Thresholding noise-free ordered mean filter based on Dempster-Shafer theory for image restoration

This work proposes a new decision-based filter, the thresholding noise-free ordered mean (TNOM) filter based on the Dempster-Shafer (D-S) evidence theory, to preserve more details of images than can other decision-based filters, while effectively suppressing impulse noise. The new filter mechanism is composed of an efficient D-S impulse detector and a noise filter that works by estimating the central noise-free ordered mean (CNOM) value. The D-S evidence theory provides a way to deal with the uncertainty in the evidence and information fusion. Pieces of evidence are extracted, and the mass functions defined using the local information in the filter window. Then, the decision rule is applied to determine whether noise exists, according to the final combined belief value. If a pixel is detected to be a corrupted pixel, then the proposed filter will be triggered to replace it. Otherwise, the pixel is kept unchanged. With respect to the noise suppression of noise on both fixed-valued and random-valued impulses without smearing the fine details in the image, extensive simulation results reveal that the proposed scheme significantly outperforms other decision-based filters.