SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2281-A2299, January 2020.
A blurring algorithm with linear time complexity can reduce the small-scale content of data observed at scattered locations in a spatially extended domain of arbitrary dimension. The method works by forming a Gaussian interpolant of the input data and then convolving the interpolant with a multiresolution Gaussian approximation of the Green function to a differential operator whose spectrum can be tuned for problem-specific considerations. Like conventional blurring algorithms, which the new algorithm generalizes to data measured at locations other than a uniform grid, applications include deblurring and separation of spatial scales. An example illustrates a possible application toward enabling importance sampling approaches to data assimilation of geophysical observations, which are often scattered over a spatial domain, since blurring observations can make particle filters more effective at state estimation of large scales. Another example, motivated by data analysis of dynamics like ocean eddies that have strong separation of spatial scales, uses the algorithm to decompose scattered oceanographic float measurements into large-scale and small-scale components.

中文翻译：

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散乱数据的快速可调模糊算法

SIAM科学计算杂志，第42卷，第4期，第A2281-A2299页，2020年1月。
具有线性时间复杂度的模糊算法可以减少在任意维度的空间扩展域中的分散位置观察到的小规模数据内容。该方法通过形成输入数据的高斯插值，然后将插值与Green函数的多分辨率高斯近似卷积到微分算子上，该算子可以针对特定问题进行调整。像传统的模糊算法一样，新算法将其概括为在统一网格以外的位置上测量的数据，其应用包括空间尺度的去模糊和分离。一个示例说明了一种可能的应用，可用于实现对地球物理观测数据进行同化的重要性采样方法，这些方法通常散布在空间域中，因为模糊的观察可以使粒子过滤器在大规模状态估计时更有效。另一个示例，是由对诸如海洋涡流这样的动力学数据进行分析而得出的，这些涡流在空间尺度上具有很强的分离性，它使用该算法将分散的海洋浮游物测量值分解为大型和小型组件。