A Fast-Forward Solver of Radiative Transfer Equation

Gao, Hao; Zhao, Hongkai

doi:10.1080/00411450903187722

Cited by 103 publications

(109 citation statements)

References 14 publications

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“…The forward problem solving is used to calculate the boundary data of prediction model and/or simulation object when the optical properties of the medium and the amount of input light are given. In this paper, we used DE and RTE to describe the light propagation in biological material, which then are used as forward problem solving [1,5,16]. While inverse problem solving is an algorithm to predict an optical coefficient distribution inside a medium by comparing the boundary data of the "object" and those of prediction model.…”

Section: Principle Of Optical Tomography (Ot)mentioning

confidence: 99%

“…Several researchers have been developing the reconstruction methods to reduce the computation time in optical tomography (OT) with the regularization parameter selection method [7], a fast-forward solver of radiative transfer equation (RTE) [5], non-iterative algorithm [8], hardware development [14], and signal processing approach [1,13,15]. This paper focused on the study of non-iterative image reconstruction based on diffusion equation (DE) and RTE.…”

Section: Introductionmentioning

confidence: 99%

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Non-iterative model based image reconstruction of diffuse optical tomography based on DE and RTE in quality control of agricultural product studies

Nadhira

Juliastuti

Garnadi

et al. 2018

J. Phys.: Conf. Ser.

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Abstract. In a previous study, we developed the non-iterative image reconstruction based on diffusion equation. Within this research, we applied the same non-iterative algorithm scheme using radiative transfer equation. Basically, the non-iterative image reconstruction is a development of model based image reconstruction that implemented truncated singular value decomposition and L-curve analysis to solve the ill-posed problem. This algorithm reduces the computation time to reconstruct the cross-sectional area. As part of continuous development on agricultural application, optical tomography based quality control is offered. An experiment was conducted on potato to evaluate these two non-iterative algorithms. The object was illuminated by the near infrared source from 8 positions on the object boundary. In this experiment, we vary the position and the amount of epoxy on the object then we analyze the residual value between measurement and reconstructed boundary data. The reconstructions were performed in continuous-wave domain. Furthermore, we compared the residual value from diffuse optical tomography using diffusion equation and radiative transfer equation. The result of this study indicates that these algorithms are promising to detect the presence of epoxy on potato which is useful for quality control of agricultural products.

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Section: Principle Of Optical Tomography (Ot)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-iterative model based image reconstruction of diffuse optical tomography based on DE and RTE in quality control of agricultural product studies

Nadhira

Juliastuti

Garnadi

et al. 2018

J. Phys.: Conf. Ser.

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“…The fast sweeping method is an efficient iterative method for solving (1.1). It has been developed and used successfully for various hyperbolic problems (e.g., see [6,7,14,15,17,20,23,26,28,30,34,35,40,[43][44][45] and references therein for development, and [3,18,21,24,25,27,29,31] and references therein for applications to different problems). The key ingredients for the success of the FSM are the following:…”

Section: 4)mentioning

confidence: 99%

Convergence analysis of the fast sweeping method for static convex Hamilton–Jacobi equations

Luo

Zhao

2016

Res Math Sci

Self Cite

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In this work, we study the convergence of an efficient iterative method, the fast sweeping method (FSM), for numerically solving static convex Hamilton-Jacobi equations. First, we show the convergence of the FSM on arbitrary meshes. Then we illustrate that the combination of a contraction property of monotone upwind schemes with proper orderings can provide fast convergence for iterative methods. We show that this mechanism produces different behavior from that for elliptic problems as the mesh is refined. An equivalence between the local solver of the FSM and the Hopf formula under linear approximation is also proved. Numerical examples are presented to verify our analysis. Keywords: Fast sweeping method, Hamilton-Jacobi equation, Contraction property, Iterative method, Fast convergence, Error estimate Mathematics Subject Classification: 35L02, 65N06, 65N12 BackgroundEfficient and robust iterative methods are highly desirable for solving a variety of static hyperbolic partial differential equations (PDEs) numerically. The most important property for hyperbolic problems is that the information propagates along the characteristics. For linear hyperbolic problems, the characteristics are known á priori and do not intersect. For nonlinear hyperbolic problems, the characteristics are not known á priori and may intersect. Consequently the information that propagates along different characteristics has to compromise in certain ways when the characteristics intersect to render the desired weak solution. When discretizing hyperbolic PDEs, monotone upwind schemes are an important class of schemes that use stencils following the characteristics in the direction from which the information comes (e.g., see [39]). How to design an effective iterative method for hyperbolic problems also needs to fully utilize the above properties. We use the fast sweeping method (FSM) [43] as an example to show that the combination of monotone upwind schemes with Gauss-Seidel iterations and proper orderings can provide fast convergence. The convergence mechanism is different from that of iterative methods for elliptic problems, where relaxation is the underlying mechanism for convergence and the key point is how to deal with long-range interactions through short-range interactions

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“…Different forms of the RTE have been used in DOT. The frequency-domain (FD) approach [15,16,17,18,19,20,21] is the most widely employed, since it is a good trade-off between time-domain [22,23,24] and steady-state domain [25]. Moreover, the FD approach provides additional information (phase shift) compared to the steady-state modality and avoids the technical limitations of the experimental setup for time-domain often expensive.…”

Section: Introductionmentioning

confidence: 99%

Optical properties reconstruction using the adjoint method based on the radiative transfer equation

Addoum

Farges

Asllanaj

2018

Journal of Quantitative Spectroscopy and Radiative Transfer

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A Fast-Forward Solver of Radiative Transfer Equation

Cited by 103 publications

References 14 publications

Non-iterative model based image reconstruction of diffuse optical tomography based on DE and RTE in quality control of agricultural product studies

Non-iterative model based image reconstruction of diffuse optical tomography based on DE and RTE in quality control of agricultural product studies

Convergence analysis of the fast sweeping method for static convex Hamilton–Jacobi equations

Optical properties reconstruction using the adjoint method based on the radiative transfer equation

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