This paper introduces a new fusion method for magnetic resonance (MR) and ultrasound (US) images, which aims at combining the advantages of each modality, i.e., good contrast and signal to noise ratio for the MR image and good spatial resolution for the US image. The proposed algorithm is based on two inverse problems, performing a super-resolution of the MR image and a denoising of the US image. A polynomial function is introduced to model the relationships between the gray levels of the two modalities. The resulting inverse problem is solved using a proximal alternating linearized minimization framework. The accuracy and the interest of the fusion algorithm are shown quantitatively and qualitatively via evaluations on synthetic and experimental phantom data.