Abhishek Harikrishnan, Freie Universität Berlin

"What is... a shearlet?"

Shortcomings in Fourier or Wavelet representations of multivariate data, most commonly images, have lead to the development of shearlets, originally introduced for the sparse approximation of functions from  L2(R2).  They are a multiscale geometric framework tuned to efficiently encode anisotropic features of such functions using parabolic scalings and shearings of some mother shearlet psi. In this talk, I will show the construction of shearlet frames, as well as a theorem showing almost-optimal sparse approximation behavior of shearlets with respect to a model class of images with anisotropic features (so-called cartoon-like functions). Moreover, I will present a few examples of applications of shearlets from image processing (denoising, inpainting, super-resolution, medical imaging...) by means of sparse regularization, which has been proven to be a useful prior in such imaging problems.