Quantized Iterative Hard Thresholding: Bridging 1-bit and High-Resolution Quantized Compressed Sensing

TL;DR

This paper introduces a unified iterative hard thresholding algorithm capable of reconstructing sparse signals from quantized measurements across all resolutions, from 1-bit to high-resolution, improving consistency with the quantization model.

Contribution

The paper generalizes the IHT algorithm to handle any scalar quantization level, unifying the approach for 1-bit and high-resolution compressed sensing.

Findings

QIHT outperforms traditional methods in various quantization scenarios.

The unified formalism simplifies reconstruction across different quantization resolutions.

Experimental results demonstrate improved accuracy and consistency.

Abstract

In this work, we show that reconstructing a sparse signal from quantized compressive measurement can be achieved in an unified formalism whatever the (scalar) quantization resolution, i.e., from 1-bit to high resolution assumption. This is achieved by generalizing the iterative hard thresholding (IHT) algorithm and its binary variant (BIHT) introduced in previous works to enforce the consistency of the reconstructed signal with respect to the quantization model. The performance of this algorithm, simply called quantized IHT (QIHT), is evaluated in comparison with other approaches (e.g., IHT, basis pursuit denoise) for several quantization scenarios.