Total Cyclic Variation and Generalizations
Total Cyclic Variation and Generalizations
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总循环变化和概括
DOI：
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发表时间：
2013
影响因子：
2
通讯作者：
Evgeny Strekalovskiy
中科院分区：
文献类型：
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作者：
D. Cremers;Evgeny Strekalovskiy
我们介绍了一个通用的框架，在一个循环的结构，如角度，相位或色调值的值的信号的正则化。这些包括总循环变差${TV_{{S}^{1}$，以及二次正则化的循环版本，Huber-TV和Mumford-Shah正则性。其关键思想是引入一个凸松弛的原始非凸优化问题。该方法以一种简单的方式处理值的周期性，对循环移位是不变的，并且具有许多其他有用的属性，例如较低的连续性。该框架允许一般的，可能是非凸的数据项。实验结果上级优于那些没有特别关心包装间隔端点。此外，我们提出了一个等价的制定的总循环变化，可以最小化与标准的总变化相同的时间和内存效率。我们表明，这些正则化的离散化版本相当于NP-难优化问题。然而，所提出的框架提供了最佳或接近最佳的解决方案，在大多数实际应用中。
We introduce a general framework for regularization of signals with values in a cyclic structure, such as angles, phases or hue values. These include the total cyclic variation ${TV_{{S}^{1}}}$, as well as cyclic versions of quadratic regularization, Huber-TV and Mumford-Shah regularity. The key idea is to introduce a convex relaxation of the original non-convex optimization problem. The method handles the periodicity of values in a simple way, is invariant to cyclical shifts and has a number of other useful properties such as lower-semicontinuity. The framework allows general, possibly non-convex data terms. Experimental results are superior to those obtained without special care about wrapping interval end points. Moreover, we propose an equivalent formulation of the total cyclic variation which can be minimized with the same time and memory efficiency as the standard total variation. We show that discretized versions of these regularizers amount to NP-hard optimization problems. Nevertheless, the proposed framework provides optimal or near-optimal solutions in most practical applications.