Methods and a system to unify reconstruction and motion estimation steps in first pass cardiac perfusion MRI include a global objective function that meets data consistency, spatial smoothness, motion and contrast dynamics constraints. The global objective decomposed into simpler sub-problems which include low pass filtering of a deformed object, TV shrinkage, analytical Fourier replacement and an l2 minimizing problem. A registration tool based on the local cross-correlation similarity measure and enabled to perform both rigid and flexile deformations, is applied. Registration parameters are tuned by rigid, semi rigid and flexible models at different stages of iterations. A system to perform the methods is also disclosed.