Efficient inversion of multiple-scattering model for optical diffraction tomography
Résumé
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.