May 25, 2009 - One of the most appealing results by Candes and Tao in their analysis of the Danzig Selector (DS) is the proof that it is log (and constant) factor away from an oracle estimator that knows the original support. Can a similar claim be made with respect to the Basis Pursuit (BP)? Together with Zvika Ben-Haim and Yonina Eldar we show such a result - see here. Furthermore, the constants obtained in our bounds are even better than those found in the DS analysis, suggesting (not claiming!!) that BP may be more accurate than DS.
May 25, 2009 - Two submitted papers to the special issue in the IEEE Proceedings are added to the journal list here. The first, with Mario Figueiredo and Yi Ma, is on the role of sparse representations in image processing, and the second, with Ron Rubinstein and Freddy Bruckstein, deals with the dictionaries used in such models.
April 6, 2009 - The slides of the presentation given in Ecole Polytechnique are now available here. This lecture describes how to exploit several sparse representations of the ame signal to get an approximation of the MMSE estimator (joint work with Irad Yavneh and Matan Protter). Two journal papers on this topic can be found here. The first with Irad Yavneh is on the general idea of approximating a Gibbs sampler of the representations, and the second with Matan Protter and Irad Yavneh is on the unitary case, where a closed-form formula for the MMSE estimator is derived.
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