Scattered data reconstruction by regularization in B-spline and associated wavelet spaces
Journal of Approximation Theory
Exemplar-Based Interpolation of Sparsely Sampled Images
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Confidence measure for temporal registration of recurrent non-uniform samples
PReMI'07 Proceedings of the 2nd international conference on Pattern recognition and machine intelligence
Invariant image reconstruction from irregular samples and hexagonal grid splines
Image and Vision Computing
A generic variational approach for demosaicking from an arbitrary color filter array
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
On the search of optimal reconstruction resolution
Pattern Recognition Letters
Enhancing the reconstruction from non-uniform point sets using persistence information
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Proceedings of the Second International Conference on Computational Science, Engineering and Information Technology
On visualization and reconstruction from non-uniform point sets using B-splines
EuroVis'09 Proceedings of the 11th Eurographics / IEEE - VGTC conference on Visualization
Reconstruction from non-uniform samples: A direct, variational approach in shift-invariant spaces
Digital Signal Processing
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We propose a novel method for image reconstruction from nonuniform samples with no constraints on their locations. We adopt a variational approach where the reconstruction is formulated as the minimizer of a cost that is a weighted sum of two terms: 1) the sum of squared errors at the specified points and 2) a quadratic functional that penalizes the lack of smoothness. We search for a solution that is a uniform spline and show how it can be determined by solving a large, sparse system of linear equations. We interpret the solution of our approach as an approximation of the analytical solution that involves radial basis functions and demonstrate the computational advantages of our approach. Using the two-scale relation for B-splines, we derive an algebraic relation that links together the linear systems of equations specifying reconstructions at different levels of resolution. We use this relation to develop a fast multigrid algorithm. We demonstrate the effectiveness of our approach on some image reconstruction examples.