3-D image reconstruction from exponential X-ray projections using Neumann series

Author

Wagner, J.-M. ; Noo, F. ; Clackdoyle, R.

Author_Institution

Liege Univ., Belgium

Volume

3

fYear

2001

fDate

2001

Firstpage

2017

Abstract

In two dimensions, the exponential X-ray transform has been well-studied due to its applications of correcting attenuation effects in single photon emission computed tomography (SPECT). Explicit inversion formulas have been known for over 15 years. The three-dimensional (3D) case has not been as thoroughly examined, and inversion formulas are available for only a few of the wide range of possible 3D geometries. The rotating slant-hole (RSH) SPECT geometry is a special case for which no inversion formula has yet appeared. This paper presents a general inversion formula for the 3D exponential X-ray transform using a Neumann series. The method applies to any geometry but convergence of the series depends on the exponential scalar and the size of the region-of-interest. The derivation is presented in the context of the RSH SPECT geometry. Results from computer simulations are given

Keywords

X-ray imaging; convergence of numerical methods; image reconstruction; inverse problems; medical image processing; series (mathematics); single photon emission computed tomography; 3D exponential X-ray transform; 3D geometries; 3D image reconstruction; Neumann series; RSH SPECT geometry; attenuation effects correction; computer simulations results; exponential X-ray projections; exponential scalar; general inversion formula; lungs; region-of-interest size; rotating slant-hole SPECT geometry; series convergence; simulated attenuation maps; simulated emission maps; single photon emission computed tomography; Attenuation; Convergence; Detectors; Geometry; Image reconstruction; Optical collimators; Optical imaging; Single photon emission computed tomography; Three dimensional displays; X-ray imaging;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 2001. Proceedings. (ICASSP '01). 2001 IEEE International Conference on

Conference_Location

Salt Lake City, UT

ISSN

1520-6149

Print_ISBN

0-7803-7041-4

Type

conf

DOI

10.1109/ICASSP.2001.941345

Filename

941345