论文标题
带有波形词典的步骤函数贪婪近似的解决方案
A Solution for the Greedy Approximation of a Step Function with a Waveform Dictionary
论文作者
论文摘要
在本文中，我们考虑了一个以任意序列序列为特征的步长函数，并使用匹配的追踪（MP）算法近似它。我们利用带有矩形窗口函数的波形字典作为该算法的一部分。我们表明，当所有标量均为非正面或非负面时，并不需要波形词典，并且整数晶格上的小波词典的参数可作为MP的一部分作为初始优化问题的封闭形式解决方案。此外，对于任何实现的标量序列，我们在算法的每种迭代中都提供一个相关小波词典的解。这允许对近似函数进行实际计算，我们用来在模拟和真实的单变量时间序列数据上提供示例，这些数据在其基础结构中显示不连续性，其中可以将步骤函数视为来自感兴趣信号的示例。
In this paper we consider a step function characterized by an arbitrary sequence of real-valued scalars and approximate it with a matching pursuit (MP) algorithm. We utilize a waveform dictionary with rectangular window functions as part of this algorithm. We show that the waveform dictionary is not necessary when all of the scalars are either non positive or non negative and the parameters of a wavelet dictionary on an integer lattice yields a closed-form solution for the initial optimization problem as part of the MP. Additionally, for any real-valued scalar sequence, we provide a solution with a related wavelet dictionary at each iteration of the algorithm. This allows for practical calculation of the approximating function, which we use to provide examples on simulated and real univariate time series data that display discontinuities in its underlying structure where the step function can be thought of as a sample from a signal of interest.
