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2011

Reconstruction of Large, Irregularly Sampled Multidimensional Images. A Tensor-Based Approach

8 years 5 months ago
Reconstruction of Large, Irregularly Sampled Multidimensional Images. A Tensor-Based Approach
Abstract—Many practical applications require the reconstruction of images from irregularly sampled data. The spline formalism offers an attractive framework for solving this problem; the currently available methods, however, are hard to deploy for large-scale interpolation problems in dimensions greater than two (3-D, 3-D+time) because of an exponential increase of their computational cost (curse of dimensionality). Here, we revisit the standard regularized least-squares formulation of the interpolation problem, and propose to perform the reconstruction in a uniform tensor-product B-spline basis as an alternative to the classical solution involving radial basis functions. Our analysis reveals that the underlying multilinear system of equations admits a tensor decomposition with an extreme sparsity of its one dimensional components. We exploit this property for implementing a parallel, memory-efficient system solver. We show that the computational complexity of the proposed algorithm...
Oleksii Vyacheslav Morozov, Michael Unser, Patrick
Added 15 May 2011
Updated 15 May 2011
Type Journal
Year 2011
Where TMI
Authors Oleksii Vyacheslav Morozov, Michael Unser, Patrick R. Hunziker
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