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

Optimal Image Smoothing and Its Applications in Anomaly Detection in Remote Sensing