  This work tackles the issue of noise removal from images, focusing on the
well-known DCT image denoising algorithm. The latter, stemming from signal
processing, has been well studied over the years. Though very simple, it is
still used in crucial parts of state-of-the-art "traditional" denoising
algorithms such as BM3D. Since a few years however, deep convolutional neural
networks (CNN) have outperformed their traditional counterparts, making signal
processing methods less attractive. In this paper, we demonstrate that a DCT
denoiser can be seen as a shallow CNN and thereby its original linear transform
can be tuned through gradient descent in a supervised manner, improving
considerably its performance. This gives birth to a fully interpretable CNN
called DCT2net. To deal with remaining artifacts induced by DCT2net, an
original hybrid solution between DCT and DCT2net is proposed combining the best
that these two methods can offer; DCT2net is selected to process non-stationary
image patches while DCT is optimal for piecewise smooth patches. Experiments on
artificially noisy images demonstrate that two-layer DCT2net provides
comparable results to BM3D and is as fast as DnCNN algorithm composed of more
than a dozen of layers.
