Direct imaging of exoplanets relies on advanced post-processing techniques to differentiate planetary signals from the bright stellar point spread function (PSF) and quasi-static speckle noise. While angular-spectral differential imaging (ASDI) with integral field spectrographs has significantly enhanced the capability to induce diversity in high-contrast imaging (HCI) observations, current post-processing methods like matrix Principal Component Analysis (PCA) are limited in their ability to fully exploit the multi-modal structure of ASDI data.

This thesis introduces tensor decomposition methods as generalizations of matrix-PCA for modeling the coronagraphic PSF in ASDI observations. These methods preserve the higher-order structure of ASDI data, enabling the modeling of complex cross-modal interactions while maintaining the strengths of PCA-based approaches. By extending PCA to higher-order tensors, these methods offer a more natural representation of the multi-dimensional nature of ASDI data.

The proposed tensor methods are evaluated using both synthetic and real observations from the SPHERE instrument on the VLT. They successfully recover known exoplanets in benchmark systems like HR 8799 and $\beta$ Pictoris, and detect a new collision-induced feature in the AU Microscopii debris disk. Notably, a new sub-stellar companion candidate is identified in the HD 108767 B system. Their performance is assessed through both quantitative metrics and qualitative analysis of residual images. Results demonstrate that tensor methods are competitive with matrix-PCA, outperforming it at small angular separations where speckle noise is most problematic.

This work establishes tensor decompositions as a powerful tool for HCI post-processing, offering increased flexibility and interpretability of factorizations while building upon the established framework of PCA. Furthermore, this approach lays the groundwork for tractable deep learning techniques on HCI datasets, and more generally for higher-order tensor methods in direct exoplanet imaging.