Then, we may use a demodulation procedure to estimate the amplitudes
of the harmonic components :
where the dimensions of the observed image are .
subtract the estimated harmonic component from the observed signal
y(n,m) and repeat this procedure iteratively until all harmonic
components whose magnitude is higher than the foregoing test threshold
are extracted. The residual field is the purely-indeterministic component of the texture.
The frequency parameter
can be easily estimated using standard techniques (Hough transform).
A procedure of demodulation of the evanescent component provides estimates of the 1-D sequences
of each evanescent field. Finally,
these sequences are fitted with their 1-D AR models. The removal of
all evanescent components of the field leaves us with a residual field
which is the purely-indeterministic component of the texture.
The parameters of the purely-indeterministic component are
estimated using a computationally efficient algorithm for estimating
its moving average model. The algorithm first fits a 2-D NSHP AR model
to the observed field, by using a ML algorithm. Note that in this
case, where all the deterministic components have already been removed, the
procedure of obtaining a maximum-likelihood estimate of the AR model
parameters is reduced to a solution of a linear least squares
problem. In the second stage, the estimated parameters of the AR model
are employed to compute the parameters of the moving average model, through a least squares solution of a system of linear equations.