Seminar - Instytut Badań Systemowych Polskiej Akademii Nauk
niedziela, 15 grudnia 2019
imieniny: Celina, Nina
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Seminar

data dodania: 2019-11-16 16:10:31

On November 19, 2019  at 11:00 in room 200 (II floor) a seminar will take place during which the following presentations will be delivered:

Professor Emilie Chouzenoux

Centrale Supelec, University Paris Saclay

 Majorization-Minimization Subspace Algorithms for Large Scale Data Processing

and

Professor Marc Castella

Centrale Supelec, University Paris Saclay

Polynomial and rational optimization, application to signal processing and sparse signal reconstruction 

 

Abstracts of both presentations are given below. 

Participants are warmly welcomed !

 

Professor Emilie Chouzenoux. Majorization-Minimization Subspace Algorithms for Large Scale Data Processing

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. IEEE Transactions on Signal Processing, Vol; 65, No. 18, pages 4770-4783, 2017.

[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.

Professor Marc Castella. Polynomial and rational optimization, application to signal processing and sparse signal reconstruction

Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non-convex least-squares fit criterion and a penalty term. We assume that the nonlinearity of the model can be accounted for by a rational function. In addition, we suppose that the signal to be sought is sparse and a rational approximation of the l0 pseudo-norm thus constitutes a suitable penalization. The resulting composite cost function belongs to the broad class of semi-algebraic functions. To find a globally optimal solution to such an optimization problem, it can be transformed into a generalized moment problem, for which a hierarchy of semidefinite programming relaxations can be built. Global optimality comes at the expense of an increased dimension and, to overcome computational limitations concerning the number of involved variables, the structure of the problem has to be carefully addressed. A situation of practical interest is when the nonlinear model consists of a convolutive transform followed by a component-wise nonlinear rational saturation. We then propose to use a sparse relaxation able to deal with up to several hundreds of optimized variables. In contrast with the naive approach consisting of linearizing the model, our experiments show that the proposed approach offers good performance. 

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Instytut Badań Systemowych
Polskiej Akademii Nauk

ul. Newelska 6
01-447 Warszawa, Polska
tel. +48 22 38 10 100
fax +48 22 38 10 105
e-mail: ibs at ibspan dot waw dot pl
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