An Algebraic View on Finite Rank in 2D-SSA
Nina E. Golyandina, Konstantin Usevich · ePrints Soton (University of Southampton) · 2009
The 2D-SSA method provides a decomposition of a 2D-array (a function of two variables, e.g. digital image) into a sum of identifiable components. For the decomposition to be proper, these components should be close to 2D-arrays of finite rank. This paper is devoted to study of arrays of finite rank by means of polynomial ideals generated by arrays. The 2D-arrays are considered as functionals of polynomials. A general form of arrays of finite rank is obtained. The structure of finite-rank arrays and their trajectory spaces is investigated.