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Anisotropic Multidimensional Savitzky Golay kernels for Smoothing, Differentiation and Reconstruction

David Thornley

Department of Computing Technical Report 2006/8
June, 2006
Department of Computing, Imperial College London

The archetypal Savitzky-Golay convolutional filter matches a polynomial to even-spaced data and uses this to measure smoothed derivatives. We synthesize a scheme in which heterogeneous, anisotropic linearly separable basis functions combine to provide a general smoothing, derivative measurement and reconsruction function for point coulds in multiple dimensions using a linear operator in the form of a convolution kernel. We use a matrix pseudo inverse for examples, but note that QR factorization is more stable when free weighting is introduced.

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