Adaptive Regularization for Three-Dimensional Optical Diffraction Tomography

Pham, Thanh-an; Soubies, Emmanuel; Ayoub, Ahmed B.; Unser, Michaël

doi:10.1109/isbi45749.2020.9098523

Cited by 8 publications

(3 citation statements)

References 28 publications

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“…The l 2 norm is a commonly chosen metric for measuring distance, along with other variants [13], [30]. R(•) is an optional regularization term to incorporate constraints, and is especially important when solving an under-determined problem [10], [31], [32]. The scalar term β is used to balance the strength of the regularization enforcement and the data fidelity term.…”

Section: B Inverse Modelmentioning

confidence: 99%

Distributed Reconstruction Algorithm for Electron Tomography with Multiple-scattering Samples

Ren,

Whittaker,

Ophus

et al. 2021

Preprint

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Three-dimensional electron tomography is used to understand the structure and properties of samples in chemistry, materials science, geoscience, and biology. With the recent development of high-resolution detectors and algorithms that can account for multiple-scattering events, thicker samples can be examined at finer resolution, resulting in larger reconstruction volumes than previously possible. In this work, we propose a distributed computing framework that reconstructs large volumes by decomposing a projected tilt-series into smaller datasets such that sub-volumes can be simultaneously reconstructed on separate compute nodes using a cluster. We demonstrate our method by reconstructing a multiple-scattering layered clay (montmorillonite) sample at high resolution from a large field-ofview tilt-series phase contrast transmission electron microscopty dataset.

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Section: B Inverse Modelmentioning

confidence: 99%

Distributed Reconstruction Algorithm for Electron Tomography with Multiple-scattering Samples

Ren,

Whittaker,

Ophus

et al. 2021

Preprint

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show abstract

“…There are several existing deep learning based approaches employing neural networks to directly reconstruct local data. They replace the established standard reconstruction methods, such as filtered back projection, and achieve good results, for instance with sparse angle tomography [19][20][21][22][23]. Synthetic data are used for training and validation.…”

Section: Introductionmentioning

confidence: 99%

Dense U-Net for Limited Angle Tomography of Sound Pressure Fields

et al. 2021

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Tomographic reconstruction allows for the recovery of 3D information from 2D projection data. This commonly requires a full angular scan of the specimen. Angular restrictions that exist, especially in technical processes, result in reconstruction artifacts and unknown systematic measurement errors. We investigate the use of neural networks for extrapolating the missing projection data from holographic sound pressure measurements. A bias flow liner was studied for active sound dampening in aviation. We employed a dense U-Net trained on synthetic data and compared reconstructions of simulated and measured data with and without extrapolation. In both cases, the neural network based approach decreases the mean and maximum measurement deviations by a factor of two. These findings can enable quantitative measurements in other applications suffering from limited angular access as well.

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“…For the regularization term, we choose the isotropic total variation (TV) [42] but one can adopt other regularizations such as the Hessian Schatten-norm [43], plug-and-play prior [44], [45], or tailored regularization [46]. The accelerated forward-backward splitting (FBS) [47], [48] is adopted here to solve (24).…”

mentioning

confidence: 99%

Diffraction Tomography with Helmholtz Equation: Efficient and Robust Multigrid-Based Solver

Hong

Pham

Treister

et al. 2021

Preprint

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Diffraction tomography is a noninvasive technique that estimates the refractive indices of unknown objects and involves an inverse-scattering problem governed by the wave equation. Recent works have shown the benefit of nonlinear models of wave propagation that account for multiple scattering and reflections. In particular, the Lippmann-Schwinger (LiS) model defines an inverse problem to simulate the wave propagation. Although accurate, this model is hard to solve when the samples are highly contrasted or have a large physical size. In this work, we introduce instead a Helmholtz-based nonlinear model for inverse scattering. To solve the corresponding inverse problem, we propose a robust and efficient multigrid-based solver. Moreover, we show that our method is a suitable alternative to the LiS model, especially for strongly scattering objects. Numerical experiments on simulated and real data demonstrate the effectiveness of the Helmholtz model, as well as the efficiency of the proposed multigrid method.

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Adaptive Regularization for Three-Dimensional Optical Diffraction Tomography

Cited by 8 publications

References 28 publications

Distributed Reconstruction Algorithm for Electron Tomography with Multiple-scattering Samples

Distributed Reconstruction Algorithm for Electron Tomography with Multiple-scattering Samples

Dense U-Net for Limited Angle Tomography of Sound Pressure Fields

Diffraction Tomography with Helmholtz Equation: Efficient and Robust Multigrid-Based Solver

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