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Planet-disk interactions in protoplanetary disks can significantly reshape the disk and influence the planet formation process. Studying these interactions is therefore crucial to better understand the formation and evolution of planetary systems. In high-contrast imaging (HCI), after most of the starlight and aberrations caused by atmospheric turbulence have been removed by the coronagraph and adaptive optics, residual atmospheric speckles and quasi-static speckles–unseen by the adaptive optics system or steaming from imperfection of the optics system itself– remain. These speckles (referred to as PSF) must be removed to reveal the faint circumstellar signal hidden in the vicinity of the star. PSF modeling and subtraction is a particularly challenging step in data post-processing. Distinguishing real astrophysical signals from artifacts, and separating point sources from filtered extended structures, remains difficult. Understanding the limitations of HCI post-processing is essential for reliably interpreting disk morphologies and identifying planet candidates. In this manuscript, we aim to analyze, compare, and develop new methods to improve the robustness of disk imaging, with a focus on algorithms tailored for the observation of disks using the Angular Differential Imaging (ADI) strategy. First, we highlight the problem of flux invariance in presence of field rotation, a major bias of ADI that has not been addressed by previous approaches. In response, we propose the MUSTARD algorithm, an inverse problem approach designed for correcting flux invariance to rotation, and we evaluate it against other approaches using a dedicated testing pipeline. The results show that the effectiveness of the prior to the correction of flux invariance to rotation is hindered by our limited knowledge of the morphological and temporal properties of the stellar speckle halo. Second, we observe that the Iterative Principal Component Analysis (IPCA) approach demonstrates great robustness and practicality, despite not correcting for the flux-invariance limitation. In light of this limitation, we propose extending IPCA to combine ADI and RDI (referred to as ARDI), mitigating ADI limitations by incorporating reference frames. Our results demonstrate that ARDI with IPCA improves the quality of recovered disk images and the sensitivity to planets embedded in disks, compared to ADI or RDI individually. Finally, we apply our methods MUSTARD and IPCA-ARDI to real datasets. With MUSTARD, we analyze the arm-like structure in PDS 70, tracking its motion over six years, and investigate the possible origins of this apparent feature. Using IPCA-ARDI, we review planet candidates in several systems with embedded disks exhibiting substructures. No planet candidate could be confirmed, either due to insufficient evidence to reach a conclusive interpretation or because they appear to be clear false positives.