2009/01/01 by Stephan Dahlke, Dahlke, Stephan, Gabriele Steidl +3
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Mathematical Analysis and Transform Methods #Optical measurement and interference techniques
paper · doi:10.4230/dagsemproc.08492.9
openalex publication_date 2009/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.