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.