Generalized methods and solvers for noise removal from piecewise constant signals. II. New methods.
Generalized methods and solvers for noise removal from piecewise constant signals. II. New methods.
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DOI：
10.1098/rspa.2010.0674
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发表时间：
2011-11-08
期刊：
影响因子：
--
通讯作者：
Jones NS
中科院分区：
文献类型：
--
作者：
Little MA;Jones NS
在许多实际的科学和工程环境中，从分段常数信号中去除噪声是一个具有挑战性的信号处理问题。在本系列的第一篇论文（第一部分）中，我们介绍了基于图像处理社区结果的背景理论，以表明这些算法中的大多数，以及在更广泛的文献中提出的更多算法，都与广义泛函的一个特殊情况相关联，当最小化时，解决了PWC去噪问题。它展示了如何通过一系列计算求解器算法获得最小值。在第二篇论文（第二部分）中，利用第一部分中发展的理解，我们介绍了几种新的PWC去噪方法，例如，将均值移位聚类的全局行为与总变异扩散的局部平滑相结合，并展示了这些新方法的示例求解器算法。将这些方法在合成信号和真实信号上进行了比较，表明我们的新方法具有重要的作用。最后，讨论了这两篇论文的广义方法与其他方法（如小波收缩、隐马尔可夫模型和分段平滑滤波）之间的重叠。
Removing noise from signals which are piecewise constant (PWC) is a challenging signal processing problem that arises in many practical scientific and engineering contexts. In the first paper (part I) of this series of two, we presented background theory building on results from the image processing community to show that the majority of these algorithms, and more proposed in the wider literature, are each associated with a special case of a generalized functional, that, when minimized, solves the PWC denoising problem. It shows how the minimizer can be obtained by a range of computational solver algorithms. In this second paper (part II), using this understanding developed in part I, we introduce several novel PWC denoising methods, which, for example, combine the global behaviour of mean shift clustering with the local smoothing of total variation diffusion, and show example solver algorithms for these new methods. Comparisons between these methods are performed on synthetic and real signals, revealing that our new methods have a useful role to play. Finally, overlaps between the generalized methods of these two papers and others such as wavelet shrinkage, hidden Markov models, and piecewise smooth filtering are touched on.
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