Magnetic resonance imaging (MRI) at field strengths higher than 1.5 Tesla suffers reduced quality due to severe perturbations caused by the inhomogeneity of the RF excitation field in the human body. If quantitative measurements are done, it is essential to correct these inhomogeneities, in order to obtain meaningful results. Several MRI methods exist to map the distribution of the actual flip angle within an investigated slice. The determined flip angle distribution is proportional to the active component of B1 and therefore also called B1-map. All in-vivo B1-mapping techniques suffer major perturbations and artifacts. Using maps for correction without appropriate post-processing would introduce new errors at the positions of these artifacts. This work investigates the performance of an elaborate variational smoothing approach, compared to the standard median filter. It gives examples on the derivation, implementation and application of the correction algorithms. Researchers interested in high-field MRI and quantitative studies will find this book useful.