An RIP-based approach to $\Sigma\Delta$ quantization for compressed sensing

TL;DR

This paper introduces a new RIP-based method for analyzing reconstruction errors in $\Sigma\Delta$ quantized compressed sensing, simplifying proofs and extending error bounds for Gaussian and subgaussian matrices.

Contribution

It presents a novel RIP-based approach to error estimation in $\Sigma\Delta$ quantized compressed sensing, providing simpler proofs and broader applicability.

Findings

Error bounds are extended to Gaussian and subgaussian matrices.

The approach simplifies existing proofs of reconstruction error.

Provides a generalized framework for error estimation.

Abstract

In this paper, we provide a new approach to estimating the error of reconstruction from $\Sigma\Delta$ quantized compressed sensing measurements. Our method is based on the restricted isometry property (RIP) of a certain projection of the measurement matrix. Our result yields simple proofs and a slight generalization of the best-known reconstruction error bounds for Gaussian and subgaussian measurement matrices.