Inversion of the Bloch transform in magnetic resonance imaging using asymmetric two-component inverse scattering

Abstract

In magnetic resonance imaging, the relation between the radio-frequency modulation of the magnetic field and the desired final magnetisation state is called the Bloch transform. Selective excitation then amounts to inverting this transform, which is highly nonlinear. Previous attempts to formulate this problem as an inverse scattering problem have restricted attention to solutions using reflectionless potentials. The author uses fast numerical algorithms for inverse scattering problems to obtain a much larger set of solutions. Numerical examples are included.