Abstract: Quantized compressive sensing (QCS) deals with the problem of coding compressive measurements of low-complexity signals (e.g., sparse vectors in a given basis, low-rank matrices) with quantized, finite precision representations, i.
Abstract: In this paper, the joint support recovery of several sparse signals whose supports present similarities is examined. Each sparse signal is acquired using the same noisy linear measurement process, which returns fewer observations than the dimension of the sparse signals.
Abstract: Under which conditions and with which distortions can we preserve the pairwise-distances of low-complexity vectors, e.g., for structured sets such as the set of sparse vectors or the one of low-rank matrices, when these are mapped in a finite set of vectors?
Abstract: Recently, many works have focused on the characterization of non-linear dimensionality reduction methods obtained by quantizing linear embeddings, e.g., to reach fast processing time, efficient data compression procedures, novel geometry-preserving embeddings or to estimate the information/bits stored in this reduced data representation.
Abstract: Several exact recovery criteria (ERC) ensuring that orthogonal matching pursuit (OMP) identifies the correct support of sparse signals have been developed in the last few years. These ERC rely on the restricted isometry property (RIP), the associated restricted isometry constant (RIC) and sometimes the restricted orthogonality constant (ROC).