Shape-Driven Interpolation With Discontinuous Kernels: Error Analysis, Edge Extraction, and Applications in Magnetic Particle Imaging

DOI10.1137/19M1248777zbMath1444.65006arXiv1903.03095MaRDI QIDQ5107790

No author found.

Publication date: 28 April 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.03095

zbMATH Keywords

Gibbs phenomenonradial basis function (RBF) interpolationmagnetic particle imaging (MPI)meshless approximation of discontinuous functionssegmentation and classification with kernel machinesvariably scaled discontinuous kernels (VSDKs)

Mathematics Subject Classification ID

Numerical interpolation (65D05) Interpolation in approximation theory (41A05) Rate of convergence, degree of approximation (41A25) Numerical radial basis function approximation (65D12)

Related Items

Convergence Results in Image Interpolation With the Continuous SSIM ⋮ Polynomial mapped bases: theory and applications ⋮ A class of \(C^2\) quasi-interpolating splines free of Gibbs phenomenon ⋮ Padua points and fake nodes for polynomial approximation: old, new and open problems ⋮ Multivariate approximation at fake nodes ⋮ Escaping Unknown Discontinuous Regions in Blackbox Optimization ⋮ Jumping with variably scaled discontinuous kernels (VSDKs) ⋮ A regularization-correction approach for adapting subdivision schemes to the presence of discontinuities ⋮ Moving least squares approximation using variably scaled discontinuous weight function ⋮ A modified kernel-based collocation method for interface boundary value problems ⋮ Approximation properties of mixed sampling-Kantorovich operators ⋮ The extension of Rippa's algorithm beyond LOOCV ⋮ On the reconstruction of discontinuous functions using multiquadric RBF-WENO local interpolation techniques ⋮ Data-driven extrapolation via feature augmentation based on variably scaled thin plate splines ⋮ Feature augmentation for the inversion of the Fourier transform with limited data ⋮ Learning via variably scaled kernels ⋮ Stable discontinuous mapped bases: the Gibbs-Runge-avoiding stable polynomial approximation (GRASPA) method ⋮ Non-oscillatory butterfly-type interpolation on triangular meshes ⋮ Mapped polynomials and discontinuous kernels for Runge and Gibbs phenomena

Uses Software

• Matlab
• GaussQR

Cites Work

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