Generalized methods and solvers for noise removal from piecewise constant signals. I. Background theory.
Generalized methods and solvers for noise removal from piecewise constant signals. I. Background theory.
复制标题
DOI：
10.1098/rspa.2010.0671
复制
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
从分段常数（PWC）信号中去除噪声是一个具有挑战性的信号处理问题，在许多实际情况下出现。例如，在勘探地球科学中，有噪声的钻孔记录需要被分成地层带，在生物物理学中，分子停留状态之间的跳跃必须从有噪声的荧光显微镜信号中提取。存在许多PWC去噪方法，包括全变分正则化、均值漂移聚类、逐步跳跃放置、运行中值、凸聚类收缩和双边滤波;传统的线性信号处理方法从根本上不适合。本文（第一部分，两个）表明，大多数这些方法都与一个特殊情况下的广义功能，最小化，以实现PWC去噪。最小值可以通过不同的求解器算法获得，包括逐步跳跃放置，凸规划，有限差分，迭代运行中位数，最小角度回归，正则化路径跟踪和坐标下降。在第二篇论文中，第二部分，我们介绍了新的PWC去噪方法，这些方法之间的比较进行合成和真实的信号，显示新的理解的问题，在第一部分中获得的新方法，有一个有用的作用发挥。
Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play.
登录
查看更多内容
影响因子：
64.8
作者：
Kerssemakers, Jacob W. J.;Munteanu, E. Laura;Dogterom, Marileen
通讯作者：
Dogterom, Marileen
影响因子：
10.6
作者：
Elad, M
通讯作者：
Elad, M
影响因子：
3.3
作者：
GODFREY, R;MUIR, F;ROCCA, F
通讯作者：
ROCCA, F
影响因子：
2.5
作者：
MALLAT, S;HWANG, WL
通讯作者：
HWANG, WL
影响因子：
1.8
作者：
Fried, Roland
通讯作者：
Fried, Roland