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. Program summary: Program title: SPIRED CPC Library link to program files:: https://doi.org/10.17632/6fsmzp6srg.1 Programming language: MATLAB Nature of problem:: Identify the sample probability distribution corresponding to inhomogeneties of the magnetic field in Nuclear Magnetic Resonance from experimental data. The data depends strongly on the control fields and their number, and needs to be sufficiently rich in order to extract all fundamental information. Solution method: Use greedy reconstruction algorithms to compute a set of control functions that allows the generation of data that are appropriate for an accurate reconstruction of the sample distribution. Additional comments including restrictions and unusual features: Some routines in the SPIRED code use MATLAB's fmincon-solver, which requires MATLAB's Optimization Toolbox to be installed.
A SPIRED code for the reconstruction of spin distribution
Ciaramella G.;
2024-01-01
Abstract
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. Program summary: Program title: SPIRED CPC Library link to program files:: https://doi.org/10.17632/6fsmzp6srg.1 Programming language: MATLAB Nature of problem:: Identify the sample probability distribution corresponding to inhomogeneties of the magnetic field in Nuclear Magnetic Resonance from experimental data. The data depends strongly on the control fields and their number, and needs to be sufficiently rich in order to extract all fundamental information. Solution method: Use greedy reconstruction algorithms to compute a set of control functions that allows the generation of data that are appropriate for an accurate reconstruction of the sample distribution. Additional comments including restrictions and unusual features: Some routines in the SPIRED code use MATLAB's fmincon-solver, which requires MATLAB's Optimization Toolbox to be installed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
