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Browsing by Author "Han, Weimin"

Now showing 1 - 2 of 2
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    A General Total Variation Minimization Theorem for Compressed Sensing Based Interior Tomography
    Han, Weimin; Yu, Hengyong; Wang, Ge (Hindawi, 2009-11-17)
    Recently, in the compressed sensing framework we found that a two-dimensional interior region-of-interest (ROI) can be exactly reconstructed via the total variation minimization if the ROI is piecewise constant (Yu and Wang, 2009). Here we present a general theorem charactering a minimization property for a piecewise constant function defined on a domain in any dimension. Our major mathematical tool to prove this result is functional analysis without involving the Dirac delta function, which was heuristically used by Yu and Wang (2009).
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    Mathematical Study and Numerical Simulation of Multispectral Bioluminescence Tomography
    Han, Weimin; Cong, Wenxiang; Wang, Ge (Hindawi, 2006-12-12)
    Multispectral bioluminescence tomography (BLT) attracts increasinglymore attention in the area of optical molecular imaging. In this paper, we analyzethe properties of the solutions to the regularized and discretized multispectralBLT problems. First, we show the solution existence, uniqueness, and itscontinuous dependence on the data. Then, we introduce stable numerical schemes andderive error estimates for numerical solutions. We report some numerical resultsto illustrate the performance of the numerical methods on the quality of multispectralBLT reconstruction.