Multidimensional Wavelets for Scalable Image Decomposition: Orbital Wavelets

Abstract

Wavelets are closely related to the Schr\"odinger's wave functions and the interpretation of Born. Similarly to the appearance of atomic orbital, it is proposed to combine anti-symmetric wavelets into orbital wavelets. The proposed approach allows the increase of the dimension of wavelets through this process. New orbital 2D-wavelets are introduced for the decomposition of still images, showing that it is possible to perform an analysis simultaneous in two distinct scales. An example of such an image analysis is shown.