The major drawback of recent image filtering algorithms for removing impulse noise is lack of the ability of preserving the image details and edges which are smaller than the size of filtering windows.To alleviate this limitation

a new image filtering algorithm using a double noise detector and edge-preserving regularization function is proposed in this paper.The proposed filter has a two-stage scheme:detecting noise and removing noise.In order to improve accurate rate of noise detection

noise candidates identified with the noise detection algorithm of the adaptive median filter are judged again by local fuzzy membership function

and then a convex objective function composed of 

1

data-fidelity term and edge-preserving regularization function is employed to deal with noise candidates.The input of edge-preserving regularization function is adaptively selected to take full advantage of local features of the image.The image corrupted by noise is restored successfully as the convex objective function gets its minimum.Experimental results show the superiority of the proposed filter in terms of the ability of removing noise and preserving the details and edges of the image in comparison with some recent methods

it is also shown that even at a very high noise level (＞70%) details and edges of the original image are preserved very well with our method.