A greedy reconstruction algorithm for the identification of spin distribution

TL;DR

This paper introduces a greedy algorithm for reconstructing the probability distribution of a parameter in inhomogeneous spin ensembles using NMR, improving identifiability through optimized control protocols.

Contribution

The paper presents a novel greedy reconstruction algorithm that designs control protocols to enhance the identifiability of the spin distribution in NMR experiments.

Findings

Algorithm effectively reconstructs distributions in simulations

Optimized controls outperform random pulses

Identifiability linked to matrix invertibility

Abstract

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.