Decision-based fuzzy image restoration for noise reduction based on evidence theory

A novel decision-based fuzzy averaging (DFA) filter consisting of a D–S (Dempster–Shafer) noise detector and a two-pass noise filtering mechanism is presented in this paper. The proposed filter can effectively deal with impulsive noise, and a mix of Gaussian and impulsive noise. Bodies of evidence are extracted, and the basic belief assignment is developed using the simple support function, which avoids the counter-intuitive problem of Dempster’s combination rule. The combination belief value is the decision rule for the D–S noise detector. A fuzzy averaging method, where the weights are constructed using a predefined fuzzy set, is developed to achieve noise cancellation. A simple second-pass filter is employed to improve the final filtering performance. Experimental results confirm the effectiveness of the new DFA filter both in suppressing impulsive noise as well as a mix Gaussian and impulsive noise and in improving perceived image quality.

Research highlights
► Bodies of evidence are extracted, and the basic belief assignment is developed using the simple support function, which avoids the counter-intuitive problem of Dempster’ss combination rule.
► The combination belief value is the decision rule for the noise detector.
► A fuzzy averaging method is developed to achieve noise cancellation.
► The proposed filter can effectively deal with impulsive noise and a mix of Gaussian and impulsive noise.