Abstarct: Medical image processing plays a crucial role in the diagnosis and analysis of diseases, and the accuracy of this process is directly dependent on the quality of feature extraction and image reconstruction. Given the complex, noisy, and multimodal nature of medical data, the use of efficient mathematical methods for dimensionality reduction and extraction of meaningful information from images is of particular importance. Among these methods, matrix decomposition techniques have received significant attention as effective tools for image data analysis. In this thesis, Singular Value Decomposition (SVD) and Generalized Singular Value De- composition (GSVD) are employed for the analysis of medical images. In the first part, a GSVD-baxsed method is proposed for feature extraction from multimodal medical im- ages with the aim of improving image classification performance. This method seeks to simultaneously extract shared and distinctive information from images and provide a more compact representation of the data. In the second part, the application of low-rank approximation baxsed on SVD for MRI image reconstruction is investigated in order to analyze the impact of dimensionality reduction on image quality. The obtained results indicate that the use of singular value decomposition-baxsed methods can contribute to improving the accuracy of medical image analysis and classification, as well as enhancing the quality of MRI image reconstruction. Overall, this study demon- strates that leveraging matrix decomposition tools can play an effective role in advancing medical image processing and supporting diagnostic systems.