A Direct MRJ Hankel Transform System Using Rotating Gradients

A novel magnetic resonance imaging system is explored which uses data collected in the presence of quadrature phase sinusoidal gradients along an excited plane. It is shown that the resulting magnetization signal (FID) is a sum of the Hankel transforms of the radial modulators of the imaged plane. An efficient processing system is suggested which extracts the different Hankel transforms from the received signal. These transforms are used to directly reconstruct the two-dimensional (2-D) image using either 1-D inverse Hankel transforms or a 2-D inverse Fourier transform. A "snapshot" data acquisition procedure is described which enables the collection of all the required data from a signal FID. The main advantages of the proposed system are rapid acquisition time, the ability to trade-off acquisition time, and SNR and resonant gradient circuits.