  Optical nonlinear Fourier transform-based communication systems require an
accurate estimation of a signal's nonlinear spectrum, computed usually by
piecewise approximation methods on the signal samples. We propose an algorithm,
named successive eigenvalue removal, to improve the spectrum estimation of a
multi-soliton pulse. It exploits a property of the Darboux transform that
allows removing eigenvalues from the nonlinear spectrum. This results in a
smaller pulse duration and smaller bandwidth. The spectral coefficients are
estimated successively after removing the eigenvalues of a signal. As a
beneficial application, we show that the algorithm decreases the computational
complexity by iteratively reducing the pulse duration.
