Undersampled Phase Retrieval with Image Priors

ABSTRACT Phase retrieval seeks to recover a complex signal from amplitude-only measurements, a challenging nonlinear inverse problem. Current theory and algorithms often ignore signal priors. By contrast, we evaluate here a variety of image priors in the context of severe undersampling with structured random Fourier measurements. Our results show that those priors significantly improve reconstruction, allowing accurate reconstruction even below the weak recovery threshold. Index T erms-- Inverse Problems, Phase Retrieval, Image Priors, Optimization, Regularization 1. INTRODUCTION In many areas of science and engineering, one requires to recover an object of interest from indirect measurements.