A series formula for inversion of the V-line Radon transform in a disc

Authors:
Gaik Ambartsoumian;Sunghwan Moon
Affiliations:
Department of Mathematics, University of Texas at Arlington, P.O. Box 19408, Arlington, TX 76019-0408, USA;Department of Mathematics, Texas A&M University, Mailstop 3368, College Station, TX, 77843-3368, USA
Venue:
Computers & Mathematics with Applications
Year:
2013

Citing 4
Cited 0

Singularities of the X-ray transform and limited data tomography in R2 and R3

SIAM Journal on Mathematical Analysis
Mellin transforms and asymptotics: harmonic sums

Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
On the V-line radon transform and its imaging applications

Journal of Biomedical Imaging - Special issue on mathematical methods for images and surfaces
Inversion of the V-line Radon transform in a disc and its applications in imaging

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.09

Visualization

Abstract

The paper presents an exact formula for a Fourier series reconstruction of a function from its V-line Radon transform in a disc. This transform (often also called broken-ray Radon transform) appears in mathematical models of several imaging modalities, e.g. single-scattering optical tomography and @c-ray emission tomography. Our inversion formula relaxes the support restriction on the image function required in the previously discovered inversion technique (Ambartsoumian, 2012) [8], and uses data from only half of the set of broken rays required before. The general strategy of the current approach was outlined in (Ambartsoumian, 2012) [8].