Anisotropic multidimensional savitzky Golay kernels for smoothing, differentiation and reconstruction
File(s)
Published version
Author(s)
Thornley, David
Type
Report
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.
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.
Date Issued
2006-01-01
Citation
Departmental Technical Report: 06/8, 2006, pp.1-12
Publisher
Department of Computing, Imperial College London
Start Page
1
End Page
12
Journal / Book Title
Departmental Technical Report: 06/8
Copyright Statement
© 2006 The Author(s). This report is available open access under a CC-BY-NC-ND (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Publication Status
Published
Article Number
06/8