In this talk, I will review some of Osher’s Bregman iterations for L1 minimizations. I will start with Osher’s linearized Bregman iterations for L1 minimizations used in compressed sensing, then show how it can be applied to low rank matrix completion. After this, Osher’s split Bregman iterations and its applications to a wavelet frame based model for image restorations will be given. Connections between this wavelet frame based approach and the famous ROF model for image restorations will be discussed. A few other applications of wavelet based approach for image analysis and restorations by using theses algorithms will also be presented.
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