Demon Registration for 2D Empirical Wavelet Transforms

The empirical wavelet transform is a fully adaptive time-scale representation that has been widely used in the last decade. Inspired by the empirical mode decomposition, it consists of filter banks based on harmonic mode supports. Recently, it has been generalized to build the filter banks from any generating function using mappings. In practice, the harmonic mode supports can have a low-constrained shape in 2D, leading to numerical difficulties to estimate mappings adapted to the construction of empirical wavelet filters. This work aims to propose an efficient numerical scheme to compute empirical wavelet coefficients using the demons registration algorithm. Results show that the proposed approach is robust, accurate, and continuous wavelet filters permitting reconstruction with a low signal-to-noise ratio. An application for texture segmentation of scanning tunneling microscope images is also presented.