2D Empirical Transforms. Wavelets, Ridgelets and Curvelets revisited
Functional Analysis
2024-11-01 v1 Computer Vision and Pattern Recognition
Image and Video Processing
Abstract
A recently developed new approach, called ``Empirical Wavelet Transform'', aims to build 1D adaptive wavelet frames accordingly to the analyzed signal. In this paper, we present several extensions of this approach to 2D signals (images). We revisit some well-known transforms (tensor wavelets, Littlewood-Paley wavelets, ridgelets and curvelets) and show that it is possible to build their empirical counterpart. We prove that such constructions lead to different adaptive frames which show some promising properties for image analysis and processing.
Keywords
Cite
@article{arxiv.2410.23533,
title = {2D Empirical Transforms. Wavelets, Ridgelets and Curvelets revisited},
author = {Jerome Gilles and Giang Tran and Stanley Osher},
journal= {arXiv preprint arXiv:2410.23533},
year = {2024}
}