“Is there life beyond Earth?“ This question has captivated humanity for centuries, driving efforts to discover planets beyond our solar system. Among the various techniques developed for exoplanet detection, direct imaging stands out as one of the most promising, as it allows for the direct capture of signals from planets themselves. Direct imaging offers crucial insights into planetary systems but encounters significant challenges, primarily due to the close angular separation between faint planetary signals and the bright host stars. Even with state-of-the-art instruments, advanced post-processing techniques are required to remove quasi-static speckles that obscure planetary signals. This thesis tackles these challenges by proposing novel algorithms and models using low-rank approximations aimed at enhancing exoplanet detection through the use of angular differential imaging datasets. The datasets, obtained from ground-based telescopes, track the host star over a few hours of a night, capturing the planet’s motion induced by Earth’s rotation. These three-dimensional datasets in the time and spatial domains contain both planetary signals and quasi-static speckles and star signals, which require separation for accurate detection. The core contributions of this work involve developing methods to isolate and subtract the quasi-static components, enhancing the visibility of planetary signals. Techniques based on using Laplacian distribution rather than Gaussian, which we propose in this thesis, play a pivotal role. Additionally, we proposed alternative solutions such as sparse modeling and matrix completion—where planetary signals are removed and later reconstructed—to improve detection accuracy. All proposed methods were thoroughly tested on both real and synthetic datasets, and their performance was evaluated against well-known algorithms in the literature, demonstrating significant improvements. (FSA - Sciences de l'ingénieur) -- UCL, 2025