Multigrid image reconstruction from arbitrarily spaced samples

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 computationallyefficient multiresolution-multigrid scheme for solving the system. We demonstrate the method with image reconstruction from contour points.

• Type: Conference
• Year: 2002
• Where: ICIP
• Authors: Michael Sühling, Michael Unser, Muthuvel Arigovindan, Patrick R. Hunziker
• Keywords: B-splines Basis Functions, Grid Points, ICIP 2002, Image Processing, Signal Reconstruction Method