Denoising Poisson Phaseless Measurements via Orthogonal Dictionary Learning

TL;DR

This paper introduces a novel dictionary learning approach with orthogonal dictionaries and sparsity to effectively denoise Poisson noise in phaseless diffraction measurements, improving image quality in phase retrieval tasks.

Contribution

It proposes a new model combining orthogonal dictionary learning, sparsity, and Kullback-Leibler divergence, with efficient algorithms and convergence guarantees for denoising Poisson phaseless data.

Findings

The methods outperform existing algorithms in denoising quality.

The algorithms are computationally efficient with closed-form solutions.

Numerical experiments demonstrate robustness and texture preservation.

Abstract

Phaseless diffraction measurements recorded by a CCD detector are often affected by Poisson noise. In this paper, we propose a dictionary learning model by employing patches based sparsity to denoise Poisson phaseless measurement. The model consists of three terms: (i) A representation term by an orthogonal dictionary, (ii) an $L^0$ pseudo norm of coefficient matrix, and (iii) a Kullback-Leibler divergence to fit phaseless Poisson data. Fast Alternating Minimization Method (AMM) and Proximal Alternating Linearized Minimization (PALM) are adopted to solve the established model with convergence guarantee, and especially global convergence for PALM is derived. The subproblems for two algorithms have fast solvers, and indeed, the solutions for the sparse coding and dictionary updating both have closed forms due to the orthogonality of learned dictionaries. Numerical experiments for phase retrieval using coded diffraction and ptychographic patterns are performed to show the efficiency and robustness of proposed methods, which, by preserving texture features, produce visually and quantitatively improved denoised images compared with other phase retrieval algorithms without regularization and local sparsity promoting algorithms.