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Abstract
In positron emission tomography (PET) studies, the voxel-wise calculation of individual rate constants describing the tracer kinetics is quite challenging because of the nonlinear relationship between the rate constants and PET data and the high noise level in voxel data. Based on preliminary simulations using a standard two-tissue compartment model, we can hypothesize that it is possible to reduce errors in the rate constant estimates when constraining the overestimation of the larger of two exponents in the model equation. We thus propose a novel approach based on infinity-norm regularization for limiting this exponent. Owing to the non-smooth cost function of this regularization scheme, which prevents the use of conventional Jacobian-based optimization methods, we examined a proximal gradient algorithm and the particle swarm optimization (PSO) through a simulation study. Because it exploits multiple initial values, the PSO method shows much better convergence than the proximal gradient algorithm, which is susceptible to the initial values. In the implementation of PSO, the use of a Gamma distribution to govern random movements was shown to improve the convergence rate and stability compared to a uniform distribution. Consequently, Gamma-based PSO with regularization was shown to outperform all other methods tested, including the conventional basis function method and Levenberg-Marquardt algorithm, in terms of its statistical properties.

Affiliations

Seung Kwan Kang  1 , Seongho Seo  2 , Chul-Hee Lee  3 , Mi Jeong Kim  4 , Su Jin Kim  5 , Jae Sung Lee  6
1 Department of Biomedical Sciences, Seoul National University College of Medicine, Seoul, Republic of Korea; Department of Nuclear Medicine, Seoul National University College of Medicine, Seoul, Republic of Korea.
2 Department of Neuroscience, Gachon University College of Medicine, Incheon, Republic of Korea; Department of Electronic Engineering, Pai Chai University, Daejeon, Republic of Korea. Electronic address: seos@pcu.ac.kr.
3 Department of Biomedical Sciences, Seoul National University College of Medicine, Seoul, Republic of Korea; Department of Nuclear Medicine, Korea Institute of Radiological and Medical Sciences, Seoul, Republic of Korea.
4 Department of Nuclear Medicine, Seoul National University College of Medicine, Seoul, Republic of Korea.
5 Department of Nuclear Medicine, Seoul National University Bundang Hospital, Seongnam, Republic of Korea.
6 Department of Biomedical Sciences, Seoul National University College of Medicine, Seoul, Republic of Korea; Department of Nuclear Medicine, Seoul National University College of Medicine, Seoul, Republic of Korea; Institute of Radiation Medicine, Medical Research Center, Seoul National University, Seoul, Republic of Korea. Electronic address: jaes@snu.ac.kr.