Équipe IMAGeS : Images, Modélisation, Apprentissage, Géométrie et Statistique

Séminaire du 13/06/2017, 10h00

De Équipe IMAGeS : Images, Modélisation, Apprentissage, Géométrie et Statistique
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mardi 13 juin 2017, 10h00

Majorization-Minimization Subspace Algorithms for Large Scale Data Processing

Conférencier : Émilie Chouzenoux (laboratoire Gaspard Monge)

Recent developments in data processing drive the need for solving optimization problems with increasingly large sizes, stretching traditional techniques to their limits. New optimization algorithms have thus to be designed, paying attention to computational complexity, scalability, and robustness. Majorization-Minimization (MM) approaches have become increasingly popular recently, in both signal/image processing and machine learning areas. Our talk will present new theoretical and practical results regarding the MM subspace algorithm [1], where the update of each iterate is restricted to a subspace spanned by few directions. We will first present the extension of this method to the online case when only a stochastic approximation of the criterion is employed at each iteration [2], and we will analyse its convergence rate properties [3]. In a second part of the talk, a novel block parallel MM subspace algorithm will be introduced, which can take advantage of the potential acceleration provided by multicore architectures [4]. Several examples, in the context of signal/image processing will be presented, to illustrate the efficiency of these methods.

  • [1] E. Chouzenoux, A. Jezierska, J.-C. Pesquet and H. Talbot. A Majorize-Minimize Subspace Approach for l2-l0 Image Regularization. SIAM Journal on Imaging Science, Vol. 6, No. 1, pages 563-591, 2013.
  • [2] E. Chouzenoux and J.-C. Pesquet. A Stochastic Majorize-Minimize Subspace Algorithm for Online Penalized Least Squares Estimation. Tech. Rep., 2016.http://arxiv.org/abs/1512.08722
  • [3] E. Chouzenoux and J.-C. Pesquet. Convergence Rate Analysis of the Majorize-Minimize Subspace Algorithm. IEEE Signal Processing Letters, Vol. 23, No. 9, pages 1284-1288, Septembre 2016.
  • [4] S. Cadoni, E. Chouzenoux, J.-C. Pesquet and C. Chaux. A Block Parallel Majorize-Minimize Memory Gradient Algorithm. In Proceedings of the 23rd IEEE International Conference on Image Processing (ICIP 2016), pages 3194-3198, Phoenix, Arizona, 25-28 septembre 2016.
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