Magnetic Resonance Imaging with Nonlinear Gradient Fields : Signal Encoding and Image Reconstruction Within the past few decades magnetic resonance imaging has become one of the most important imaging modalities in medicine. For a reliable diagnosis of pathologies further technological improvements are of primary importance. This text deals with a radically new approach of image encoding: The fundamental principle of gradient linearity is challenged by investigating the possibilities of acquiring anatomical images with the help of nonlinear gradient fields. Besides a thorough theoretical analysis with a focus on signal encoding and image reconstruction initial hardware implementations are tested using phantom as well as in vivo measurements. Several applications are presented that give an impression about the implications that this technological advancement may have for future medical diagnostics. Contentsn Image Reconstruction in MRIn Nonlinear Gradient Encoding: PatLoc Imagingn Presentation of Initial Hardware Designsn Basics of Signal Encoding and Image Reconstruction in PatLoc Imagingn Direct and Iterative Reconstruction Techniques Target Groups· Researchers and students in the fields of physics mathematics medicine and engineering with interest in imaging technology.· Industrial practitioners with focus on medical imaging. About the AuthorGerrit Schultz studied Physics and Mathematics at the Universities of Heidelberg and Geneva. He joined the Medical Physics Group at the University Medical Center in Freiburg in 2007 where he is currently working as a postdoctoral researcher.