Impulse noise removal using sparse representation with fuzzy weights

Many impulse noise removal algorithms do not reach good denoising performance mainly due to the imperfect filters they adopted. In this paper, the popular used sparse representation model is extended for impulse noise removal by using a fuzzy weight matrix. This fuzzy weight is used to describe the noise-like level of the current pixel, and to determine how much information of this pixel should be used in the sparse land model. Besides, a regularization term which counts the proximity between the reconstructed image and the noisy image is also added into the sparse model. This makes the proposed model more robust to the noise detector which generates the fuzzy weight matrix. Moreover, unlike other sparse model, the dictionary used in our model is trained from some reference images that keep the similar structure information of the original image. Therefore, it is more suitable for reconstructing the original image. Simulation results show that our method is superior to all the tested state-of-the-art impulse noise removal methods.