Extended Successive Convex Approximation for Phase Retrieval with Dictionary Learning

TL;DR

This paper introduces two scalable algorithms based on successive convex approximation for phase retrieval with dictionary learning, effectively estimating signals and dictionaries from magnitude-only measurements, especially in diverse mixture models.

Contribution

It develops two novel parallel algorithms extending the SCA framework for joint dictionary and sparse signal estimation from phase measurements, with improved scalability and flexibility.

Findings

Algorithms outperform state-of-the-art methods in simulations.

Compact-SCAphase is effective for less diverse mixtures.

SCAphase handles highly diverse mixture models well.

Abstract

Phase retrieval aims at reconstructing unknown signals from magnitude measurements of linear mixtures. In this paper, we consider the phase retrieval with dictionary learning problem, which includes an additional prior information that the measured signal admits a sparse representation over an unknown dictionary. The task is to jointly estimate the dictionary and the sparse representation from magnitude-only measurements. To this end, we study two complementary formulations and develop efficient parallel algorithms by extending the successive convex approximation framework using a smooth majorization. The first algorithm is termed compact-SCAphase and is preferable in the case of less diverse mixture models. It employs a compact formulation that avoids the use of auxiliary variables. The proposed algorithm is highly scalable and has reduced parameter tuning cost. The second algorithm, referred to as SCAphase, uses auxiliary variables and is favorable in the case of highly diverse mixture models. It also renders simple incorporation of additional side constraints. The performance of both methods is evaluated when applied to blind sparse channel estimation from subband magnitude measurements in a multi-antenna random access network. Simulation results demonstrate the efficiency of the proposed techniques compared to state-of-the-art methods.