Unsupervised multiobjective design for weighted median filters using genetic algorithm

In this paper, a new unsupervised design method of the weighted median filter (WMF) is proposed for recovering images from impulse noise. A design problem of WMFs is to determine a suitable window shape, and an appropriate weight for each element in the window. The purpose of the filter for the noise removal is generally to estimate the original values precisely for corrupted pixels while preserving the original values of non-corrupted pixels. WMF is required to output the image with higher preservation quality and higher restoration quality, however, these qualities often have a trade-off relation. Here, we formulate the design of WMF as a multi-objective optimization problem that treats the preservation performance and the restoration performance as trade-off functions. Through the experiments, we show our method obtains a wide variety of filters that have the high preservation performance or the high restoration performance at one search process. In addition, we also discuss how to select a good set of sophisticated filters from the designed filters.