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- W2899337583 abstract "Many imaging problems, such as total variation reconstruction of X-ray computed tomography (CT) and positron-emission tomography (PET), are solved via a convex optimization problem with near-circulant, but not actually circulant, linear systems. The popular methods to solve these problems, alternating direction method of multipliers (ADMM) and primal-dual hybrid gradient (PDHG), do not directly utilize this structure. Consequently, ADMM requires a costly matrix inversion as a subroutine, and PDHG takes too many iterations to converge. In this paper, we present near-circulant splitting (NCS), a novel splitting method that leverages the near-circulant structure. We show that NCS can converge with an iteration count close to that of ADMM, while paying a computational cost per iteration close to that of PDHG. Through experiments on a CUDA GPU, we empirically validate the theory and demonstrate that NCS can effectively utilize the parallel computing capabilities of CUDA." @default.
- W2899337583 created "2018-11-09" @default.
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- W2899337583 date "2018-10-31" @default.
- W2899337583 modified "2023-09-24" @default.
- W2899337583 title "Splitting with Near-Circulant Linear Systems: Applications to Total Variation CT and PET" @default.
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- W2899337583 doi "https://doi.org/10.48550/arxiv.1810.13100" @default.
- W2899337583 hasPublicationYear "2018" @default.
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