Sparse Component Analysis (SCA) in Random-valued and Salt and Pepper   Noise Removal
  In this paper, we propose a new method for impulse noise removal from images. It uses the sparsity of images in the Discrete Cosine Transform (DCT) domain. The zeros in this domain give us the exact mathematical equation to reconstruct the pixels that are corrupted by random-value impulse noises. The proposed method can also detect and correct the corrupted pixels. Moreover, in a simpler case that salt and pepper noise is the brightest and darkest pixels in the image, we propose a simpler version of our method. In addition to the proposed method, we suggest a combination of the traditional median filter method with our method to yield better results when the percentage of the corrupted samples is high. 
Hadi. Zayyani, Seyyedmajid Valiollahzadeh, Massoud. Babaie-Zadeh