Abstract—Currently, Maximum Likelihood Expectation Maximization (MLEM) method and its accelerated version called Ordered-Subsets EM (OSEM) method have been used for image reconstruction in PET. It is known that the former has a drawback of slow convergence and the latter does not converge to a minimizer of cost function. Recently, image reconstruction methods using a new mathematical framework called proximal splitting have been actively studied. So far, most of the proximal splitting frameworks used for image reconstruction are based on splitting the cost function into two terms. With these conventional frameworks, it is impossible to obtain iterative methods that converge fast such as OSEM method and row-action-type iterative methods. To overcome this drawback, in this paper, we propose a unified approach to construct row-action-type iterative methods using three different types of multi proximal splitting frameworks. Results of simulation studies show that all the iterative methods obtained from the proposed approach can reduce the effect of statistical noise well and converge to a minimizer of the cost function with a high speed comparable to that of OSEM method.

Index Terms—image reconstruction, PET, row-action-type acceleration

Cite: Kazuya Sadakata, Heejeong Kim, and Hiroyuki Kudo, "Unified Approach to Fast Convergent Row-Action-Type Iterative Methods for PET Image Reconstruction Using Multi Proximal Splitting," Journal of Image and Graphics, Vol. 10, No. 2, pp. 82-87, June 2022.

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