Iterative Potts Minimization for the Recovery of Signals with Discontinuities from Indirect Measurements: The Multivariate Case
Iterative Potts Minimization for the Recovery of Signals with Discontinuities from Indirect Measurements: The Multivariate Case
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DOI：
10.1007/s10208-020-09466-9
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发表时间：
2018-12
影响因子：
3
通讯作者：
Lukas Kiefer;M. Storath;A. Weinmann
中科院分区：
文献类型：
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作者：
Lukas Kiefer;M. Storath;A. Weinmann
在生物学、医学、机械学和电子工程等不同领域的许多问题中，都存在着不连续性信号和图像。具体的数据往往是离散的，间接的和噪声测量的一些数量描述的信号正在考虑。一个常见的任务是找到信号或图像的片段，这对应于找到数据中的不连续或跳跃。基于最小化分段常数Mumford-Shah泛函（其离散化版本被称为Potts能量）的方法在这种情况下是有利的，特别是与分割有关。然而，由于它们的非凸性，最小化这些能量是具有挑战性的。在本文中，我们提出了一个新的迭代最小化策略的多元波茨能量处理间接，噪声测量。我们提供了一个收敛性分析，并支持我们的研究结果与数值实验。
Signals and images with discontinuities appear in many problems in such diverse areas as biology, medicine, mechanics and electrical engineering. The concrete data are often discrete, indirect and noisy measurements of some quantities describing the signal under consideration. A frequent task is to find the segments of the signal or image which corresponds to finding the discontinuities or jumps in the data. Methods based on minimizing the piecewise constant Mumford–Shah functional—whose discretized version is known as Potts energy—are advantageous in this scenario, in particular, in connection with segmentation. However, due to their non-convexity, minimization of such energies is challenging. In this paper, we propose a new iterative minimization strategy for the multivariate Potts energy dealing with indirect, noisy measurements. We provide a convergence analysis and underpin our findings with numerical experiments.