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A Fast Fully 4-D Incremental Gradient Reconstruction Algorithm for List Mode PET Data

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4 Author(s)
Quanzheng Li ; Signal & Image Process. Inst., Univ. of Southern California, Los Angeles, CA ; Asma, E. ; Sangtae Ahn ; Leahy, R.M.

We describe a fast and globally convergent fully four-dimensional incremental gradient (4DIG) algorithm to estimate the continuous-time tracer density from list mode positron emission tomography (PET) data. Detection of 511-keV photon pairs produced by positron-electron annihilation is modeled as an inhomogeneous Poisson process whose rate function is parameterized using cubic B-splines. The rate functions are estimated by minimizing the cost function formed by the sum of the negative log-likelihood of arrival times, spatial and temporal roughness penalties, and a negativity penalty. We first derive a computable bound for the norm of the optimal temporal basis function coefficients. Based on this bound we then construct and prove convergence of an incremental gradient algorithm. Fully 4-D simulations demonstrate the substantially faster convergence behavior of the 4DIG algorithm relative to preconditioned conjugate gradient. Four-dimensional reconstructions of real data are also included to illustrate the performance of this method

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Medical Imaging, IEEE Transactions on  (Volume:26 ,  Issue: 1 )