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.
Highlights
Optical diffraction tomography (ODT) was introduced in [1] by E
It proceeds by solving an inverse scattering problem, where the scattering phenomenon is governed by the wave equation
It is worth noting that the scattering model, along with its associated inverse problem, is generic and not limited to optical diffraction tomography
Summary
Optical diffraction tomography (ODT) was introduced in [1] by E. It is a microscopic technique that retrieves the distribution of refractive indices in biological samples out of holographic measurements of the scattered complex field produced when the sample is illuminated by an incident wave This method is of particular interest in biology because, contrarily to fluorescence imaging, it does not require any staining of the sample [2]. It is worth noting that the scattering model, along with its associated inverse problem, is generic and not limited to optical diffraction tomography. It is encountered in many other fields such as acoustics, microwave imaging, or radar applications [8]
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