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Multigrid image reconstruction from arbitrarily spaced samples

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4 Author(s)
Arigovindan, M. ; Biomed. Imaging Group, Swiss Fed. Inst. of Technol., Lausanne, Switzerland ; Suhling, M. ; Hunziker, P. ; Unser, M.

We propose a novel multiresolution-multigrid based signal reconstruction method from arbitrarily spaced samples. The signal is reconstructed on a uniform grid using B-splines basis functions. The computation of spline weights is formulated as a variational problem. Specifically, we minimize a cost that is a weighted sum of two terms: (i) the sum of squared errors at the specified points; (ii) a quadratic functional that penalizes the lack of smoothness. The problem is equivalent to solving a very large system of linear equations, with the dimension equal to the number of grid points. We develop a computationally efficient multiresolution-multigrid scheme for solving the system. We demonstrate the method with image reconstruction from contour points.

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Image Processing. 2002. Proceedings. 2002 International Conference on  (Volume:3 )

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