Image reconstruction from scattered Radon data by weighted positive definite kernel functions

Algebraic Medical Image Reconstruction from Scattered Radon Data by Positive Definite Kernels

Computerized tomography requires customized numerical methods for the approximation of a bivariate target function f from a finite set of discrete Radon data, each of whose data samples represents one line integral of f . In standard reconstruction methods, specific assumptions concerning the distribution of the sample lines are usually made, e.g. by parallel line geometry. In relevant applicat...

Armin Iske * Scattered Data Approximation by Positive Definite Kernel Functions

Kernel functions are suitable tools for scattered data interpolation and approximation. We first review basic features of kernel-based multivariate interpolation, before we turn to the construction and the characterization of positive definite kernels and their associated reproducing kernel Hilbert spaces. The optimality of the resulting kernel-based interpolation scheme is shown. Moreover, we ...

Kernel-based Image Reconstruction from Scattered Radon Data

Computerized tomography requires suitable numerical methods for the approximation of a bivariate function f from a finite set of discrete Radon data, each of whose data samples represents one line integral of f . In standard reconstruction methods, specific assumptions concerning the geometry of the Radon lines are usually made. In relevant applications of image reconstruction, however, such as...

Image Reconstruction from Incomplete Data

Reconstruction of Multivariate Functions from Scattered Data