Fast Two-Dimensional Smoothing with Discrete Cosine Transform

Smoothing is the process of removing "noise" and "insignificant" fragments while preserving the most important properties of the data structure. We propose a fast spline method for two-dimensional smoothing. Data smoothing usually attained by parametric and nonparametric regression. The nonparametric regression requires a prior knowledge of the regression equation form. However, most of the investigated data can't be parameterized simply. From this point of view, our algorithm belongs to nonparametric regression. Our simulation study shows that smoothing with discrete cosine transform is orders of magnitude faster to compute than other two-dimensional spline smoothers.