Robust phase retrieval and super-resolution from one bit coded diffraction patterns. arXiv preprint arXiv:1402.2255

Abstract

In this paper we study a realistic setup for phase retrieval, where the signal of interest is modulated or masked and then for each modulation or mask a diffraction pattern is collected, producing a coded diffraction pattern (CDP) [CLM13]. We are interested in the setup where the resolution of the collected CDP is limited by the Fraunhofer diffraction limit of the imaging system. We investigate a novel approach based on a geometric quantization scheme of phase-less linear measurements into (one-bit) coded diffraction patterns, and a corresponding recovery scheme. The key novelty in this approach consists in comparing pairs of coded diffractions pat-terns across frequencies: the one bit measurements obtained rely on the order statistics of the un-quantized measurements rather than their values. This results in a robust phase recovery, and unlike currently available methods, allows to efficiently perform phase recovery from mea-surements affected by severe (possibly unknown) non linear, rank preserving perturbations, such as distortions. Another important feature of this approach consists in the fact that it enables also super-resolution and blind-deconvolution, beyond the diffraction limit of a given imaging system.