Mathematics of biomedical imaging today-a perspective
Mathematics of biomedical imaging today-a perspective
复制标题
当今生物医学成像数学——一个视角
DOI：
10.1088/2516-1091/acd973
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Betcke M
中科院分区：
文献类型：
--
作者：
Betcke M
生物医学成像是一个迷人的，丰富的和动态的研究领域，在生物医学研究和临床实践中具有巨大的重要性。成像数据的处理、自动分析和量化背后的关键技术是数学。从图像采集的优化和从间接断层扫描测量数据重建图像开始，一直到医学图像中肿瘤的自动分割和基于图像生物标志物的最佳治疗计划的设计，数学以不同的风格出现在所有这些中。在稀疏促进图像先验的背景下的非平滑优化，用于图像配准和运动估计的偏微分方程，以及用于图像分割的深度神经网络，仅举几例。在这篇文章中，我们提出和审查的数学主题，出现在整个生物医学成像管道，从断层测量到临床支持工具，并强调一些现代的主题和开放的问题。这篇文章是写给两个生物医学研究人员谁想要得到一个味道的数学出现在生物医学成像以及数学家谁感兴趣的数学挑战生物医学成像研究需要。
Biomedical imaging is a fascinating, rich and dynamic research area, which has huge importance in biomedical research and clinical practice alike. The key technology behind the processing, and automated analysis and quantification of imaging data is mathematics. Starting with the optimisation of the image acquisition and the reconstruction of an image from indirect tomographic measurement data, all the way to the automated segmentation of tumours in medical images and the design of optimal treatment plans based on image biomarkers, mathematics appears in all of these in different flavours. Non-smooth optimisation in the context of sparsity-promoting image priors, partial differential equations for image registration and motion estimation, and deep neural networks for image segmentation, to name just a few. In this article, we present and review mathematical topics that arise within the whole biomedical imaging pipeline, from tomographic measurements to clinical support tools, and highlight some modern topics and open problems. The article is addressed to both biomedical researchers who want to get a taste of where mathematics arises in biomedical imaging as well as mathematicians who are interested in what mathematical challenges biomedical imaging research entails.