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arXiv · 2108.11745

A greedy reconstruction algorithm for the identification of spin distribution

S. Buchwald·G. Ciaramella·J. Salomon·D. Sugny
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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.

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S. Buchwald, G. Ciaramella, J. Salomon, D. Sugny. 2021-08-26. A greedy reconstruction algorithm for the identification of spin distribution. https://doi.org/10.1103/physreva.104.063112

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