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Fast algorithms for free-discontinuity problems on high-dimensional biomedical data

高维生物医学数据自由不连续问题的快速算法

基本信息

批准号：
318064553
负责人：
Professor Dr. Martin Storath
金额：
--
依托单位：
Fakultät Angewandte Natur- und Geisteswissenschaften
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2016
资助国家：
德国
起止时间：
2015-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/318064553?language=en
关键词：
Fast algorithms free discontinuity problems

项目摘要

Functions with discontinuities are ubiquitous in our everyday life and in almost all types of biomedical data. The discontinuities encode significant information: for instance, they represent the boundaries of cellular structures in microscopic images, they correspond to change points in microarray data, and they define tissue layers in tomographic images. Since classical methods destroy this important information, discontinuity preserving models such as the Mumford-Shah model have been developed. Such free-discontinuity problems are algorithmically challenging as they lead to nonsmooth and nonconvex problems. Even for low-dimensional data, the currently used algorithms are computationally demanding. Since the dimensionality of the acquired data increases tremendously, there is urgent need for new algorithms that scale reasonably with the high-dimensionality in terms of trade-off between complexity and accuracy. In this project we aim at developing new efficient algorithms for free-discontinuity problems for high-dimensional biomedical data. We deal with high-dimensional linear data spaces (magnetic particle imaging, feature images) and manifold-valued data spaces (diffusion tensor imaging, shape spaces) that might be defined on higher dimensional lattices. On the one hand, we evaluate the developed methods on real life data from biomedical problems, and on the other hand, we provide mathematical analysis and foundation. Extending our present software toolbox, we will make the algorithms publicly available to help practitioners to process their data.

具有不连续性的函数在我们的日常生活中以及几乎所有类型的生物医学数据中无处不在。不连续性编码重要信息：例如，它们表示显微图像中细胞结构的边界，它们对应于微阵列数据中的变化点，并且它们定义断层图像中的组织层。由于经典的方法破坏了这一重要信息，不连续性保持模型，如Mumford-Shah模型已经开发出来。这种自由不连续性问题在算法上具有挑战性，因为它们导致非光滑和非凸问题。即使是低维数据，目前使用的算法计算要求很高。由于所获得的数据的维数极大地增加，因此迫切需要新的算法，该算法在复杂性和准确性之间的权衡方面合理地扩展高维。在这个项目中，我们的目标是开发新的高效算法的自由不连续性问题的高维生物医学数据。我们处理高维线性数据空间（磁粒子成像，特征图像）和流形值数据空间（扩散张量成像，形状空间），可能会被定义在高维格。一方面，我们评估的发展方法对真实的生活数据的生物医学问题，另一方面，我们提供了数学分析和基础。扩展我们目前的软件工具箱，我们将公开提供算法，以帮助从业者处理他们的数据。