Optical tomography with the discontinuous Galerkin formulation of the radiative transfer equation in frequency domain

2012 ◽  
Vol 113 (10) ◽  
pp. 805-814 ◽  
Author(s):  
O. Balima ◽  
Y. Favennec ◽  
J. Boulanger ◽  
A. Charette
Keyword(s):  
Radiative Transfer ◽  
Frequency Domain ◽  
Discontinuous Galerkin ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Optical Tomography ◽  
Galerkin Formulation

scholarly journals Image Reconstruction for Diffuse Optical Tomography Based on Radiative Transfer Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-23 ◽  
Author(s):  
Bo Bi ◽  
Bo Han ◽  
Weimin Han ◽  
Jinping Tang ◽  
Li Li
Keyword(s):  
Image Reconstruction ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Optical Tomography ◽  
Measurement Data ◽  
Diffuse Optical Tomography ◽  
Forward Model ◽  
Sparsity Regularization ◽  
Reconstruction Methods

Diffuse optical tomography is a novel molecular imaging technology for small animal studies. Most known reconstruction methods use the diffusion equation (DA) as forward model, although the validation of DA breaks down in certain situations. In this work, we use the radiative transfer equation as forward model which provides an accurate description of the light propagation within biological media and investigate the potential of sparsity constraints in solving the diffuse optical tomography inverse problem. The feasibility of the sparsity reconstruction approach is evaluated by boundary angular-averaged measurement data and internal angular-averaged measurement data. Simulation results demonstrate that in most of the test cases the reconstructions with sparsity regularization are both qualitatively and quantitatively more reliable than those with standardL2regularization. Results also show the competitive performance of the split Bregman algorithm for the DOT image reconstruction with sparsity regularization compared with other existingL1algorithms.

scholarly journals Mixed Total Variation and L1 Regularization Method for Optical Tomography Based on Radiative Transfer Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Jinping Tang ◽  
Bo Han ◽  
Weimin Han ◽  
Bo Bi ◽  
Li Li
Keyword(s):  
Radiative Transfer ◽  
Total Variation ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Imaging Modality ◽  
Optical Tomography ◽  
Identification Problem ◽  
Split Bregman ◽  
Computation Efficiency ◽  
Reconstruction Methods

Optical tomography is an emerging and important molecular imaging modality. The aim of optical tomography is to reconstruct optical properties of human tissues. In this paper, we focus on reconstructing the absorption coefficient based on the radiative transfer equation (RTE). It is an ill-posed parameter identification problem. Regularization methods have been broadly applied to reconstruct the optical coefficients, such as the total variation (TV) regularization and the L1 regularization. In order to better reconstruct the piecewise constant and sparse coefficient distributions, TV and L1 norms are combined as the regularization. The forward problem is discretized with the discontinuous Galerkin method on the spatial space and the finite element method on the angular space. The minimization problem is solved by a Jacobian-based Levenberg-Marquardt type method which is equipped with a split Bregman algorithms for the L1 regularization. We use the adjoint method to compute the Jacobian matrix which dramatically improves the computation efficiency. By comparing with the other imaging reconstruction methods based on TV and L1 regularizations, the simulation results show the validity and efficiency of the proposed method.

Propagation of Ultra-Short-Pulse Radiation in Participating Media: A Laguerre-Galerkin Solution

2007 ◽  
Author(s):  
Tuba Okutucu ◽  
Yaman Yener
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Transfer Problem ◽  
Short Pulse ◽  
Optical Tomography ◽  
Time Derivative ◽  
Product Analysis ◽  
Participating Media ◽  
Radiative Transfer Problem

Transient analysis of the radiative transfer problem in participating media has become essential due to the recent applications involving extremely small time scales. In classical radiation problems, the time derivative term in the radiative transfer equation has a negligible order of magnitude compared to the others. Lasers of pico- to femtosecond pulse durations are now being used to investigate the properties of scattering and absorbing media in such applications as, optical tomography, combustion product analysis, and remote sensing. For such applications, the time derivative in the radiative transfer equation can no longer be neglected. Numerous approaches such as, integral formulation, direct numerical approach, discrete ordinates method, Monte Carlo simulations, and Galerkin technique have been introduced for the solution of transient radiative transfer problems in participating media. In the present work, Laguerre-Galerkin solutions for both rectangular and Gaussian incident pulse profiles are presented.

Utilizing the Radiative Transfer Equation in Optical Tomography

PIERS Online ◽  
2008 ◽  
Vol 4 (6) ◽  
pp. 655-660 ◽  
Author(s):  
Tanja Tarvainen ◽  
Marko Vauhkonen ◽  
Ville Kolehmainen ◽  
Jari P. Kaipio ◽  
Simon R. Arridge
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Optical Tomography
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