  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.
