A regularized nonnegative third order tensor decomposition using a Primal-Dual Projected Gradient Algorithm: application to 3D fluorescence spectroscopy

K. El Qate (1) , M. El Rhabi (2) , A. Hakim (1) , E. Moreau (3, 4, 5) , Nadège Thirion-Moreau (3, 4, 5)

1 UCA - Université Cadi Ayyad [Marrakech]
2 ENPC - École des Ponts ParisTech
3 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
4 SIIM - Signal et Image
5 UTLN SeaTech - Université de Toulon - École d’ingénieurs SeaTech

This paper investigates the use of Primal-Dual optimization algorithms on multidimensional signal processing problems. The data blocks interpreted in a tensor way can be modeled by means of multi-linear decomposition. Here we will focus on the Canonical Polyadic Decomposition (CPD), and we will present an application to fluorescence spectroscopy using this decomposition. In order to estimate the factors or latent variables involved in these decompositions, it is usual to use criteria optimization algorithms. A classical cost function consists of a measure of the modeling error (fidelity term) to which a regularization term can be added if necessary. Here, we consider one of the most efficient optimization methods, Primal-Dual Projected Gradient. The effectiveness and the robustness of the proposed approach are shown through numerical examples.

Mots clés: Constrained optimization; Nonnegative tensor decomposition; Projected Gradient; Regularization; Primal-Dual

Domaines: Sciences de l'ingénieur [physics]; Traitement du signal et de l'image [eess.SP]

K. El Qate, M. El Rhabi, A. Hakim, E. Moreau, Nadège Thirion-Moreau. A regularized nonnegative third order tensor decomposition using a Primal-Dual Projected Gradient Algorithm: application to 3D fluorescence spectroscopy. International Conference on Smart Multimedia, Aug 2018, Toulon, France. ⟨10.1007/978-3-030-04375-9_16⟩. ⟨hal-01858112⟩