We introduce a novel technique for magnetic resonance image (MRI) restoration, using a physical model (spin equation). We determine a set of three basis images (proton density and nuclear relaxation times) from the MRI data using a nonlinear optimization method, and use those images to obtain restorations of the original image. MRIs depend nonlinearly on proton density, two nuclear relaxation times, T1 and T2, and two control parameters, echo time (TE) and relaxation time (TR). We model images as Markov random fields and introduce a maximum a posteriori restoration method, based on nonlinear optimization, which reduces noise while preserving resolution.