Shaped extensions of singular spectrum analysis

Abstract

Extensions of singular spectrum analysis (SSA) for processing of non-rectangular images and time series with gaps are considered. A circular version is suggested, which allows application of the method to the data given on a circle or on a cylinder, e.g. cylindrical projection of a 3D ellipsoid. The constructed Shaped SSA method with planar or circular topology is able to produce low-rank approximations for images of complex shapes. Together with Shaped SSA, a shaped version of the subspace-based ESPRIT method for frequency estimation is developed. Examples of 2D circular SSA and 2D Shaped ESPRIT are presented.