A greedy reconstruction algorithm for the identification of spin distribution

• URL: http://arxiv.org/abs/2108.11745v1
• Date: Thu, 26 Aug 2021 12:40:52 GMT
• Title: A greedy reconstruction algorithm for the identification of spin distribution
• Authors: S. Buchwald, G. Ciaramella, J. Salomon and D. Sugny
• Abstract summary: We show that the identifiability of a piecewise constant approximation of the probability distribution is related to the invertibility of a matrix. The algorithm aims to design specific controls which ensure that this matrix is as far as possible from a singular matrix.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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