Multidimensional Extension of singular Spectrum Analysis Based on Filtering Interpretation

Singular spectrum analysis is a nonparametric spectral decomposition of a time series. The singular spectrum analysis can be viewed as the two-step filtering with the complete set of eigenfilter adaptively constructed from the original time series. Based on this viewpoint, we present a flexible and quite simple algorithm for the singular spectrum analysis which can be applied to the multidimensional data series with arbitrary dimension. We have carried out the decomposition of two-dimensional image data, and the optimally constructed filters are found to be the smoothing or the edge enhancement filters of various type. We have also examined a simple example for the decomposition of 3D data.