Strobl22

Applied Harmonic Analysis and Friends

June 19th - 25th 2022

Strobl, AUSTRIA

"Samplets: Construction and scattered data compression"

Multerer, Michael

We introduce the concept of samplets by transferring the construction of Tausch-White wavelets to scattered data. This way, we obtain a multiresolution analysis tailored to discrete data which directly enables data compression, feature detection and adaptivity. The cost for constructing the samplet basis and for the fast samplet transform, respectively, is O(N), where N is the number of data points. Samplets with vanishing moments can be used to compress kernel matrices, resulting in sparse matrices with only O(Nlog N) remaining entries. We provide estimates for the compression error and present an algorithm that computes the compressed kernel matrix with computational cost O(Nlog N). The accuracy of the approximation is controlled by the number of vanishing moments. Numerical studies are presented to benchmark the approach.

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