Present trends in communication links between devices have opted for wireless instead of wired solutions. As a consequence, unlicensed bands have seen a rise in the interference level as more and more devices are introduced into the market place that take advantage of these free bands for their communication needs. Under these conditions, the receiver's ability to recognize and identify the presence of interference becomes increasingly important. In order for the receiver to make an optimal decision on the signal-of-interest, it has to be aware of the type (modulation) of interference as well as how the received signals are affected (channel) by these impediments in order to appropriately mitigate them. This dissertation addresses the blind (unaided) identification of the signal modulations and the channel in a Multiple Input Multiple Output (MIMO) system. The method presented herein takes advantage of the modulation induced periodicities of the signals in the system and uses higher-order cyclostationary statistics to extract the signal and channel unknowns. This method can be used to identify more signals in the system than antenna elements at the receiver (overloaded case). This dissertation presents a system theoretic analysis of the problem as well as describes the development of an algorithm that can be used in the identification of the channel and the modulation of the signals in the system. Linear and non-linear receivers are examined at the beginning of the manuscript in order to review the a priori information that is needed for each receiver configuration to function properly. / Ph. D.

Cette thèse concerne la restauration aveugle d’images (formulée comme un problème inverse mal-posé et mal-conditionné), en considérant particulièrement les systèmes SIMO. Dans un premier temps une technique d’identification aveugle de ce système où l’ordre du canal est inconnu (surestimé) est introduite. Nous introduisons d’abord une version simplifiée à coût réduit SCR de la méthode des relations croisées (CR). Ensuite, une version robuste R-SCR basée sur la recherche d’une solution parcimonieuse minimisant la fonction de coût CR est proposée. La restauration d’image est ensuite assurée par une nouvelle approche inspirée des techniques de décodage des signaux 1D et étendue ici aux cas de la restauration d’images en se basant sur une recherche arborescente efficace (algorithme ‘Stack’). Plusieurs améliorations de la méthode ‘Stack’ ont été introduites afin de réduire sa complexité et d’améliorer la qualité de restauration lorsque les images sont fortement bruitées. Ceci en utilisant une technique de régularisation et une approche d’optimisation all-at-once basée sur la descente du gradient qui permet de raffiner l’image estimée et mieux converger vers la solution optimale. Ensuite, les mesures de la qualité d’images sont utilisées comme fonctions de coûts (intégrées dans le critère global) et ce afin d’étudier leur potentiel pour améliorer les performances de restauration. Dans le contexte où l’image d’intérêt est corrompue par d’autres images interférentes, sa restauration nécessite le recours aux techniques de séparation aveugle de sources. Pour cela, une étude comparative de certaines techniques de séparation basées sur la propriété de décorrélation au second ordre et la parcimonie est réalisée. / This thesis concerns the blind restoration of images (formulated as an ill-posed and illconditioned inverse problem), considering a SIMO system. Thus, a blind system identification technique in which the order of the channel is unknown (overestimated) is introduced. Firstly, a simplified version at reduced cost SCR of the cross relation (CR) method is introduced. Secondly, a robust version R-SCR based on the search for a sparse solution minimizing the CR cost function is proposed. Image restoration is then achieved by a new approach (inspired from 1D signal decoding techniques and extended here to the case of 2D images) based on an efficient tree search (Stack algorithm). Several improvements to the ‘Stack’ method have been introduced in order to reduce its complexity and to improve the restoration quality when the images are noisy. This is done using a regularization technique and an all-at-once optimization approach based on the gradient descent which refines the estimated image and improves the algorithm’s convergence towards the optimal solution. Then, image quality measurements are used as cost functions (integrated in the global criterion), in order to study their potential for improving restoration performance. In the context where the image of interest is corrupted by other interfering images, its restoration requires the use of blind sources separation techniques. In this sense, a comparative study of some separation techniques based on the property of second-order decorrelation and sparsity is performed.