Kernel-based Image Reconstruction from Scattered Radon Data

Abstract

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 assumptions are often too restrictive. In this case, one would rather prefer to work with reconstruction methods allowing for arbitrary distributions of scattered Radon lines.This paper proposes a novel image reconstruction method for scattered Radon data, which combines kernel-based scattered data approximation with a well-adapted regularization of the Radon transform. This results in a very flexible numerical algorithm for image reconstruction, which works for arbitrary distributions of Radon lines. This is in contrast to the classical filtered back projection, which essentially relies on a regular distribution of the Radon lines, e.g. parallel beam geometry. The good performance of the kernel-based image reconstruction method is illustrated by numerical examples and comparisons.

De Marchi S., Iske A., Sironi A. (2016) "Kernel-based Image Reconstruction from Scattered Radon Data " Dolomites Research Notes on Approximation, 9(Special_Issue), 19-31. DOI: 10.14658/PUPJ-DRNA-2016-Special_Issue-4  
Year of Publication
2016
Journal
Dolomites Research Notes on Approximation
Volume
9
Issue Number
Special_Issue
Start Page
19
Last Page
31
Date Published
09/2016
ISSN Number
2035-6803
Serial Article Number
4
DOI
10.14658/PUPJ-DRNA-2016-Special_Issue-4
Issue
Section
SpecialIssue