The Continuous Shearlet Transform in Arbitrary Space Dimensions, Frame Construction, and Analysis of Singularities

Stephan Dahlke (1) , Gabriela Steidl (2) , Gerd Teschke (3)

1 FB12 Mathematik und Informatik
2 Fakultät für Mathematik und Informatik, Institut für Mathematik
3 Institute for Computational Mathematics in Science and Technology

This note is concerned with the generalization of the continuous shearlet transform to higher dimensions. Similar to the two-dimensional case, our approach is based on translations, anisotropic dilations and specific shear matrices. We show that the associated integral transform again originates from a square-integrable representation of a specific group, the full n-variate shearlet group. Moreover, we verify that by applying the coorbit theory, canonical scales of smoothness spaces and associated Banach frames can be derived. We also indicate how our transform can be used to characterize singularities in signals.

Domaines: Analyse classique [math.CA]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Stephan Dahlke, Gabriela Steidl, Gerd Teschke. The Continuous Shearlet Transform in Arbitrary Space Dimensions, Frame Construction, and Analysis of Singularities. SAMPTA'09, May 2009, Marseille, France. Special session on geometric multiscale analysis. ⟨hal-00451798⟩