Fast Magnetic Resonance Imaging with Simultaneously Oscillating and Rotating Fiell Gradients

We present an approach to magnetic resonance imaging employing a magnetic field gradient that rotates 180 degrees in the image plane while the gradient magnitude oscillates rapidly during the rotation. A single free induction decay recorded during this rotation contains all the information needed to reconstruct a two-dimensional image. In effect, each sinusoidal oscillation of the gradient provides information corresponding to one projection in more conventional Fourier-projection approaches. Since the data acquisition can be achieved in a period less than T2, the method offers the potential of great speed, which is limited only by the gradient modulation frequency. An explicit image reconstruction formula is derived that gives, when evaluated, a reconstruction of the magnetization equal to the true magnetization convolved with a space-invariant point spread function. This point spread function is derived and characterizes the resolving power and sidelobe response of the technique. Moreover, we derive a similar reconstruction formula which is valid when known inhomogeneities in the static field H0 and T2 are present. Finally, we show how the general approach can be extended to three dimensions.