Theoretical analysis of the max/Median filter

Median filtering has been used successfully for extracting features from noisy one-dimensional signals; however, the extension of the one-dimensional case to higher dimensions has not always yielded satisfactory results. Although noise suppression is obtained, too much signal distortion is introduced and many features of interest are lost. In this paper, we introduce a multidimensional filter based on a combination of one-dimensional median estimates. It is shown that threshold decomposition holds for this class of filters, making the deterministic analysis simpler. Invariant signals to the filter, called root signals, consist of very low resolution features making this filter much more attractive than conventional median filters.