OPTIMAL WEIGHTED MEDIAN FILTERING UNDER STRUCTURAL CONSTRAINTS

A new expression for the output moments of weighted median filtered da ta is derived in this paper. The noise attenuation capability of a wei ghted median filter can now be assessed using the L-vector and M-vecto r parameters in the new expression. The second major contribution of t he paper is the development of a new optimality theory for weighted me dian filters. This theory is based on the new expression for the outpu t moments, and combines the noise attenuation and some structural cons traints on the filter's behavior. In certain special eases, the optima l weighted median filter can be obtained by merely solving a set of li near inequalities. This leads in some cases to closed form solutions f or optimal weighted median filters. Some applications of the theory de veloped in this paper, in 1-D signal processing and image processing a re discussed. Throughout the analysis, some striking similarities are pointed out between linear FIR filters and weighted median filters.