A computable fourier condition generating alias-free sampling lattices
IEEE Transactions on Signal Processing
Tomographic reconstruction of diffusion propagators from DW-MRI using optimal sampling lattices
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Symmetric box-splines on the A*n lattice
Journal of Approximation Theory
IEEE Transactions on Signal Processing
Symmetric box-splines on root lattices
Journal of Computational and Applied Mathematics
GPU isosurface raycasting of FCC datasets
Graphical Models
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The generalization of the sampling theorem to multidimensional signals is considered, with or without bandwidth constraints. The signal is modeled as a stationary random process and sampled on a lattice. Exact expressions for the mean-square error of the best linear interpolator are given in the frequency domain. Moreover, asymptotic expansions are derived for the average mean-square error when the sampling rate tends to zero and infinity, respectively. This makes it possible to determine the optimal lattices for sampling. In the low-rate sampling case, or equivalently for rough processes, the optimal lattice is the one which solves the packing problem, whereas in the high-rate sampling case, or equivalently for smooth processes, the optimal lattice is the one which solves the dual packing problem. In addition, the best linear interpolation is compared with ideal low-pass filtering (cardinal interpolation).