Abstract / truncated to 115 words (read the full abstract)

Many scientific and engineering problems require us to process measurements and data in order to extract information. Since we base decisions on information, it is important to design accurate and efficient processing algorithms. This is often done by modeling the signal of interest and the noise in the problem. One type of modeling is Compressed Sensing, where the signal has a sparse or low-rank representation. In this thesis we study different approaches to designing algorithms for sparse and low-rank problems. Greedy methods are fast methods for sparse problems which iteratively detects and estimates the non-zero components. By modeling the detection problem as an array processing problem and a Bayesian filtering problem, we improve the detection ... toggle 10 keywords

compressed sensing – greedy search methods – bayesian estimation – relevance vector machine – low-rank matrix estimation – matrix completion – robust pca – bayesian cramer-rao bounds – phase retrieval – l1-minimization.

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