Then, we may use a demodulation procedure to estimate the amplitudes
of the harmonic components :

and similarly :

where the dimensions of the observed image are .
Next we
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
and the
can be easily estimated using standard techniques (Hough transform).

A procedure of demodulation of the **evanescent component** provides estimates of the 1-D sequences
and
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.