Document Detail


Preconditioned Alternating Projection Algorithms for Maximum a Posteriori ECT Reconstruction.
MedLine Citation:
PMID:  23271835     Owner:  NLM     Status:  Publisher    
Abstract/OtherAbstract:
We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constrain involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the preconditioned alternating projection algorithm. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality.
Authors:
Andrzej Krol; Si Li; Lixin Shen; Yuesheng Xu
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Publication Detail:
Type:  JOURNAL ARTICLE    
Journal Detail:
Title:  Inverse problems     Volume:  28     ISSN:  0266-5611     ISO Abbreviation:  Inverse Probl     Publication Date:  2012 Nov 
Date Detail:
Created Date:  2012-12-28     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101189510     Medline TA:  Inverse Probl     Country:  -    
Other Details:
Languages:  ENG     Pagination:  115005     Citation Subset:  -    
Affiliation:
Department of Radiology, SUNY Upstate Medical University, Syracuse, NY 13210, USA. krola@upstate.edu.
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