CAPRL: Signal Recovery from Compressive Affine Phase Retrieval via Lifting

TL;DR

This paper introduces CAPRL, a convex optimization approach using lifting and nuclear norm relaxation for sparse affine phase retrieval, with an efficient algorithm and proven convergence, enabling exact and stable signal recovery.

Contribution

It develops a novel convex model for compressive affine phase retrieval using lifting and relaxations, along with an inertial proximal ADMM algorithm and convergence analysis.

Findings

Sparse signals can be exactly recovered.

The proposed algorithm is stable and effective.

Applications extend beyond phase retrieval.

Abstract

In this paper, we consider compressive/sparse affine phase retrieval proposed in [B. Gao B, Q. Sun, Y. Wang and Z. Xu, Adv. in Appl. Math., 93(2018), 121-141]. By the lift technique, and heuristic nuclear norm for convex relaxation of rank and $\ell$ one norm convex relaxation of sparsity, we establish convex models , which are called compressive affine phase retrieval via lifting (CAPRL). In order to compute these models, we develop inertial proximal ADMM for multiple separated operators and also give out its convergence analysis. Our numerical experiments via proposed algorithm show that sparse signal can be exactly and stably recovered via CAPRL. We also list some other applications of our proposed algorithm.