Reproducing kernels of generalized Sobolev spaces via a Green function approach with distributional operators

GE Fasshauer, Q Ye - Numerische Mathematik, 2011 - Springer
In this paper we introduce a generalized Sobolev space by defining a semi-inner product
formulated in terms of a vector distributional operator P consisting of finitely or countably …

Approximation of stochastic partial differential equations by a kernel-based collocation method

I Cialenco, GE Fasshauer, Q Ye - International Journal of …, 2012 - Taylor & Francis
In this paper we present the theoretical framework needed to justify the use of a kernel-
based collocation method (meshfree approximation method) to estimate the solution of high …

Kernel bundle diffeomorphic image registration using stationary velocity fields and wendland basis functions

A Pai, S Sommer, L Sørensen… - IEEE transactions on …, 2015 - ieeexplore.ieee.org
In this paper, we propose a multi-scale, multi-kernel shape, compactly supported kernel
bundle framework for stationary velocity field-based image registration (Wendland kernel …

Green's functions: Taking another look at kernel approximation, radial basis functions, and splines

GE Fasshauer - Approximation Theory XIII: San Antonio 2010, 2011 - Springer
The theories for radial basis functions (RBFs) as well as piecewise polynomial splines have
reached a stage of relative maturity as is demonstrated by the recent publication of a number …

Learning with boundary conditions

G Gnecco, M Gori, M Sanguineti - Neural computation, 2013 - ieeexplore.ieee.org
Kernel machines traditionally arise from an elegant formulation based on measuring the
smoothness of the admissible solutions by the norm in the reproducing kernel Hilbert space …

Combining the boundary shift integral and tensor-based morphometry for brain atrophy estimation

M Michalkiewicz, A Pai, KK Leung… - Medical Imaging …, 2016 - spiedigitallibrary.org
Brain atrophy from structural magnetic resonance images (MRIs) is widely used as an
imaging surrogate marker for Alzheimers disease. Their utility has been limited due to the …