论文标题
通过超级巨星随机过程及其在傅立叶和小波空间中的合成的稀疏抽样时间序列的随机插值
Stochastic interpolation of sparsely sampled time series by a superstatistical random process and its synthesis in Fourier and wavelet space
论文作者
论文摘要
我们提出了一种基于由多元高斯尺度混合物产生的超级巨星随机过程的稀疏抽样时间信号的随机插值的新方法。与其他随机插值方法（例如高斯过程回归）相比，我们的方法具有强大的多重型特性，因此适用于广泛的现实时间序列，例如来自太阳风或大气湍流。此外，我们根据混合过程提供了一种采样算法，该过程包括生成1 + 1维场u（t，ξ），其中每个高斯组件u了uξ（t）均与相同的潜在噪声合成，但通过log-nortage-normate-normator normate normater normation normate normation-nortage-normation spartuted参数参数分布了不同的噪声，但由不同的噪声组成。由于每个组件Uξ（t）的高斯性，我们可以利用标准采样的空中克（例如傅立叶或小波方法），最重要的是，将过程约束在稀疏测量点上的方法。然后，通过分配每个时间点t aξ（t）来初始化比例混合物u（t），从而初始化u（t，ξ）的特定值，其中与时间依赖的参数ξ（t）遵循与u（t，ξ）相关时间相比的对数正态过程，其对数正态过程具有较大的相关时间尺度。我们并置了傅立叶和小波方法，并证明了基于多波维特的插值路径的层次层次近似，产生稀疏的协方差结构，为局部插入大型和稀疏数据集提供了足够的方法。
We present a novel method for stochastic interpolation of sparsely sampled time signals based on a superstatistical random process generated from a multivariate Gaussian scale mixture. In comparison to other stochastic interpolation methods such as Gaussian process regression, our method possesses strong multifractal properties and is thus applicable to a broad range of real-world time series, e.g. from solar wind or atmospheric turbulence. Furthermore, we provide a sampling algorithm in terms of a mixing procedure that consists of generating a 1 + 1-dimensional field u(t, ξ), where each Gaussian component uξ(t) is synthesized with identical underlying noise but different covariance function Cξ(t,s) parameterized by a log-normally distributed parameter ξ. Due to the Gaussianity of each component uξ(t), we can exploit standard sampling alogrithms such as Fourier or wavelet methods and, most importantly, methods to constrain the process on the sparse measurement points. The scale mixture u(t) is then initialized by assigning each point in time t a ξ(t) and therefore a specific value from u(t, ξ), where the time-dependent parameter ξ(t) follows a log-normal process with a large correlation time scale compared to the correlation time of u(t, ξ). We juxtapose Fourier and wavelet methods and show that a multiwavelet-based hierarchical approximation of the interpolating paths, which produce a sparse covariance structure, provide an adequate method to locally interpolate large and sparse datasets.
