Papers › Perturbed Amplitude Flow for Phase Retrieval
Perturbed Amplitude Flow for Phase Retrieval
Bing Gao, Xinwei Sun, Yang Wang, Zhiqiang Xu
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In this paper, we propose a new non-convex algorithm for solving the phase retrieval problem, i.e., the reconstruction of a signal ∈ⁿ (=̋ or $\C$) from phaseless samples bⱼ=⟨ⱼ, ⟩, j=1,…,m. The proposed algorithm solves a new proposed model, perturbed amplitude-based model, for phase retrieval and is correspondingly named as {\em Perturbed Amplitude Flow} (PAF). We prove that PAF can recover c (c = 1) under 𝒪(n) Gaussian random measurements (optimal order of measurements). Starting with a designed initial point, our PAF algorithm iteratively converges to the true solution at a linear rate for both real and complex signals. Besides, PAF algorithm needn't any truncation or re-weighted procedure, so it enjoys simplicity for implementation. The effectiveness and benefit of the proposed method are validated by both the simulation studies and the experiment of recovering natural images.
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