We propose to apply three of the multiple variants of the 2 and 3-dimensional of the cosine transform. We consider the Lie groups leading to square lattices, namely SU(2)xSU(2) and O(5) in the 2-dimensional space, and the cubic lattice SU(2)xSU(2)xSU(2) in the 3-dimensional space. We aim at evaluating the benefits of some Discrete Group Transform (DGT) techniques, in particular the Continuous Extension of the Discrete Cosine Transform (CEDCT), and at developing new techniques that refine image quality: this refinement is called the high-resolution process. This highest quality is useful to increase the effectiveness of standard features extraction, fusion and classification algorithms. All algorithms based on the 2 and 3-dimensional DGT have the advantage to give the exact value of the original data at the points of the grid lattice, and interpolate well the data values between the grid points. The quality of the interpolation is comparable with the most efficient data interpolation, which are currently used for purposes of image zooming. In our first application, we use DGT techniques to refine fully polarimetric radar images, and to increase the effectiveness of standard features extraction algorithms. In our second application, we apply DGT techniques on medical images extracted from a system and a Magnetic Resonance Imaging (MRI) system.