An adaptive filter for removal of noise in interferometrically derived digital elevation models

A low-pass filter that chooses the window size depending on the degree of smoothing required by detecting isolated as well as clustered noise in the DEM is developed and tested. In the noise-free case, the standard deviation of the values of the pixels inside a window increases as the size of the window increases, due to the inclusion of height values that are either lower or higher than the central pixel value. If the standard deviation of the window pixels decreases as the size of the filter window increases then the presence of noise, either isolated or clustered, is indicated. Changes in the value of the standard deviation of the window pixels as the window size is increased can thus be used to fix an appropriate window size. Given a specific window size, the ´sigma operator´ (Lee, 1983) is used to produce a ´noise-free´ estimate of the central pixel value. In this operation, the values of pixels within the window that lie between an upper and a lower limit are averaged. The median is preferred as the measure of central tendency in determining the lower and the upper limit, because the value of the median is less affected by the presence of a minority of aberrant pixel values, whereas the mean value is computed from the values of all pixels in the window, including noise pixels. Hence the smoothing operation employed in this study is called the ´modified sigma operator´. The performance of the modified sigma operator is compared with that of a median filter in removing noise present in InSAR DEM. The performance of the filter was evaluated by comparing the distribution of root mean square (RMS) error against percentage of pixels (Balan and Mather, 2000), for unfiltered and filtered DEMs. The results show that the adaptive lowpass filter is more effective in reducing noise in the DEM