A SPIRED code for the reconstruction of spin distribution

In Nuclear Magnetic Resonance (NMR), it is of crucial importance to have an accurate knowledge of the spin probability distribution corresponding to inhomogeneities of the magnetic fields. An accurate identification of the sample distribution requires a set of experimental data that is sufficiently rich to extract all fundamental information. These data depend strongly on the control fields (and their number) used experimentally to perturb the spin system. In this work, we present and analyze a greedy reconstruction algorithm, and provide the corresponding SPIRED code, for the computation of a set of control functions allowing the generation of data that are appropriate for the accurate reconstruction of a sample probability distribution. In particular, the focus is on NMR and spin dynamics governed by the Bloch system with inhomogeneities in both the static and radio-frequency magnetic fields applied to the sample. We show numerically that the algorithm is able to reconstruct non trivial joint probability distributions of the two inhomogeneous Hamiltonian parameters. A rigorous convergence analysis of the algorithm is also provided.