We prove that the unitary affine Radon transform intertwines the quasi-regular representation of a class of semidirect products, built by shearlet dilation groups and translations, and the tensor product of a standard wavelet representation with a wavelet-like representation. This yields a formula for shearlet coefficients that involves only integral transforms applied to the affine Radon transform of the signal, thereby opening new perspectives in the inversion of the Radon transform.
The Radon transform intertwines wavelets and shearlets
Bartolucci, Francesca;De Mari, Filippo;De Vito, Ernesto;Odone, Francesca
2019
Abstract
We prove that the unitary affine Radon transform intertwines the quasi-regular representation of a class of semidirect products, built by shearlet dilation groups and translations, and the tensor product of a standard wavelet representation with a wavelet-like representation. This yields a formula for shearlet coefficients that involves only integral transforms applied to the affine Radon transform of the signal, thereby opening new perspectives in the inversion of the Radon transform.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
shearlet_radon_bw.pdf
non disponibili
Tipologia:
Documento in Post-print
Dimensione
187.51 kB
Formato
Adobe PDF
|
187.51 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
|
The-Radon-transform-intertwines-wavelet_2018_Applied-and-Computational-Harmo.pdf
non disponibili
Tipologia:
Documento in versione editoriale
Dimensione
1.22 MB
Formato
Adobe PDF
|
1.22 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
