Applied Math Seminar
Spring Quarter 2007
Friday November 09, 3:15p.m.Gitta Kutyniok
Shearlets: A Wavelet-Based Approach to Sparse Decompositions of Anisotropic Phenomena.
Efficient representations of anisotropic structures are essential in a variety of areas in applied mathematics such as in the analysis of images or hyperbolic PDE. It is well known that wavelets - although perfectly suited for isotropic structures - do not perform equally well when dealing with anisotropic phenomena. Although the last years have seen many new representation systems designed for this task, it was still an open problem to introduce a representation system suited for anisotropic phenomena which provides the benefits of wavelets. In this talk we will introduce the representation system of shearlets, and show that this system indeed satisfies all those needs. Shearlets are an affine system which precisely detects orientations of singularities, in the sense of resolving the wavefront set, while providing optimally sparse representations, and are moreover equipped with a multiresolution analysis leading to a fast shearlet decomposition.
Seminar website: http://math.stanford.edu/~applmath/