This paper introduces a novel algorithm for the fusion of magnetic resonance and ultrasound images, based on a patch-wise polynomial model relating the gray levels of the two imaging systems (called modalities). Starting from observation models adapted to each modality and exploiting a patch-wise polynomial model, the fusion problem is expressed as the minimization of a cost function including two data fidelity terms and two regularizations. This minimization is performed using a PALM-based algorithm, given its ability to handle nonlinear and possibly non-convex functions. The efficiency of the proposed method is evaluated on phantom data. The resulting fused image is shown to contain complementary information from both magnetic resonance (MR) and ultrasound (US) images, i.e., with a good contrast (as for the MR image) and a good spatial resolution (as for the US image).