說明 
260 p 
附註 
Source: Dissertation Abstracts International, Volume: 7105, 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 steadystate or frequencydomain 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 illposed problems, such as multilevel approach with L1+TV regularization for bioluminescence tomography, multilevel regularization for diffuse optical tomography, linear complexsource 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 7105B

主題 
Mathematics


Physics, Nuclear


Physics, Optics


0405


0610


0752

Alt Author 
University of California, Irvine. Mathematics  Ph.D

