Empirical Voronoi Wavelets

TL;DR

This paper introduces a method for constructing 2D empirical wavelets using Voronoi diagrams to balance adaptability and geometric regularity in Fourier domain partitions.

Contribution

It proposes a novel approach combining Voronoi diagrams with empirical wavelet construction for improved partition regularity.

Findings

Enhanced geometric regularity in wavelet partitions

Maintained adaptability in Fourier domain segmentation

Applicable to various signal processing tasks

Abstract

Recently, the construction of 2D empirical wavelets based on partitioning the Fourier domain with the watershed transform has been proposed. If such approach can build partitions of completely arbitrary shapes, for some applications, it is desirable to keep a certain level of regularity in the geometry of the obtained partitions. In this paper, we propose to build such partition using Voronoi diagrams. This solution allows us to keep a high level of adaptability while guaranteeing a minimum level of geometric regularity in the detected partition.