9 October 1995 Multiresolution regularized least squares image reconstruction based on wavelet in optical tomography
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Abstract
In this paper, we present a wavelet based multigrid approach to solve the perturbation equation encountered in optical tomogrpahy. With this scheme, the unkown image, the data, as well as weight matrix are all represented by wavelet expansions, and thus yielding a multiresolution representation of the original perturbation equation in the wavelet domain. This transformed equation is then solved using multigrid scheme, by which an increasing portion of wavelet coefficients of the unknown image are solved in successive approximations. One can also quickly identify regions of interest from a coarse level reconstruction and restrict the reconstruction in the following fine resolutions to those regions. At each resolution level, a regularized least squares solution is obtained using a conjugate gradient descent method. Compared to a previously reported one grid algorithm, the multigrid method requires substantially shorter computation time under the same reconstruction quality criterion.
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Wenwu Zhu, Wenwu Zhu, Yao Wang, Yao Wang, Yining Deng, Yining Deng, Yuqi Yao, Yuqi Yao, Randall Locke Barbour, Randall Locke Barbour, } "Multiresolution regularized least squares image reconstruction based on wavelet in optical tomography", Proc. SPIE 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, (9 October 1995); doi: 10.1117/12.224161; https://doi.org/10.1117/12.224161
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