A Bayesian Model for Dynamic Mass Reconstruction from PET Listmode Data

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-03 DOI:10.1137/23m161923x

Marco Mauritz, Bernhard Schmitzer, Benedikt Wirth

引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 5840-5880, October 2024.
Abstract. Positron emission tomography (PET) is a classical imaging technique to reconstruct the mass distribution of a radioactive material. If the mass distribution is static, this essentially leads to inversion of the X-ray transform. However, if the mass distribution changes temporally, the measurement signals received over time (the so-called listmode data) belong to different spatial configurations. We suggest and analyze a Bayesian approach to solve this dynamic inverse problem that is based on optimal transport regularization of the temporally changing mass distribution. Our focus lies on a rigorous derivation of the Bayesian model and the analysis of its properties, treating both the continuous as well as the discrete (finitely many detectors and time binning) setting.

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从 PET 列表模式数据重建动态质量的贝叶斯模型

SIAM 数学分析期刊》，第 56 卷第 5 期，第 5840-5880 页，2024 年 10 月。摘要正电子发射断层扫描（PET）是一种重建放射性物质质量分布的经典成像技术。如果质量分布是静态的，这基本上会导致 X 射线变换的反转。但是，如果质量分布随时间发生变化，那么随时间接收到的测量信号（即所谓的列表模式数据）就属于不同的空间配置。我们提出并分析了一种贝叶斯方法来解决这一动态逆问题，该方法基于对随时间变化的质量分布进行最佳传输正则化。我们的重点是严格推导贝叶斯模型并分析其特性，同时处理连续和离散（有限多个探测器和时间分档）设置。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.