In this work, a two-step technique for constructing a super-resolution (SR) image from a single multi-valued low-resolution (LR) input image is proposed. The problem of SR is treated from the perspective of image geometry-oriented interpolation. The first step consists of computing the image geometry of the LR image by using the grouplet transform. Having well represented the geometry of each color channel in the LR image, we propose a grouplet-based structure tensor whose role is to couple the geometrical information of the different image color components. In a second step, a functional is defined on the multispectral geometry defined by this structure tensor. The minimization of this functional insures the synthesize of the SR image. The proposed super-resolution algorithm outperforms the state-of-the-art methods in terms of visual quality of the interpolated image.