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

Estimation in high dimensions: a geometric perspective

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse recovery, matrix completion, quantization, linear and logistic regression and generalized linear models.Comment: 56 pages, 9 figures. Multiple minor change

Video querying via compact descriptors of visually salient objects

We consider the problem of extracting descriptors that represent visually salient portions of a video sequence. Most state-of-the-art schemes generate video descriptors by extracting features, e.g., SIFT or SURF or other keypoint-based features, from individual video frames. This ap-proach is wasteful in scenarios that impose constraints on storage, communication overhead and on the allowable computational complexity for video querying. More importantly, the descrip-tors obtained by this approach generally do not provide semantic clues about the video content. In this paper, we investigate new feature-agnostic approaches for efficient retrieval of similar video content. We evaluate the efficiency and accuracy of retrieval when k-means clustering is applied to image features extracted from video frames. We also propose a new approach in which the extraction of compact video descriptors is cast as a Non-negative Matrix Factorization (NMF) problem. Initial experiments on video-based matching suggest that compact descriptors obtained via low-rank matrix factorization improve discriminability and robustness to parameter selection compared to k-means clustering