Cyclic generalized projection MRI

Progress in the development of portable MRI hinges on the ability to use lightweight magnets that have non-uniform magnetic fields. An image encoding method and mathematical procedure for recovering the image from the NMR signal from non-uniform magnets with closed isomagnetic contours is given. Individual frequencies in an NMR signal from an object in a non-uniform magnetic field give rise to integrals of the object along contours of constant magnetic field: generalized projections. With closed isomagnetic field contours a simple, cyclic, direct reconstruction of the image from the generalized projections is possible when the magnet and RF transmit coil are held fixed relative to the imaged object while the RF receive coil moves. Numerical simulations, using the Shepp and Logan mathematical phantom, were completed to show that the mathematical method works and to illustrate numerical limitations. The method is numerically verified and exact reconstruction demonstrated for discrete mathematical image phantoms. Correct knowledge of the RF receive field is necessary or severe image distortions will result. The cyclic mathematical reconstruction method presented here will be useful for portable MRI schemes that use non-uniform magnets with closed isomagnetic contours along with mechanically or electronically moving the RF receive coils.