Sparse Representation in Redundant Systems

CSIC Building (#406), Seminar Room 4122.
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Shearlets: A New Wavelet-based Approach Towards Sparse Representations of Singularities in the Plane

Dr. Gitta Kutyniok

Justus-Liebig-University Giessen

Abstract:   In this talk we introduce the Continuous Shearlet Transform, which is a directional transform based on analyzing elements called shearlets. These are non-separable wavelets built out of parabolic scaling, shear, and translation operations. We show that they satisfy a Calderon-like reproducing formula. Further we discuss several types of singularities in the plane, showing that our systems detect both their location and their orientation. Finally, we compare our transform to closely related directional transforms. This is part of ongoing research joint with Demetrio Labate (North Carolina State University).