Multidimensional Wavelets for Scalable Image Decomposition: Orbital Wavelets

TL;DR

This paper introduces orbital wavelets, a new class of multidimensional wavelets inspired by quantum atomic orbitals, enabling simultaneous multi-scale image analysis with potential for advanced image decomposition techniques.

Contribution

It proposes a novel method to increase wavelet dimensionality using anti-symmetric orbital wavelets for improved image analysis.

Findings

New orbital 2D-wavelets for image decomposition

Demonstration of simultaneous multi-scale analysis

Potential for enhanced image processing techniques

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.