Multidimensionally encoded magnetic resonance imaging

Magnetic resonance imaging (MRI) typically achieves spatial encoding by measuring the projection of a q‐dimensional object over q‐dimensional spatial bases created by linear spatial encoding magnetic fields (SEMs). Recently, imaging strategies using nonlinear SEMs have demonstrated potential advantages for reconstructing images with higher spatiotemporal resolution and reducing peripheral nerve stimulation. In practice, nonlinear SEMs and linear SEMs can be used jointly to further improve the image reconstruction performance. Here, we propose the multidimensionally encoded (MDE) MRI to map a q‐dimensional object onto a p‐dimensional encoding space where p > q. MDE MRI is a theoretical framework linking imaging strategies using linear and nonlinear SEMs. Using a system of eight surface SEM coils with an eight‐channel radiofrequency coil array, we demonstrate the five‐dimensional MDE MRI for a two‐dimensional object as a further generalization of PatLoc imaging and O‐space imaging. We also present a method of optimizing spatial bases in MDE MRI. Results show that MDE MRI with a higher dimensional encoding space can reconstruct images more efficiently and with a smaller reconstruction error when the k‐space sampling distribution and the number of samples are controlled. Magn Reson Med, 2013. © 2012 Wiley Periodicals, Inc.