First-order convex feasibility algorithms for x-ray CT
Abstract
Purpose: Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this paper, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for rapidly convergent algorithms for their solution-thereby facilitating the IIR algorithm design process. Methods: An accelerated version of the Chambolle-Pock (CP) algorithm is adapted to various convex feasibility problems of potential interest to IIR in CT. One of the proposed problems is seen to be equivalent to least-squares minimization, and two other problems provide alternatives to penalized, least-squares minimization. Results: The accelerated CP algorithms are demonstrated on a simulation of circular fan-beam CT with a limited scanning arcmore »
- Authors:
-
- Department of Radiology, University of Chicago, 5841 South Maryland Avenue, Chicago, Illinois, 60637 (United States)
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, Matematiktorvet, Building 303B, 2800 Kongens Lyngby (Denmark)
- Publication Date:
- OSTI Identifier:
- 22130545
- Resource Type:
- Journal Article
- Journal Name:
- Medical Physics
- Additional Journal Information:
- Journal Volume: 40; Journal Issue: 3; Other Information: (c) 2013 American Association of Physicists in Medicine; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-2405
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; 62 RADIOLOGY AND NUCLEAR MEDICINE; ALGORITHMS; APPROXIMATIONS; COMPUTERIZED TOMOGRAPHY; DESIGN; IMAGE PROCESSING; ITERATIVE METHODS; LEAST SQUARE FIT; MINIMIZATION; SIMULATION; X RADIATION
Citation Formats
Sidky, Emil Y., Xiaochuan, Pan, and Jorgensen, Jakob S. First-order convex feasibility algorithms for x-ray CT. United States: N. p., 2013.
Web. doi:10.1118/1.4790698.
Sidky, Emil Y., Xiaochuan, Pan, & Jorgensen, Jakob S. First-order convex feasibility algorithms for x-ray CT. United States. https://doi.org/10.1118/1.4790698
Sidky, Emil Y., Xiaochuan, Pan, and Jorgensen, Jakob S. 2013.
"First-order convex feasibility algorithms for x-ray CT". United States. https://doi.org/10.1118/1.4790698.
@article{osti_22130545,
title = {First-order convex feasibility algorithms for x-ray CT},
author = {Sidky, Emil Y. and Xiaochuan, Pan and Jorgensen, Jakob S.},
abstractNote = {Purpose: Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this paper, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for rapidly convergent algorithms for their solution-thereby facilitating the IIR algorithm design process. Methods: An accelerated version of the Chambolle-Pock (CP) algorithm is adapted to various convex feasibility problems of potential interest to IIR in CT. One of the proposed problems is seen to be equivalent to least-squares minimization, and two other problems provide alternatives to penalized, least-squares minimization. Results: The accelerated CP algorithms are demonstrated on a simulation of circular fan-beam CT with a limited scanning arc of 144 Degree-Sign . The CP algorithms are seen in the empirical results to converge to the solution of their respective convex feasibility problems. Conclusions: Formulation of convex feasibility problems can provide a useful alternative to unconstrained optimization when designing IIR algorithms for CT. The approach is amenable to recent methods for accelerating first-order algorithms which may be particularly useful for CT with limited angular-range scanning. The present paper demonstrates the methodology, and future work will illustrate its utility in actual CT application.},
doi = {10.1118/1.4790698},
url = {https://www.osti.gov/biblio/22130545},
journal = {Medical Physics},
issn = {0094-2405},
number = 3,
volume = 40,
place = {United States},
year = {Fri Mar 15 00:00:00 EDT 2013},
month = {Fri Mar 15 00:00:00 EDT 2013}
}