  This paper is focused on deriving an optimal image smoother. The optimization
is done through the minimization of the norm of the Laplace operator in the
image coordinate system. Discretizing the Laplace operator and using the method
of Euler-Lagrange result in a weighted average scheme for the optimal smoother.
Satellite imagery can be smoothed by this optimal smoother. It is also very
fast and can be used for detecting the anomalies in the image. A real anomaly
detecting problem is considered for the Qom region in Iran. Satellite image in
different bands are smoothed. Comparing the smoothed and original images in
different bands, the maps of anomalies are presented. Comparison between the
derived method and the existing methods reveals that it is more efficient in
detecting anomalies in the region.
