Orthogonal series approach to reconstructing 2D PET images using data obtained from detector tubes of arbitrary width

Raymond B. Carroll; Bernard A. Mair

doi:10.1117/12.402440

4 October 2000 Orthogonal series approach to reconstructing 2D PET images using data obtained from detector tubes of arbitrary width

Raymond B. Carroll, Bernard A. Mair

Author Affiliations +

Proceedings Volume 4121, Mathematical Modeling, Estimation, and Imaging; (2000) https://doi.org/10.1117/12.402440
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

This paper describes a method for reconstructing two dimensional profiles from positron emission tomography (PET) emission data. Unlike the usual methods which assume the detectors are small, the method is based on an accurate system response model which is valid for PET detectors of arbitrary size. The emission profile is represented as an orthogonal series of basis functions (on the circular region inside the scanner ring) which are tensor products of Bessel functions in the radial direction, and classical harmonics in the angular direction. By applying a simple linear transformation to the emission sinogram, it can be viewed as data corresponding to detector arcs, and represented by basis functions involving Chebyshev polynomials and classical harmonics. The coefficients in the orthogonal series for the emission intensity are obtained by solving a block diagonal linear system in which the data vector consists of the coefficients of the orthogonal series of the transformed sinogram. The coefficient matrix of this system is obtained from an orthogonal series representation of the probability that an emission is detected in one of the detector arcs. The mathematical description of this probability and the reconstruction method was developed in a recent paper by the authors. In this paper we discuss details of the numerical implementation and present numerical results obtained from applying this method to simulated data. The results indicate that our method produces reconstructions which are comparable in quality to the maximum likelihood expectation maximization (MLEM) method wiht a speed which is similar that of the filtered back projection (FBP) method.

Citation Download Citation

Raymond B. Carroll and Bernard A. Mair "Orthogonal series approach to reconstructing 2D PET images using data obtained from detector tubes of arbitrary width", Proc. SPIE 4121, Mathematical Modeling, Estimation, and Imaging, (4 October 2000); https://doi.org/10.1117/12.402440

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
11 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Sensors

Positron emission tomography

Reconstruction algorithms

Data modeling

Expectation maximization algorithms

Detection and tracking algorithms

Scanners

Show All Keywords

Keywords/Phrases

Search In:

Publication Years