Reconstruction of Signals from Magnitudes of Redundant Representations

TL;DR

This paper addresses the challenge of reconstructing signals from magnitude-only measurements in redundant representations, introducing new invertibility results and a robust iterative algorithm with analyzed noise performance.

Contribution

It provides novel invertibility conditions and an iterative reconstruction algorithm for signals from magnitude measurements in redundant linear systems.

Findings

Algorithm effectively reconstructs signals from magnitude data.

Reconstruction method is robust to noise.

Performance approaches Cramer-Rao bounds.

Abstract

This paper is concerned with the question of reconstructing a vector in a finite-dimensional real or complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new invertibility results as well an iterative algorithm that finds the least-square solution and is robust in the presence of noise. We analyze its numerical performance by comparing it to two versions of the Cramer-Rao lower bound.