title: Reconstruction for 3D PET Based on Total Variation Constrained Direct Fourier Method.
abstract: This paper presents a total variation (TV) regularized reconstruction algorithm for 3D positron emission tomography (PET). The proposed method first employs the Fourier rebinning algorithm (FORE), rebinning the 3D data into a stack of ordinary 2D data sets as sinogram data. Then, the resulted 2D sinogram are ready to be reconstructed by conventional 2D reconstruction algorithms. Given the locally piece-wise constant nature of PET images, we introduce the total variation (TV) based reconstruction schemes. More specifically, we formulate the 2D PET reconstruction problem as an optimization problem, whose objective function consists of TV norm of the reconstructed image and the data fidelity term measuring the consistency between the reconstructed image and sinogram. To solve the resulting minimization problem, we apply an efficient methods called the Bregman operator splitting algorithm with variable step size (BOSVS). Experiments based on Monte Carlo simulated data and real data are conducted as validations. The experiment results show that the proposed method produces higher accuracy than conventional direct Fourier (DF) (bias in BOSVS is 70% of ones in DF, variance of BOSVS is 80% of ones in DF).
authors.affiliation: Department of Optical Engineering, Zhejiang University, Hangzhou, Zhejiang, China.
authors.forename: Haiqing
authors.initials: H
authors.lastname: Yu
authors.affiliation: Department of Optical Engineering, Zhejiang University, Hangzhou, Zhejiang, China.
authors.forename: Zhi
authors.initials: Z
authors.lastname: Chen
authors.affiliation: Shenzhen Institutes of Advanced Technology, Shenzhen, Guangdong, China.
authors.forename: Heye
authors.initials: H
authors.lastname: Zhang
authors.affiliation: School of Computer Science and Software Engineering, The University of Western Australia, Crawley, Australia.
authors.forename: Kelvin Kian Loong
authors.initials: KK
authors.lastname: Wong
authors.affiliation: Department of Mathematics, University of Florida, Gainesville, United States of America.
authors.forename: Yunmei
authors.initials: Y
authors.lastname: Chen
authors.affiliation: Department of Optical Engineering, Zhejiang University, Hangzhou, Zhejiang, China.
authors.forename: Huafeng
authors.initials: H
authors.lastname: Liu
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005583:Fourier Analysis; D006801:Humans; D021621:Imaging, Three-Dimensional; D009010:Monte Carlo Method; D019047:Phantoms, Imaging; D049268:Positron-Emission Tomography