During the last decade, research has shown compressive sensing (CS) to be a promising theoretical framework for reconstructing high-dimensional sparse signals. Leveraging a sparsity hypothesis, algorithms based on CS reconstruct signals on the basis of a limited set of (often random) measurements. Such algorithms require fewer measurements than conventional techniques to fully reconstruct a sparse signal, thereby saving time and hardware resources. This thesis addresses several challenges. The first is to theoretically understand how some parameters—such as noise variance—affect the performance of simultaneous orthogonal matching pursuit (SOMP), a greedy support recovery algorithm tailored to multiple measurement vector signal models. Chapters 4 and 5 detail novel improvements in understanding the performance of SOMP. Chapter 4 presents analyses of SOMP for noiseless measurements; using those analyses, Chapter 5 extensively studies the performance of SOMP in the noisy case. A second challenge consists in optimally weighting the impact of each measurement vector on the decisions of SOMP. If measurement vectors feature unequal signal-to-noise ratios, properly weighting their impact improves the performance of SOMP. Chapter 6 introduces a novel weighting strategy from which SOMP benefits. The chapter describes the novel weighting strategy, derives theoretically optimal weights for it, and presents both theoretical and numerical evidence that the strategy improves the performance of SOMP. Finally, Chapter 7 deals with the tendency for support recovery algorithms to pick support indices solely for mapping a particular noise realization. To ensure that such algorithms pick all the correct support indices, researchers often make the algorithms pick more support indices than the number strictly required. Chapter 7 presents a support reduction technique, that is, a technique removing from a support the supernumerary indices solely mapping noise. The advantage of the technique, which relies on cross-validation, is that it is universal, in that it makes no assumption regarding the support recovery algorithm generating the support. Theoretical results demonstrate that the technique is reliable. Furthermore, numerical evidence proves that the proposed technique performs similarly to orthogonal matching pursuit with cross-validation (OMP-CV), a state-of-the-art algorithm for support reduction. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished