Research on high-order approximation of radiative transfer equation for image reconstruction

2011 ◽  
Author(s):  
Wenjuan Ma ◽  
Feng Gao ◽  
Linhui Wu ◽  
Xi Yi ◽  
Pingping Zhu ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Order Approximation ◽  
High Order ◽  
High Order Approximation

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.

The SKN Approximation for Solving Radiative Transfer Problems in Absorbing, Emitting, and Isotropically Scattering Plane-Parallel Medium: Part 1

2002 ◽  
Vol 124 (4) ◽  
pp. 674-684 ◽  
Author(s):  
Zekeriya Altac¸
Keyword(s):  
Integral Equation ◽  
Radiative Transfer ◽  
Differential Equations ◽  
Order Approximation ◽  
High Order ◽  
High Order Approximation ◽  
One Dimensional ◽  
Second Order Differential Equations ◽  
Plane Parallel ◽  
Transfer Problems

A high order approximation, the SKN method—a mnemonic for synthetic kernel—is proposed for solving radiative transfer problems in participating medium. The method relies on approximating the integral transfer kernel by a sum of exponential kernels. The radiative integral equation is then reducible to a set of coupled second-order differential equations. The method is tested for one-dimensional plane-parallel participating medium. Three quadrature sets are proposed for the method, and the convergence of the method with the proposed sets is explored. The SKN solutions are compared with the exact, PN, and SN solutions. The SK1 and SK2 approximations using quadrature Set-2 possess the capability of solving radiative transfer problems in optically thin systems.

scholarly journals A High-Order-Accurate GPU-Based Radiative Transfer Equation Solver for Combustion and Propulsion Applications

2013 ◽  
Vol 63 (6) ◽  
pp. 457-484 ◽  
Author(s):  
Xing He ◽  
Euntaek Lee ◽  
Lucas Wilcox ◽  
Ramakanth Munipalli ◽  
Laurent Pilon
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
High Order
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