Mário A. T. Figueiredo (IT, IST)
Sparse Optimization and Applications to Information Processing (1)
Much of modern data processing requires identification of low-dimensional structures in high-dimensional spaces, using observations that are incomplete or noisy. This general paradigm applies to the restoration of images (where natural images form a low-dimensional subset of the space of all possible images), compressed sensing (where the signal can be represented in terms of just a few elements of an appropriate basis), regularized regression (where we seek to explain observations in terms of just a few predictive variables), matrix completion (where we seek a low-rank matrix that fits partial information about the matrix), and so on.
Sparse optimization provides valuable tools for formulating and solving problems of this type. A key concept is regularization, whereby we introduce functions into the optimization formulation that induce the required type of structure in the solutions. In the simplest case, the 1-norm of a vector x is used to derive solutions in which x is sparse, that is, it contains relatively few nonzero components. Often (not always) the regularized formulations are convex but nonsmooth. Customized optimization algorithms are required to handle the large data size and dimension. This talks will survey the scope of applications of sparse optimization in data processing, and then describe the formulation techniques and algorithms that are being used to solve these problems.
Bio: Mário A. T. Figueiredo received MSc, PhD, and "Agregado" degrees in electrical and computer engineering, both from Instituto Superior Técnico (IST), the engineering school of the University of Lisbon, in 1990, 1994, and 2004. Since 1994, he has been with the faculty of the Department of Electrical and Computer Engineering, IST, where he is now a full Professor. He is also area coordinator and group leader at Instituto de Telecomunicações, a private non-profit research institute.
His research interests include image processing and analysis, pattern recognition, statistical learning, and optimization. M. Figueiredo is a Fellow of the IEEE and of the IAPR. He received the 1995 Portuguese IBM Scientific Prize, the 2008 UTL/Santander-Totta Scientific Prize, the 2011 IEEE Signal Processing Society Best Paper Award, the 2014 IEEE W. R. G. Baker Award, and several conference best paper awards. He is/was associate editor of several journals (among others, the IEEE Transactions on Image Processing, the IEEE Transactions on Pattern Analysis and Machine Intelligence, the SIAM Journal on Imaging Sciences). He co-chaired the 2001 and 2003 Workshops on Energy Minimization Methods in Computer Vision and Pattern Recognition, co-organized all the editions (2011-2014) of the Lisbon Machine Learning School, and is the technical program chair of the 2014 European Signal Processing Conference. He presented invited lectures in many conferences and workshops and served in the technical/program committees of many international conference.