Mathematical Foundations for Magnetic Resonance Imaging

摘要

Over the past decade, the technical development of Magnetic Resonance Imaging(MRI) has been very rapid. This report provides the theoretical framework for the understanding and the design of new imaging sequences, and points out limitations of achievable imaging speed, signal/noise-ratio, image resolution etc. imposed by the imaging hardware, but also by the laws of physics. A relatively new imaging technique, the spiral scan, which may reduce the imaging time without increased demands for gradient rise time and data sampling speed, is thoroughly studied analytically, and with computer simulations. This method further promises a better suppression of artifacts caused by motion, than the commonly used spin echo and gradient echo methods. The computer simulations also implies an improved signal/noise-ratio. A method for design of radio-frequency pulses with arbitrary frequency response is also discussed. The method is based on the principles for digital filter design. An improved signal uniformity in 3-dimensional images was demonstrated using a radio-frequency pulsed of this design.