Efficient Inversion of Multiple-Scattering Model for Optical Diffraction Tomography
This work addresses the computational bottleneck of nonlinear multiple-scattering models for high-contrast samples in optical diffraction tomography, offering a more efficient reconstruction method.
The authors derived an explicit Jacobian formula for the nonlinear Lippmann-Schwinger model in optical diffraction tomography, enabling efficient gradient evaluation and solving the inverse problem with sparsity constraints, improving reconstruction quality for samples with high refractive-index contrasts.
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.