EXACT HALF PULSE SYNTHESIS VIA THE INVERSE SCATTERING TRANSFORM

A method of obtaining an arbitrary, admissible transverse magnetization profile as the summed response of two, self refocused selective “half pulse” excitations for use in, e.g., magnetic resonance imaging pulse generation. The problem of finding the pair of half pulses is rephrased in the inverse scattering formalism and a simple closed form algorithm for the solution is given, provided the target transverse profile has constant phase (modulo 180°). The problem has a unique low energy solution for sufficiently small, complex valued data, and an algorithm for finding the solution is provided. This solution is used to generate pairs of half pulses for given target transverse profiles.