Generalized Turbo Signal Recovery for Nonlinear Measurements and Orthogonal Sensing Matrices

TL;DR

This paper introduces a generalized turbo signal recovery algorithm designed for estimating signals from quantized measurements using row-orthogonal sensing matrices, with theoretical analysis and numerical validation showing its effectiveness.

Contribution

It presents a novel turbo-based recovery algorithm for nonlinear measurements with orthogonal sensing matrices, supported by state evolution analysis and empirical validation.

Findings

Algorithm accurately estimates signals from quantized measurements.

State evolution analysis matches theoretical predictions.

Numerical experiments confirm the algorithm's effectiveness.

Abstract

In this study, we propose a generalized turbo signal recovery algorithm to estimate a signal from quantized measurements, in which the sensing matrix is a row-orthogonal matrix, such as the partial discrete Fourier transform matrix. The state evolution of the proposed algorithm is derived and is shown to be consistent with that obtained with the replica method. Numerical experiments illustrate the excellent agreement of the proposed algorithm with theoretical state evolution.