Optimal weighted median filtering under structural constraints
- 1 March 1995
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Signal Processing
- Vol. 43 (3) , 591-604
- https://doi.org/10.1109/78.370615
Abstract
A new expression for the output moments of weighted median filtered data is derived in this paper. The noise attenuation capability of a weighted median filter can now be assessed using the L-vector and M-vector parameters in the new expression. The second major contribution of the paper is the development of a new optimality theory for weighted median filters. This theory is based on the new expression for the output moments, and combines the noise attenuation and some structural constraints on the filter's behavior. In certain special eases, the optimal weighted median filter can be obtained by merely solving a set of linear inequalities. This leads in some cases to closed form solutions for optimal weighted median filters. Some applications of the theory developed in this paper, in 1-D signal processing and image processing are discussed. Throughout the analysis, some striking similarities are pointed out between linear FIR filters and weighted median filtersKeywords
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