current results in the theory of compressed sensing. CS-SPLIT can be readily used in sensor networks thanks to its extreme simplicity. We developed two new joint reconstruction algorithms (Difference and Texas Difference) that significantly improve over existing algorithms for the JSM-1 model, when the number of measurements is limited. This is relevant to multiple descriptions because it allows to get a better quality in the reconstruction of the single descriptions of CS-SPLIT when joint decoding is not possible.