Quantization and Compressive Sensing

Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This book chapter explores the interaction of quantization and compressive sensing and examines practical quantization strategies for compressive acquisition systems. Specifically, we first provide a brief overview of quantization and examine fundamental performance bounds applicable to any quantization approach. Next, we consider several forms of scalar quantizers, namely uniform, non-uniform, and 1-bit. We provide performance bounds and fundamental analysis, as well as practical quantizer designs and reconstruction algorithms that account for quantization. Furthermore, we provide an overview of Sigma-Delta ($\Sigma\Delta$) quantization in the compressed sensing context, and also discuss implementation issues, recovery algorithms and performance bounds. As we demonstrate, proper accounting for quantization and careful quantizer design has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing and Its Applications", 201

Compressive Sensing Theory for Optical Systems Described by a Continuous Model

A brief survey of the author and collaborators' work in compressive sensing applications to continuous imaging models.Comment: Chapter 3 of "Optical Compressive Imaging" edited by Adrian Stern published by Taylor & Francis 201

Conditions for recovery of sparse signals correlated by local transforms

This paper addresses the problem of correct recovery of multiple sparse correlated signals using distributed thresholding. We consider the scenario where multiple sensors capture the same event, but observe different signals that are correlated by local transforms of their sparse components. In this context, the signals do not necessarily have the same sparse support, but instead the support of one signal is built on local transformations of the atoms in the sparse support of another signal. We establish the sufficient condition for the correct recovery of such correlated signals using independent thresholding of the multiple signals. The validity of the derived recovery condition is confirmed by experimental results in noiseless and noisy scenarios