This paper addresses the problem of rank tracking in real time hyperspectral image unmixing. Based on the On-line Alternating Direction Method of Multipliers (ADMM), we propose a new hyperspectral unmixing approach that integrates prior information as well as joint sparsity regularization, allowing to select only the active components on each sample of the image. This results in a semi-supervised algorithm, well adapted for on-line rank tracking for pushbroom imager. Experimental results on synthetic and real data sets demonstrate the effectiveness of our method for parameter estimation and rank change detection.

Pushbroom imaging systems are emerging techniques for real-time acquisition of hyperspectral images. These systems are frequently used in industrial applications to control and sort products on-the-fly. In this paper, the on-line hyperspectral image blind unmixing is addressed. We propose a new on-line method based on Alternating Direction Method of Multipliers (ADMM) approach, adapted to pushbroom imaging systems. Because of the generally ill-posed nature of the unmixing problem, we impose a minimum endmembers dispersion regularization to stabilize the solution; this regularization can be interpreted as a convex relaxation of the minimum volume regularization and therefore, presents interesting optimization properties. The proposed algorithm presents faster convergence rate and lower computational complexity compared to the algorithms based on multiplicative update rules. Experimental results on synthetic and real datasets, and comparison to state-of-the-art algorithms, demonstrate the effectiveness of our method in terms of rapidity and accuracy.

Cette thèse aborde le démélange en-ligne d’images hyperspectrales acquises par un imageur pushbroom, pour la caractérisation en temps réel du matériau bois. La première partie de cette thèse propose un modèle de mélange en-ligne fondé sur la factorisation en matrices non-négatives. À partir de ce modèle, trois algorithmes pour le démélange séquentiel en-ligne, fondés respectivement sur les règles de mise à jour multiplicatives, le gradient optimal de Nesterov et l’optimisation ADMM (Alternating Direction Method of Multipliers) sont développés. Ces algorithmes sont spécialement conçus pour réaliser le démélange en temps réel, au rythme d'acquisition de l'imageur pushbroom. Afin de régulariser le problème d’estimation (généralement mal posé), deux sortes de contraintes sur les endmembers sont utilisées : une contrainte de dispersion minimale ainsi qu’une contrainte de volume minimal. Une méthode pour l’estimation automatique du paramètre de régularisation est également proposée, en reformulant le problème de démélange hyperspectral en-ligne comme un problème d’optimisation bi-objectif. Dans la seconde partie de cette thèse, nous proposons une approche permettant de gérer la variation du nombre de sources, i.e. le rang de la décomposition, au cours du traitement. Les algorithmes en-ligne préalablement développés sont ainsi modifiés, en introduisant une étape d’apprentissage d’une bibliothèque hyperspectrale, ainsi que des pénalités de parcimonie permettant de sélectionner uniquement les sources actives. Enfin, la troisième partie de ces travaux consiste en l’application de nos approches à la détection et à la classification des singularités du matériau bois.

In this paper, the estimation of the regularization parameter of the on-line Non-negative Matrix Factorization (NMF) with minimum volume constraint on sources is addressed. Adding a volume constraint in the model is important to ensure uniqueness of the solution and good data representation. However, the effectiveness of this approach is hampered by the optimal determination of the strength of minimum volume term. To solve this problem, we formulate it as a bi-objective optimization problem and three Minimum Distance Criterion (MDC) strategies are proposed and evaluated. The three strategies yield similar results but one of them in particular yields an interesting tradeoff between accuracy and computation time.

This work is a part of the CNRS project “ALOHA: Analyse en Ligne de dOnnees Hyperspectrales pour l’industrie Agroalimentaire” and of the ANR-OPTIFIN (Agence Nationale de la Recherche-OPTImisation des FINitions). The aim of these projects is to develop analytical tools adapted to the high throughput online analysis of samples by acquisition and processing of hyperspectral images. One output of the ALOHA and ANR OPTIFIN projects consists in the development of sequential algorithms for the deconvolution and on-the-fly unmixing of hyperspectral data. The main goal is to be able to predict and classify the quality of wood pieces renderings.

In this paper, the on-line hyperspectral image blind unmixing is addressed. Inspired by the Incremental Non-negative Matrix Factorization (INMF) method [2], we propose an on-line NMF which is adapted to the acquisition scheme of a pushbroom imager. Because of the non-uniqueness of the NMF model, a minimum volume constraint on the endmembers is added allowing to reduce the set of admissible solutions. This results in a stable algorithm yielding results similar to those of standard off-line NMF methods, but drastically reducing the computation time. The algorithm is applied to wood hyperspectral images showing that such a technique is effective for the on-line prediction of wood piece rendering after finishing.