Adaptive Median Type Filter Based on Dempster-Shafer Evidence Theory for Fuzzy Image Restoration

An adaptive median-type filter controlled by evidence fusion is proposed for fuzzy image restoration. The fusion of evidence based on the Dempster-Shafer evidence theory, providing a way to deal with the uncertainty in the evidence fusion, indicates to what extent an impulsive noise is considered. The setting membership function of impulsive corruption is based on the belief value of the input signal sequence, and the weight is indicated for filtering operation. The efficient step-like function is used to partition the belief space, and the least mean square (LMS) algorithm is applied to obtain the optimal weight for each block. Experimental results have demonstrated that the proposed filter can outperform many well-accepted median based filters in preserving image details while effectively suppressing impulsive noise.