Partition belief median filter based on Dempster–Shafer theory for image processing

A novel median-type filter controlled by evidence fusion is proposed for removing noise from images. 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 a noise is considered. The filter proposed here is obtained as a weighted sum of the current pixel value and the output of the median filter, and the weight is set based on the belief value of the input signal sequence. 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. Moreover, to improve the performance, the new filter is recursively implemented. Experimental results have demonstrated that the proposed filter can outperform many well-accepted median-based filters in preserving image details while effectively suppressing impulsive noises, and it also works satisfactorily in reducing Gaussian as well as the mixture of Gaussian and impulsive noise.