  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's 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.

Computation;Computer Vision and Pattern Recognition;Machine Learning