Samplet basis pursuit: Multiresolution scattered data approximation with sparsity constraints

arXiv:2306.10180v3 Announce Type: replace-cross
Abstract: We consider scattered data approximation in samplet coordinates with $\ell_1$-regularization. The application of an $\ell_1$-regularization term enforces sparsity of the coefficients with respect to the samplet basis. Samplets are wavelet-type signed measures, which are tailored to scattered data. They provide similar properties as wavelets in terms of localization, multiresolution analysis, and data compression. By using the Riesz isometry, we embed samplets into reproducing kernel Hilbert spaces and discuss the properties of the resulting functions. We …

abstract application approximation arxiv constraints cs.lg cs.na data math.na regularization sparsity stat.ml type wavelet