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

Abstract: 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.