Applied Mathematics Colloquium

Discrete images, composed of patches of slowly-varying pixel values, have sparse or compressible wavelet representations which allow the techniques from compressed sensing such as L1-minimization to be utilized. In addition, such images also have sparse or compressible discrete derivatives which motivate the use of total variation minimization for image reconstruction. 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 numerical studies showing the benefits of total variation approaches and provable near-optimal reconstruction guarantees for total-variation minimization using properties of the bivariate Haar transform. This is joint work with Rachel Ward.