Robust image recovery via total variation minimization
Discrete images, composed of patches of slowly-varying pixel values, have sparse or compressible representations with respect to their discrete derivative. Although image compression is a primary motivation for compressed sensing, stability results for total-variation minimization do not follow directly from the standard theory. In this talk, we present near-optimal reconstruction guarantees for total-variation minimization using properties of the bivariate Haar transform; we end by discussing several related open problems. This is joint work with Deanna Needell.