On the Use of Alternating Direction Optimization in Imaging

The alternating direction method of multipliers (ADMM) has been shown to be a flexible and efficient convex optimization tool for a variety of imaging inverse problems. This talk will review our recent work on the application of ADMM to several imaging inverse problems. We willshow how ADMM provides an efficient and modular optimization tool,which allows addressing a wide variety of problems (namely, image restoration under Gaussian, Poisson, or multiplicative noise) usingseveral types of regularizers (namely total variation, frame-based analysis, frame-based synthesis, or hybrid/balanced analysis-synthesis), and formulations (constrained or unconstrained optimization). We will also describe very recent work on the use of ADMM for blinddeconvolution and in dealing efficiently with non-periodic boundary conditions.
Mario A. T. Figueiredo received MSc (1990) and PhD (1994) degrees in electrical and computer engineering, both from Instituto Superior Técnico (IST), the engineering school
of the University of Lisbon. Since 1994, he has been with the faculty of the Department of Electrical and Computer Engineering, IST, where he is now a Professor. He is also area coordinator and group leader at Instituto de
Telecomunications, a private non-profit research institute.

His research interests include image processing and analysis, pattern recognition, statistical learning, and optimization. He is a Fellow of the IEEE and of the IAPR, and received several awards: 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 has been associate editor of several journals (namely, the IEEE Transactions on Image Processing, the IEEE Transactions on Pattern Analysis and Machine Intelligence, the SIAM Journal on Imaging Sciences, the Journal of Mathematical Imaging and Vision), presented invited lectures in many conferences and workshops, and served in the technical/program committees of many international conferences.