Applied Mathematics Colloquium

Monday March 5, 2012 4:15 PM

Robust Image Recovery via Total Variation Minimization

Speaker: Deanna Needell, Mathematics, Claremont McKenna College
Location: Annenberg 105
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.
Series Applied Mathematics Colloquium Series

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