Rapid magnetic resonance imaging using the Hankel tranform approach

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 reconstructs the two dimensional (2-D) image using either 1-D inverse Hankel transforms or a 2-D inverse Fourier transform. The main advantages of the proposed system are the potential for rapid imaging (not discussed here), the ability to trade-off acquisition time and SNR and resonant gradient circuits.