We show that the cone-adapted shearlet coefficients can be computed by means of three classical transforms: the affine Radon transform, a 1D wavelet transform and a 1D convolution. This yields formulas that open new perspectives both for finding a new algorithm to compute shearlet coefficients and for the inversion of the Radon transform. Furthermore, the strong connection between shearlets and wavelets suggests an alternative proof of the wavefront set resolution properties of the shearlet transform.

This presentation is part of Contributed Presentation “CP5 - Contributed session 5”

Authors:

Francesca Bartolucci (University of Genoa)

Ernesto De Vito (University of Genoa)

Filippo De Mari (University of Genoa)

Francesca Odone (University of Genoa)

Keywords:

computed tomography, image enhancement, inverse problems, radon transform, shearlets, wavelets