Performance Bounds for Vector Quantized Compressive Sensing

TL;DR

This paper analyzes the performance bounds of quantized compressive sensing with sparse reconstruction, providing theoretical guarantees for different estimators under high-rate vector quantization.

Contribution

It introduces a framework for predicting reconstruction error bounds in quantized CS using Gaussian mixture models and optimal rate allocation.

Findings

Derived upper and lower bounds on reconstruction error

Analyzed performance of basis pursuit de-noising and oracle estimators

Provided theoretical insights into quantized CS performance guarantees

Abstract

In this paper, we endeavor for predicting the performance of quantized compressive sensing under the use of sparse reconstruction estimators. We assume that a high rate vector quantizer is used to encode the noisy compressive sensing measurement vector. Exploiting a block sparse source model, we use Gaussian mixture density for modeling the distribution of the source. This allows us to formulate an optimal rate allocation problem for the vector quantizer. Considering noisy CS quantized measurements, we analyze upper- and lower-bounds on reconstruction error performance guarantee of two estimators - convex relaxation based basis pursuit de-noising estimator and an oracle-assisted least-squares estimator.