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 L^{2}(R^{2}). 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.