Abstract. We introduce a novel technique for Magnetic Resonance Image (MRI) restoration, using a physical model (spin equation) and corresponding basis images. We determine the basis images (proton density and nuclear relaxation times) from the MRI data and use them to obtain excellent restorations.Magnetic Resonance Images depend nonlinearly on proton density, p, two nuclear relaxation times, T1 and Tz, and two control parameters, TE and TR. We model images a Markov random fields and introduce two maximum a posteriori (MAP) restorations; quadratic smoothing and a nonlinear technique. We also introduce a novel method of global optimization necessary for the nonlinear technique.