2d-extension of Singular Spectrum Analysis: Algorithm and Elements of Theory
نویسنده
چکیده
Singular Spectrum Analysis is a nonparametric method, which allows one to solve problems like decomposition of a time series into a sum of interpretable components, extraction of periodic components, noise removal and others. In this paper, the algorithm and theory of the SSA method are extended to analyse two-dimensional arrays (e.g. images). The 2D-SSA algorithm based on the SVD of a Hankel-block-Hankel matrix is introduced. Another formulation of the algorithm by means of Kronecker-product SVD is presented. Basic SSA notions such as separability are considered. Results on ranks of Hankel-block-Hankel matrices generated by exponential, sinewave and polynomial 2D-arrays are obtained. An example of 2D-SSA application is presented.
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