Imaging Components, Systems, and Processing

# Fast and accurate computation of system matrix for area integral model-based algebraic reconstruction technique

[+] Author Affiliations
Shunli Zhang

Northwestern Polytechnical University, Key Laboratory of Contemporary Design & Integrated Manufacturing Technology of Ministry of Education, Xi’an 710072, China

Dinghua Zhang

Northwestern Polytechnical University, Key Laboratory of Contemporary Design & Integrated Manufacturing Technology of Ministry of Education, Xi’an 710072, China

Hao Gong

Virginia Tech, Virginia Tech-Wake Forest University School of Biomedical Engineering and Sciences, Blacksburg, Virginia 24061, United States

Virginia Tech, Department of Mechanical Engineering, Blacksburg, Virginia 24061, United States

Ge Wang

Rensselaer Polytechnic Institute, Department of Biomedical Engineering, Troy, New York 12180, United States

Guohua Cao

Virginia Tech, Virginia Tech-Wake Forest University School of Biomedical Engineering and Sciences, Blacksburg, Virginia 24061, United States

Opt. Eng. 53(11), 113101 (Nov 03, 2014). doi:10.1117/1.OE.53.11.113101
History: Received January 20, 2014; Revised August 29, 2014; Accepted September 30, 2014
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## Abstract

Abstract.  Iterative algorithms, such as the algebraic reconstruction technique (ART), are popular for image reconstruction. For iterative reconstruction, the area integral model (AIM) is more accurate for better reconstruction quality than the line integral model (LIM). However, the computation of the system matrix for AIM is more complex and time-consuming than that for LIM. Here, we propose a fast and accurate method to compute the system matrix for AIM. First, we calculate the intersection of each boundary line of a narrow fan-beam with pixels in a recursive and efficient manner. Then, by grouping the beam-pixel intersection area into six types according to the slopes of the two boundary lines, we analytically compute the intersection area of the narrow fan-beam with the pixels in a simple algebraic fashion. Overall, experimental results show that our method is about three times faster than the Siddon algorithm and about two times faster than the distance-driven model (DDM) in computation of the system matrix. The reconstruction speed of our AIM-based ART is also faster than the LIM-based ART that uses the Siddon algorithm and DDM-based ART, for one iteration. The fast reconstruction speed of our method was accomplished without compromising the image quality.

© 2014 Society of Photo-Optical Instrumentation Engineers

## Topics

Matrices ; Numerical simulations

Citation

Shunli Zhang ; Dinghua Zhang ; Hao Gong ; Omid Ghasemalizadeh ; Ge Wang, et al.
"Fast and accurate computation of system matrix for area integral model-based algebraic reconstruction technique", Opt. Eng. 53(11), 113101 (Nov 03, 2014). ; http://dx.doi.org/10.1117/1.OE.53.11.113101

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