Undersampled Phase Retrieval with Outliers

Abstract

We propose a general framework for reconstructing transform-sparse images from undersampled (squared)-magnitude data corrupted with outliers. This framework is implemented using a multi-layered approach, combining multiple initializations (to address the nonconvexity of the phase retrieval problem), repeated minimization of a convex majorizer (surrogate for a nonconvex objective function), and iterative optimization using the alternating directions method of multipliers. Exploiting the generality of this framework, we investigate using a Laplace measurement noise model better adapted to outliers present in the data than the conventional Gaussian noise model. Using simulations, we explore the sensitivity of the method to both the regularization and penalty parameters. We include 1D Monte Carlo and 2D image reconstruction comparisons with alternative phase retrieval algorithms. The results suggest the proposed method, with the Laplace noise model, both increases the likelihood of correct support recovery and reduces the mean squared error from measurements containing outliers. We also describe exciting extensions made possible by the generality of the proposed framework, including regularization using analysis-form sparsity priors that are incompatible with many existing approaches.

11 pages, 9 figures

References in corpus (4)

• Phase Retrieval via Wirtinger Flow: Theory and Algorithms
• A unified evaluation of iterative projection algorithms for phase retrieval
• Phase Retrieval with Application to Optical Imaging
• Phase retrieval and saddle-point optimization

Cited by in corpus (6)

• Undersampled Phase Retrieval via Majorization-Minimization
• Proximity Operators for Phase Retrieval
• Phase retrieval from noisy data based on sparse approximation of object phase and amplitude
• Accelerated Wirtinger Flow: A fast algorithm for ptychography
• Inexact Alternating Optimization for Phase Retrieval In the Presence of Outliers
• Robust Recovery via Implicit Bias of Discrepant Learning Rates for Double Over-parameterization