Multi-frequency phase retrieval from noisy data

TL;DR

This paper introduces a novel iterative algorithm for multi-frequency phase retrieval that effectively reconstructs complex objects and denoises data in noisy conditions using maximum likelihood and BM3D priors.

Contribution

The paper presents a new algorithm combining maximum likelihood and BM3D sparsity priors for simultaneous phase retrieval and denoising of complex objects from noisy multi-frequency data.

Findings

High-accuracy reconstruction in noisy conditions

Effective denoising of complex-valued images

Successful application to Fourier and diffraction data

Abstract

The phase retrieval from multi-frequency intensity (power) observations is considered. The object to be reconstructed is complex-valued. A novel algorithm is presented that accomplishes both the object phase (absolute phase) retrieval and denoising for Poissonian and Gaussian measurements. The algorithm is derived from the maximum likelihood formulation with Block Matching 3D (BM3D) sparsity priors. These priors result in two filtering: one is in the complex domain for complex-valued multi-frequency object images and another one in the real domain for the object phase. The algorithm is iterative with alternating projections between the object and measurement variables. The simulation experiments are produced for Fourier transform image formation and random phase modulations of the object, then the observations are random object diffraction patterns. The results demonstrate the success of the algorithm for reconstruction of the complex phase objects with the high-accuracy performance even for very noisy data.