Prof. Khalide Jbilou

University Littoral Côte d’Opale, France

New Developements in Multilinear Algebra Computation with Applications for Image Processing

Abstract:

In this talk, we present some recent developments in multilinear algebra with some applications in image processing.

In the first part, we present a new method for the computation of some large singular values of multidimensional data by using the t-product of tensors. Methods for determining a couple of ingular triplets associated with the smallest singular values also are presented. The proposed methods generalize available restarted Lanczos bidiagonalization methods for computing a few of the largest or smallest singular triplets of a matrix. We use Ritz and harmonic Ritz lateral slices to determine accurate approximations of the largest and smallest singular triplets, respectively. Computed examples show applications to data compression and face recognition for color images.

The second part of this talk is devoted to the application of some tensor Krylov subspace methos such as Arnoldi or Lanczos for video or color image restoration for large problems using some regularization techniques

Keywords : Golub-Kahan Bidiagonalization, Face Recognition, Singular Value

Decomposition, Tensors, T-product

Khalide Jbilou is a full professor of mathematics in the mathematic laboratory LMPA of University Littoral Côte d’Opale (ULCO). He got his PhD in numerical analysis at university of Lille and he habilitation thesis at ULCO . His research topics are scientific computing, matrix and tensor computation, ill-posed problems, extrapolation, radial basis functions for some PDE’s, model reduction methods, with applications to image processing, control theory and other domains.

He has more than 140 publications in international journals and he is a member of the editorial board of many international journals. He also edited, as a managing guest editor (or guest editor), more than 13 special issues in high quality international scientific journals. He has supervised about 18 PhD students and participated in many doctoral thesis and habilitation committees. He also organized many international conferences related to linear algebra, numerical analysis and scientific computing He is the leader of the approximation and matrix computation group at the applied mathematic laboratory in university of Littoral Côte d’Opale in Calais. Currently, he is working on tensors with applications in deep learning and machine learning for large problems focussing in the development of model reduction procedures.

For more details, please visit the webpage at: http://www-lmpa.univ-littoral.fr/~jbilou/

You can also visit : Google Scholar or ResearchGate for recent works.

Khalide Jbilou,

Professor Laboratoire LMPA,

50 rue F. Buisson, Calais

University ULCO

France

email : jbilou@univ-littoral.fr