Reconstruction of Signals from Magnitudes of Redundant Representations

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.

arXiv comment20 pages, 5 figures

References in corpus (4)

• A new proof for the existence of mutually unbiased bases
• SIC-POVMs and the Extended Clifford Group
• Equiangular lines, mutually unbiased bases, and spin models
• On PSI-complete and PSIR-complete measurements

Cited by in corpus (7)

• Phase Retrieval Using Feasible Point Pursuit: Algorithms and Cramér-Rao Bound
• The local convexity of solving systems of quadratic equations
• Stable phase retrieval with low-redundancy frames
• Invertibility and Robustness of Phaseless Reconstruction
• Reconstruction of Signals from Magnitudes of Redundant Representations: The Complex Case
• On Lipschitz Analysis and Lipschitz Synthesis for the Phase Retrieval Problem
• Phase Retrieval using Lipschitz Continuous Maps