  This paper presents a fast algorithm to solve a spectral estimation problem
for two-dimensional random fields. The latter is formulated as a convex
optimization problem with the Itakura-Saito pseudodistance as the objective
function subject to the constraints of moment equations. We exploit the
structure of the Hessian of the dual objective function in order to make
possible a fast Newton solver. Then we incorporate the Newton solver to a
predictor-corrector numerical continuation method which is able to produce a
parametrized family of solutions to the moment equations. We have performed two
sets of numerical simulations to test our algorithm and spectral estimator. The
simulations on the frequency estimation problem shows that our spectral
estimator outperforms the classical windowed periodograms in the case of two
hidden frequencies and has a higher resolution. The other set of simulations on
system identification indicates that the numerical continuation method is more
robust than Newton's method alone in ill-conditioned instances.
