Polyharmonic Smoothing Splines for Multi-Dimensional Signals with 1/W - Like Spectra
SWISS FEDERAL INST OF TECHNOLOGY LAUSANNE (SWITZERLAND)
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Motivated by the fractal-like behavior of natural images, we propose a new smoothing technique that uses a regularization functional which is a fractional iterate of the Laplacian. This type of functional has previously been introduced by Duchon in the context of radial basis functions RBFs for the approximation of non-uniform data. Here, we introduce a new solution to Duchons smoothing problem in multiple dimensions using non-separable fractional polyharmonic B-splines. The smoothing is performed in the Fourier domain by filtering, thereby making the algorithm fast enough for most multi-dimensional real-time applications.
- Numerical Mathematics
- Theoretical Mathematics