  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.
