on 03-06-2011
Tomas Kopf (U Opave, Czech Republic).
June 3, 2011, Friday, 15h.
Location: Room P4.35, Post-Graduation Building, IST.
Abstract: Variational free energy, as used in generative model inversion, is reviewed. It is pointed out to be just a relative entropy (Kullback- eibler divergence), if non-normalized states are allowed. This allows to formulate model inversion in the framework of information geometry.
Support: CAMGSD, CFIF, CFP and SQIG/IT with support from FCT and FEDER, namely via projects PTDC/EEA-TEL/103402/2008 QuantPrivTel and PTDC/EIA/67661/2006 QSec.
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on 02-06-2011
Jorge Gomes da Silva
Research Scientist, Sr., Duke University, USA
This work addresses the problem of simultaneous signal recovery and dictionary learning based on compressive measurements. Multiple signals are analyzed jointly, with multiple sensing matrices, under the assumption that the unknown signals come from a union of a small number of disjoint subspaces. This problem is important, for instance, in image inpainting applications, in which the multiple signals are constituted by (incomplete) image patches taken from the overall image. This work extends standard dictionary learning and block-sparse dictionary optimization, by considering compressive measurements (e.g., incomplete data). Previous work on blind compressed sensing is also generalized by using multiple sensing matrices and relaxing some of the restrictions on the learned dictionary. Drawing on results developed in the context of matrix completion, it is proven that both the dictionary and signals can be recovered with high probability from compressed measurements. The solution is unique up to block permutations and invertible linear transformations of the dictionary atoms. The recovery is contingent on the number of measurements per signal and the number of signals being sufficiently large; bounds are derived for these quantities. In addition, a computationally practical algorithm that performs dictionary learning and signal recovery is derived, and conditions for convergence to a local optimum are established. Experimental results for image inpainting demonstrate the capabilities of the method.
Date and time: June 2, 15:00 – 16:00.
Place: IST (Alameda), Torre Norte, 5th floor, room 5.9 (DEEC meeting room).
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