  Over the last decades, images have become an important source of information
in many domains, thus their high quality has become necessary to acquire better
information. One of the important issues that arise is image denoising, which
means recovering a signal from inaccurately and/or partially measured samples.
This interpretation is highly correlated to the compressive sensing theory,
which is a revolutionary technology and implies that if a signal is sparse then
the original signal can be obtained from a few measured values, which are much
less, than the ones suggested by other used theories like Shannon's sampling
theories. A strong factor in Compressive Sensing (CS) theory to achieve the
sparsest solution and the noise removal from the corrupted image is the
selection of the basis dictionary. In this paper, Discrete Cosine Transform
(DCT) and moment transform (Tchebichef, Krawtchouk) are compared in order to
achieve image denoising of Gaussian additive white noise based on compressive
sensing and sparse approximation theory. The experimental results revealed that
the basis dictionaries constructed by the moment transform perform
competitively to the traditional DCT. The latter transform shows a higher PSNR
of 30.82 dB and the same 0.91 SSIM value as the Tchebichef transform. Moreover,
from the sparsity point of view, Krawtchouk moments provide approximately
20-30% more sparse results than DCT.
