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...

• Type: Journal
• Year: 2011
• Where: TMI
• Authors: Oleksii Vyacheslav Morozov, Michael Unser, Patrick R. Hunziker
• Keywords: Interpolation Problem, Large-scale Interpolation Problems, Tensor-product B-spline Basis, TMI 2011