Through-the-wall Imaging (TWI) is crucial for various applications such as law enforcement, rescue missions and defense. TWI methods aim to provide detailed information of spaces that cannot be seen directly. Current state-of-the-art TWI systems utilise ultra-wideband (UWB) signals to simultaneously achieve wall penetration and high resolution. These TWI systems transmit signals and mathematically back-project the reflected signals received to image the scenario of interest. However, these systems are diffraction-limited and encounter problems due to multipath signals in the presence of multiple scatterers. Time reversal (TR) methods have become popular for remote sensing because they can take advantage of multipath signals to achieve superresolution (resolution that beats the diffraction limit). The Decomposition Of the Time-Reversal Operator (DORT in its French acronym) and MUltiple SIgnal Classification (MUSIC) methods are both TR techniques which involve taking the Singular Value Decomposition (SVD) of the Multistatic Data Matrix (MDM) which contains the signals received from the target(s) to be located. The DORT and MUSIC imaging methods have generated a lot of interests due to their robustness and ability to locate multiple targets. However these TR-based methods encounter problems when the targets are behind an obstruction, particularly when the properties of the obstruction is unknown as is often the case in TWI applications. This dissertation introduces a novel total sub-MDM algorithm that uses the highly acclaimed MUSIC method to image targets hidden behind an obstruction and achieve superresolution. The algorithm utilises spatio-temporal windows to divide the full-MDM into sub-MDMs. The summation of all images obtained from each sub-MDM give a clearer image of a scenario than we can obtain using the full-MDM. Furthermore, we propose a total sub-differential MDM algorithm that uses the MUSIC method to obtain images of moving targets that are hiddenbehind an obstructing material.

Le travail présenté dans cette thèse concerne la mise en oeuvre numérique de techniques temporelles pour des applications en compatibilité électromagnétique (CEM) impulsionnelle, essentiellement pour des études en chambre réverbérante à brassage de modes (CRBM). Prenant le contre-pied des approches fréquentielles, adaptées par nature aux études de cavités résonantes, l’idée directrice de ce mémoire a été d’étudier des moyens temporels originaux d’investigation de CRBM en vue de proposer de nouveaux paradigmes pour la caractérisation d’équipements. Originellement développé en acoustique, le processus de retournement temporel (RT) récemment appliqué aux ondes électromagnétiques permet une focalisation spatiale et temporelle de ces dernières d’autant meilleur que le milieu de propagation est réverbérant. Les chambres réverbérantes (CR) sont ainsi des endroits idéaux pour l’application du processus de RT. Après une nécessaire étude des nombreux paramètres qui gouvernent ce dernier couplée à la définition de méthodologies numériques spécifiques, les applications du RT en CRBM sont exposées. En particulier, l’intérêt d’une focalisation sélective pour des tests en susceptibilité rayonnée est démontré. L’importance des coefficients d’absorption et de diffraction des équipements en CRBM justifie leur caractérisation précise et efficace. À cette fin, la mise en oeuvre d’un calcul temporel de section efficace totale de diffraction (TSCS en anglais) est détaillée. L’application de cette nouvelle technique à différentes formes de brasseurs de modes permet au final de confronter ces résultats avec ceux obtenus à l’aide de tests normatifs CEM. / The work presented in this thesis concerns the use of time techniques for impulsive ElectroMagnetic Compatibility (EMC) applications, mainly for Modes Stirred Reverberation Chamber (MSRC) studies. Contrary to approaches from frequency domain, obviously well-fitted for studies in resonant cavities, the main idea of this thesis was to study an original time method for MSRC investigation to propose new paradigms for equipment characterization. Originally developed in acoustics, the Time Reversal (TR) process recently applied to electromagnetic waves allows focusing it both in time and space. The process quality is even higher if the propagation environment is reverberant. Thus, the Reverberation Chambers (RC) are an ideal locations for TR implementation. After a study of parameters involved in the TR process coupled with the definition of specific numerical methods, the applications of TR in MSRC are exposed. In particular, the interest of selective focusing for radiated susceptibility tests is demonstrated. The importance of absorption and diffraction coefficients for MSRC equipment justifies their accurate and efficient characterization. To this end, the implementation of a temporal calculation of the Total Scattering Cross Section (TSCS) in RC is detailed. The application of this new technique to different forms of stirrers allows finally to face these results with those obtained from standard EMC test.