2 APPLICATIONS OF WAVELET TRANSFORMS IN MAGNETIC-RESONANCE-IMAGING

This paper describes two different applications of wavelet transforms in magnetic resonance imaging (MRI). In each case, the use of wavelets offers tangible benefits over the traditional Fourier transform based imaging. These stem from the simultaneous time and frequency localization properties of the wavelets. The first application utilizes the localization properties of wavelets to acquire single T2 weighted images in times which are short relative to current methods. An interesting combinatorial scheduling problem arises from the multiscale structure inherent in the formulation of this procedure. Its solution is sketched and applied to the imaging process. The second example is a technique for potentially "instant" imaging. Image acquisition is modeled as an inverse wavelet transform of the spin density in the region in question. Signal acquisition takes place in as few as one or two echoes after the excitation by radio frequency (RF) pulses designed to excite a moving band of spins in a slice. These sweeping RF pulses excite strips of spins which rephase at different times during acquisition. They replace phase-encoding gradients; no fast pulsed gradients are required as in echo planar imaging, which is the "instant" imaging technique presently being developed by MR researchers. Some applications of these techniques in medical imaging are described, with specific examples presented by means of simulations. Comparisons with corresponding traditional methods are given.