2D Empirical Transforms. Wavelets, Ridgelets and Curvelets revisited
This work provides adaptive image processing methods, but it is incremental as it builds on existing 1D techniques.
The authors extended the Empirical Wavelet Transform to 2D signals, revisiting transforms like wavelets, ridgelets, and curvelets to build adaptive frames for images, showing promising properties for analysis and processing.
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.