Greedy reconstruction algorithm for the identification of spin distribution

We propose a greedy reconstruction algorithm to find the probability distribution of a parameter characterizing an inhomogeneous spin ensemble in nuclear magnetic resonance. 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 in different examples. A systematic comparison with respect to random constant pulses is done.