Документ взят из кэша поисковой машины. Адрес
оригинального документа
: http://www.stsci.edu/stsci/meetings/irw/proceedings/molinar.dir/section3_4.html
Дата изменения: Mon Apr 18 22:44:17 1994 Дата индексирования: Sun Dec 23 19:49:10 2007 Кодировка: |
Consider an image with no stars but only with regions of smoothly varying
luminosity. We then expect and
to be spatially smooth. Probably the simplest probability models
that can be used to model smoothness are spatial autoregressions
(Ripley 1981).
The conditional autoregression (CAR) model is defined by
where is the unknown hyper-parameter, matrix
is such that
if cells
and
are spatial neighbors (pixels
at distance one) and zero otherwise, and scalar
is just less
than 0.25. The term
represents in matrix notation the sum of
squares of the values
minus
times the sum of
for neighboring pixels
and
.
The parameters can be interpreted by the following expressions describing the conditional distribution
where the suffix `' denotes the four neighbor
pixels at distance one from pixel
. The parameter
measures
the smoothness of the `true' image.
Assuming a toroidal edge correction, the eigenvalues of the matrix
are
. So, the density of
f has the form
where ,
.
This prior model can be easily modified to work at log scale, which is the right scale for the deconvolution of galaxies (Molina et al. 1992a). Furthermore, this model can also take into account the existence of different objects in the image (Molina et al. 1992b).
Let us now examine the prior model used in the R-L restoration method.
This method aims at maximizing when this conditional
distribution is Poissonian. Under the Bayesian framework this is the same
as maximizing the posterior distribution for the prior model
, together with the
Poissonian noise model. The meaning of this prior is simple; all possible
restorations have the same probability.