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The properties of the positronium lifetime image reconstruction based on maximum likelihood estimation

Chen Zhuo, An Lingling, Kao Chien-Min, Huang Hsin-Hsiung

Bio-Algorithms and Med-Systems

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2023

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Vol. 19, no. 1

1--8

EN

The positronium lifetime imaging (PLI) reconstruction is a technique used in time-of-flight (TOF) positron emission tomography (PET) imaging that involves measuring the lifespan of positronium, which is a metastable electron-positron pair that arises when a PET molecule releases a positron, prior to its annihilation. We have previously developed a maximum likelihood (ML) algorithm for PLI reconstruction and demonstrated that it can generate quantitatively accurate lifetime images for a 570 ps (pico-seconds) TOF PET system. In this study, we conducted further investigations into the statistical properties of the algorithm, including the variability of the reconstruction results, the sensitivity of the algorithm to the number of acquired PLI events and its robustness to hyperparameter choices. Our findings indicate that the proposed ML method produces sufficiently stable lifetime images to enable reliable distinction of regions of interest. Moreover, the number of PLI events required to produce quantitatively accurate lifetime images is computationally plausible. These results demonstrate the potential of our ML algorithm for advancing the capabilities of TOF PET imaging.

2

Error bounds for convex constrained systems in Banach spaces

Song W.

Control and Cybernetics

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2007

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Vol. 36, no 3

775-792

EN

In this paper, we first establish both primal (involving directional derivatives and tangent cones) and dual characterizations (involving subdifferential and normal cones) for the local (global) error bounds of constrained set-valued systems; as an application, we then derive both primal and dual characterizations for the local (global) error bounds of the constrained convex inequality systems in a general Banach space and also some sufficient conditions. The obtained results improve or generalize some known results.

3

Inequality-Based Approximation of Matrix Eigenvectors

Kocsor A., Dombi J., Balint I.

International Journal of Applied Mathematics and Computer Science

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2002

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Vol. 12, no 4

533-538

EN

A novel procedure is given here for constructing non-negative functions with zero-valued global minima coinciding with eigenvectors of a general real matrix A. Some of these functions are distinct because all their local minima are also global, offering a new way of determining eigenpairs by local optimization. Apart from describing the framework of the method, the error bounds given separately for the approximation of eigenvectors and eigenvalues provide a deeper insight into the fundamentally different nature of their approximations.

4

Weak sharp minima revisited Part I : basic theory

Burke J., Deng S.

Control and Cybernetics

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2002

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Vol. 31, no 3

439-469

EN

The notion of sharp minima, or strongly unique local minima, emerged in the late 1970's as an important tool in the analysis of the perturbation behavior of certain classes of optimization problems as well as in the convergence analysis of algorithms designed to solve these problems. The work of Cromme and Polyak is of particular importance in this development. In the late 1980's Ferris coined the term weak sharp minima to describe the extension of the notion of sharp minima to include the possibility of a non-unique solution set. This notion was later extensively studied by many authors. Of particular note in this regard is the paper by Burke and Ferrris which gives an extensive exposition of the notion and its impact on convex programming and convergence analysis in finite dimensions. In this paper we build on the work of Burke and Ferris. Specifically, we generalize their work to the normed linear space setting, further dissect the normal cone inclusion characterization for weak sharp minima, study the asymptotic properties of weak sharp minima in terms of associated recession functions, and give new characterizations for local weak sharp minima and boundely weak sharp minima. This paper is the first of a two part work on this subject. In Part II, we study the links between the notions of weak sharp minima, bounded linear regularity, linear regularity, metric regularity, and error bounds in convex programming. Along the way, we obtain both new results and reproduce many existing results from a fresh perspective.