Reconstruction from non-uniform samples: A direct,variational approach in shift-invariant spaces |
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Authors: | Laurent Condat |
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Affiliation: | GIPSA-lab, Grenoble, France |
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Abstract: | We propose a new approach for signal reconstruction from non-uniform samples, without any constraint on their locations. We look for a function that minimizes a classical regularized least-squares criterion, but with the additional constraint that the solution lies in a chosen linear shift-invariant space—typically, a spline space. In comparison with a pure variational treatment involving radial basis functions, our approach is resolution dependent; an important feature for many applications. Moreover, the solution can be computed exactly by a fast non-iterative algorithm, that exploits at best the particular structure of the problem. |
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