Shearlet Coorbit Spaces and Related Banach Frames
given at strobl07 (18.06.07 14:00)
In recent years, a lot of attempts have been made to extract directional information from images such as curvelets, ridgelets, contourlets and shearlets. Among these, the shearlet transform stands out since it is related with group theory, i.e., it stems from a square-integrable representation of a locally compact group, the shearlet group. This specific feature
makes it possible to combine the shearlet approach with the coorbit space theory developed by Feichtinger and Gröchenig. In this talk, we show that indeed all the assumptions needed to apply the coorbit theory can be satisfied. We establish the corresponding smoothness spaces, the shearlet coorbit spaces, and we explain how the representation can be discretized in order to obtain atomic decompositions and Banach frames for these new smoothness spaces.
(joint work with G. Kutyniok, G. Steidl and G. Teschke)