Abstract
The problem in nuclear magnetic resonnance imaging is to control the orientation of the nuclear magnetization vector. The nuclear magnetic momenta are initially oriented by a static magnetic field. A radio-frequency magnetic field is then added to the system. Under the influence of this last field, the nuclear magnetization changes in time. The basic equations of the system show a bilinear form with a so(3) Lie algebra structure. Lie algebra techniques are first used to get a numerically simpler system. An iterative procedure is then applied in order to determine the input radio-frequency magnetic field design for the problem of slice selection, in which one wants to obtain a given spatial profile of the nuclear magnetization vector.
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