We propose a greedy reconstruction algorithm to find the probability distribution of a parameter characterizing an inhomogeneous spin ensemble in Nuclear Magnetic Resonace. The identification is based on the application of a number of constant control processes during a given time for which the final ensemble magnetization vector is measured. From these experimental data, we show that the identifiability of a piecewise constant approximation of the probability distribution is related to the invertibility of a matrix which depends on the different control protocols applied to the system. The algorithm aims to design specific controls which ensure that this matrix is as far as possible from a singular matrix. Numerical simulations reveal the efficiency of this algorithm on different examples. A systematic comparison with respect to random constant pulses is done.
@article{arxiv.2108.11745,
title = {A greedy reconstruction algorithm for the identification of spin distribution},
author = {S. Buchwald and G. Ciaramella and J. Salomon and D. Sugny},
journal= {arXiv preprint arXiv:2108.11745},
year = {2021}
}