Quantization and Compressive Sensing

Abstract

Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This 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 (Σ∆) 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.

Quantity over Quality: Dithered Quantization for Compressive Radar Systems

“…However, as made clear in Sec. III, QCS aims to reduce the impact of signal measurement quantization in signal estimation by possibly increasing the number of measurements beyond N ; what truly matters in QCS is indeed the total bit-rate B (i.e., M × the bit depth b) used to encode the observations [4], [11].…”

Latency Analysis for Sequential Detection in Low-Complexity Binary Radio Systems

“…While the potential of binary sampling has been extensively studied, e.g., regarding wireless communication capabilities [3]- [10], signal reconstruction error [11]- [13], estimation sensitivity [14]- [19], and detection reliability [20]- [22], here we focus on the analysis of the sensing latency [23].…”

Near-Optimal Compression for Compressed Sensing

“…So, using simple MSQ coupled with standard reconstruction algorithms only guarantees an approximation error that scales with δ, the step-size in the quantization alphabet. One can devise more sophisticated reconstruction methods to improve the error behavior as the number of measurement increases, see [4]. However, lower bounds obtained in the frame [5] and compressed sensing [6,7] quantization settings show that the error associated with MSQ can at best decay linearly in the number of measurements, hence the number of bits (provided every measurement is quantized with the same alphabet).…”

“…For a comprehensive review of results on the use of MSQ (1-bit as well as high-resolution) in the compressed sensing framework, see [10,11] cf. [4].…”