Stationary partitions in 2D nonstationary processes: nondyadic anisotropic Malvar´s decomposition and two-dimensional spectral distance tree

In this article, we propose a simple algorithm allowing the research of stationary partitions in locally stationary 2D processes, by use of adapted local bases like the local 2D DCT. The algorithm aims at finding some windows for which the width is adapted to the rate of change in the 2D spectrum. For this, we define an anisotropic Malvar´s decomposition with a weak complexity and we propose a robust estimation of the difference in spectra, based on a denoising of the 2D log-periodogram with the help of the undecimated wavelet transform. Then, we consider the “symmetrical case” in the best partition selection method and a post-treatment that permits us to deal with the 2D nonuniform partitions is introduced. Our algorithm obtains better results than the classical Malvar´s decomposition. It must be considered as a first treatment, which selects a global segmentation