Accelerated Image Reconstruction for Nonlinear Diffractive Imaging

TL;DR

This paper introduces CISOR, a novel nonlinear diffractive imaging reconstruction method using a nonconvex optimization approach with TV regularization, demonstrating improved efficiency and convergence over existing methods in 2D and 3D.

Contribution

The paper presents CISOR, a new nonlinear image reconstruction method with a specialized FISTA variant, offering fast, memory-efficient solutions with proven convergence for diffractive imaging.

Findings

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

CISOR is effective on experimentally measured 2D and 3D data.

The proposed FISTA variant converges reliably for nonconvex problems.

Abstract

The problem of reconstructing an object from the measurements of the light it scatters is common in numerous imaging applications. While the most popular formulations of the problem are based on linearizing the object-light relationship, there is an increased interest in considering nonlinear formulations that can account for multiple light scattering. In this paper, we propose an image reconstruction method, called CISOR, for nonlinear diffractive imaging, based on a nonconvex optimization formulation with total variation (TV) regularization. The nonconvex solver used in CISOR is our new variant of fast iterative shrinkage/thresholding algorithm (FISTA). We provide fast and memory-efficient implementation of the new FISTA variant and prove that it reliably converges for our nonconvex optimization problem. In addition, we systematically compare our method with other state-of-the-art methods on simulated as well as experimentally measured data in both 2D and 3D settings.