Dictionary Learning Phase Retrieval from Noisy Diffraction Patterns

TL;DR

This paper introduces DLPR, a novel algorithm that combines dictionary learning and sparse coding within an alternating projection framework to improve phase retrieval from noisy diffraction patterns, outperforming existing methods.

Contribution

The paper presents a new dictionary learning-based approach for phase retrieval that jointly learns the dictionary and reconstructs images from noisy data, enhancing robustness and accuracy.

Findings

DLPR outperforms state-of-the-art methods on simulated data.

The algorithm effectively handles heavily noisy (Poissonian or Gaussian) observations.

Experimental results on real images demonstrate noticeable improvements.

Abstract

This paper proposes a novel algorithm for image phase retrieval, i.e., for recovering complex-valued images from the amplitudes of noisy linear combinations (often the Fourier transform) of the sought complex images. The algorithm is developed using the alternating projection framework and is aimed to obtain high performance for heavily noisy (Poissonian or Gaussian) observations. The estimation of the target images is reformulated as a sparse regression, often termed sparse coding, in the complex domain. This is accomplished by learning a complex domain dictionary from the data it represents via matrix factorization with sparsity constraints on the code (i.e., the regression coefficients). Our algorithm, termed dictionary learning phase retrieval (DLPR), jointly learns the referred to dictionary and reconstructs the unknown target image. The effectiveness of DLPR is illustrated through experiments conducted on complex images, simulated and real, where it shows noticeable advantages over the state-of-the-art competitors.