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arXiv · 1810.13100

Splitting with Near-Circulant Linear Systems: Applications to Total Variation CT and PET

Ernest K. Ryu·Seyoon Ko·Joong-Ho Won
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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.

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Ernest K. Ryu, Seyoon Ko, Joong-Ho Won. 2018-10-31. Splitting with Near-Circulant Linear Systems: Applications to Total Variation CT and PET. https://arxiv.org/abs/1810.13100

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