Jump-Penalized Least Absolute Values Estimation of Scalar or Circle-Valued Signals
Jump-Penalized Least Absolute Values Estimation of Scalar or Circle-Valued Signals
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DOI：
10.1093/imaiai/iaw022
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发表时间：
2017-01
期刊：
影响因子：
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通讯作者：
M. Storath;A. Weinmann;M. Unser
中科院分区：
文献类型：
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作者：
M. Storath;A. Weinmann;M. Unser
我们研究了基于最小绝对偏差的跳罚估计量，通常称为Potts估计量。它们是对具有较重尾部或导致许多严重异常值的噪声分布的噪声数据的简洁分段常数表示的估计。我们考虑实值数据和圆值数据，例如，作为角度或相位信号的时间序列。我们提出了计算实值标量和圆值数据的Potts估计量的有效算法。实值版本改进了最先进的求解器w.r.t.计算时间。特别是对于量化数据，最坏情况的复杂度得到了提高。圆值版本是这类算法中第一个有效的算法。作为一个例子，我们将我们的方法应用于基于真实生物数据的细菌鞭毛马达旋转步骤的估计，以及风向的估计。
We study jump-penalized estimators based on least absolute deviations which are often referred to as Potts estimators. They are estimators for a parsimonious piecewise constant representation of noisy data having a noise distribution which has heavier tails or which leads to many severe outliers. We consider real-valued data as well as circle-valued data which appear, for instance, as time series of angles or phase signals. We propose efficient algorithms that compute Potts estimators for real-valued scalar as well as for circle-valued data. The real-valued version improves upon the state-of-the-art solver w.r.t. to computational time. In particular for quantized data, the worst case complexity is improved. The circle-valued version is the first efficient algorithm of this kind. As an illustration, we apply our method to estimate the steps in the rotation of the bacterial flagella motor based on real biological data, and to the estimation of wind directions.