22 May 2002 Adaptive Mallow's optimization for weighted median filters
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Abstract
This work extends the idea of spectral optimization for the design of Weighted Median filters and employ adaptive filtering that updates the coefficients of the FIR filter from which the weights of the median filters are derived. Mallows' theory of non-linear smoothers [1] has proven to be of great theoretical significance providing simple design guidelines for non-linear smoothers. It allows us to find a set of positive weights for a WM filter whose sample selection probabilities (SSP's) are as close as possible to a SSP set predetermined by Mallow's. Sample selection probabilities have been used as a basis for designing stack smoothers as they give a measure of the filter's detail preserving ability and give non-negative filter weights. We will extend this idea to design weighted median filters admitting negative weights. The new method first finds the linear FIR filter coefficients adaptively, which are then used to determine the weights of the median filter. WM filters can be designed to have band-pass, high-pass as well as low-pass frequency characteristics. Unlike the linear filters, however, the weighted median filters are robust in the presence of impulsive noise, as shown by the simulation results.
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Raghu Rachuri, Raghu Rachuri, Sathyanarayana S. Rao, Sathyanarayana S. Rao, } "Adaptive Mallow's optimization for weighted median filters", Proc. SPIE 4667, Image Processing: Algorithms and Systems, (22 May 2002); doi: 10.1117/12.468013; https://doi.org/10.1117/12.468013
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