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Title: Scattered data reconstruction by regularization in B-spline and associated wavelet spaces
Authors: XU YUHONG
Keywords: scattered data reconstruction; regularized least square; principal shift invariant spaces; B-splines; wavelets
Issue Date: 9-Mar-2009
Citation: XU YUHONG (2009-03-09). Scattered data reconstruction by regularization in B-spline and associated wavelet spaces. ScholarBank@NUS Repository.
Abstract: The problem of fitting a nice curve or surface to scattered, possibly noisy, data arises in many applications in science and engineering. This work studies the role of principal shift-invariant(PSI) space, as well as associated wavelet space, as an approximation space for the data fitting problem. We formulate the problem in PSI spaces for both smooth and non-smooth reconstruction. In either case, we provide error analysis on the theoretical side and develop efficient algorithm for its practical use. For smooth reconstruction, numerical experiments have demonstrated that the performance of our method is very much equivalent to that of the classical smoothing spline method; however, our method offers advantages in terms of numerical efficiency. For non-smooth reconstruction, our method is particularly suitable for fitting data that contains discontinuities or edges.
Appears in Collections:Ph.D Theses (Open)

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