Fundamental Limits and Algorithms

Compressed sensing is a non-adaptive compression method that takes advantage of natural sparsity at the input and is fast gaining relevance to both researchers and engineers for its universality and applicability. First developed by Candès et al., the subject has seen a surge of high-quality results both in its theory and applica-tions. This thesis extends compressed sensing ideas to sensor networks and other bandwidth-constrained communication systems. In particular, we explore the limits of performance of compressive sensor networks in relation to fundamental operations such as quantization and parameter estimation. Since compressed sensing is originally formulated as a real-valued problem, quanti-zation of the measurements is a very natural extension. Although several researchers have proposed modified reconstruction methods that mitigate quantization noise for