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作者 Gao, Hao
書名 Numerical methods for forward and inverse problems in optical imaging
國際標準書號 9781109764956
book jacket
說明 260 p
附註 Source: Dissertation Abstracts International, Volume: 71-05, Section: B, page:
Adviser: Hongkai Zhao
Thesis (Ph.D.)--University of California, Irvine, 2010
The main objective of this work is to develop efficient and accurate numerical algorithms for mathematical problems in optical imaging: forward modeling and inverse problems. Radiative transfer equation (RTE) can be regarded as the gold standard of modeling in vivo photon migration, however an efficient solver of RTE is extremely computationally challenging. In this work we develop a fast multigrid solver for steady-state or frequency-domain RTE on 2D and 3D structured and unstructured meshes with vacuum or reflection boundary condition. The error estimate and convergence analysis of the algorithm is given. The subsequent effort is devoted to quantitatively improve the reconstruction from ill-posed problems, such as multilevel approach with L1+TV regularization for bioluminescence tomography, multilevel regularization for diffuse optical tomography, linear complex-source method for fluorescence tomography, and Bregman method for quantitative photoacoustic tomography. Most of the developed methods are general in the sense that they are not limited to a particular reconstruction problem and can be combined in a synergetic way
School code: 0030
Host Item Dissertation Abstracts International 71-05B
主題 Mathematics
Physics, Nuclear
Physics, Optics
Alt Author University of California, Irvine. Mathematics - Ph.D
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