Dictionary Learning Phase Retrieval from Noisy Diffraction Patterns.

Joshin Krishnan,José Bioucas-Dias,Vladimir Katkovnik

doi:10.3390/s18114006

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.

Highlights

We propose a novel idea, based on sparse modeling of the object wavefront using complex-valued dictionaries, which we term as Dictionary Learning Phase Retrieval (DLPR), to address the ProblemPhase Retrieval (PR) problem discussed in Equation (3)
We present a series of strong empirical evidence, using semi-real and synthetic data, to illustrate the effectiveness of DLPR
The details regarding the experimental setup are described below: Optical setup: We restrict our optical setup to the lensless imaging scenario, as illustrated in Figure 2, which uses coded diffraction patterns for optical imaging

Summary

Introduction

PR is a crucial step in most diffraction- or scattering-based physical measurement systems. In such systems, the signals being used, namely a coherent photon flux, laser, X-ray, or any other variants of the electromagnetic radiation, are diffracted through an object under examination. The signals being used, namely a coherent photon flux, laser, X-ray, or any other variants of the electromagnetic radiation, are diffracted through an object under examination These diffracted signals encode the structural information of the object such as thickness, density, or refractive index, and are detected using a suitable sensor. Since the detectors sense the diffracted signals by converting the photon flux to electrons, the information related to the phase of the signal is not recorded This is a major limitation as important structural information of the object are often coded mainly in the phase. PR aims at estimating the unknown phase from the intensity measurements

Methods

Results

Conclusion