Anisotropic multidimensional savitzky Golay kernels for smoothing, differentiation and reconstruction

Abstract

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.