  This paper investigates the possibility of reconstruction of images
considering that they are sparse in the DCT transformation domain. Two
approaches are considered. One when the image is pre-processed in the DCT
domain, using 8x8 blocks. The image is made sparse by setting the smallest DCT
coefficients to zero. In the other case the original image is considered
without pre-processing, assuming the sparsity as intrinsic property of the
analyzed image. A gradient based algorithm is used to recover a large number of
missing pixels in the image. The case of a salt-and-paper noise affecting a
large number of pixels is easily reduced to the case of missing pixels and
considered within the same framework. The reconstruction of images affected
with salt-and-paper impulsive is compared with the images filtered using a
median filter. The same algorithm can be used considering transformation of the
whole image. Reconstructions of black and white and colour images are
considered.
