Sparse Approximation and Atomic Decomposition: Considering Atom Interactions in Evaluating and Building Signal Representations

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• Bob Sturm, Chateaubriand Fellow post-doctoral researcher at UPMC - Paris 06 with Professor Laurent Daudet
• Thursday 02 July 2009, 11:30-12:30
• LR11, Engineering, Department of.

If you have a question about this talk, please contact Rachel Fogg.

I will present work from my recent dissertation, which makes contributions to the sparse approximation and efficient representation of complex signals, e.g., acoustic signals, using greedy iterative descent pursuits and overcomplete dictionaries. As others have noted before, peculiar problems arise when a signal model is mismatched to the signal content, and a pursuit makes bad selections from the dictionary. These result in a model that contains atoms having no physical significance to the signal, existing to correct the representation through destructive interference, which diminishes its efficiency, and hinder the useful application of sparse approximation to signal analysis (e.g., source identification), visualization (e.g., source selection), and modification (e.g., source extraction). While past works have addressed these problems by reformulating a pursuit to avoid them, in this dissertation we use these corrective terms to learn about the signal, the pursuit algorithm, the dictionary, and the model. We show that a better signal model results when a pursuit builds it considering the interactions between its components.

This talk is part of the Signal Processing and Communications Lab Seminars series.

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