Efficient Inversion of Multiple-Scattering Model for Optical Diffraction Tomography

TL;DR

This paper introduces an efficient method for solving the inverse scattering problem in optical diffraction tomography by deriving an explicit Jacobian formula for the nonlinear model, enabling improved reconstruction of complex samples.

Contribution

The paper presents a novel explicit Jacobian formula for the nonlinear Lippmann-Schwinger model, reducing computational complexity in optical diffraction tomography reconstructions.

Findings

Enhanced reconstruction quality for complex samples.

Reduced computational complexity and memory usage.

Effective application of sparsity constraints in inverse problem solving.

Abstract

Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their applicability to thin samples with low refractive-index contrasts. More recent works have shown the benefit of adopting nonlinear models. They account for multiple scattering and reflections, improving the quality of reconstruction. To reduce the complexity and memory requirements of these methods, we derive an explicit formula for the Jacobian matrix of the nonlinear Lippmann-Schwinger model which lends itself to an efficient evaluation of the gradient of the data- fidelity term. This allows us to deploy efficient methods to solve the corresponding inverse problem subject to sparsity constraints.