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.

翻译：这项工作解决了从图像中去除噪音的问题,侧重于众所周知的 DCT 图像去除无效算法,后者来自信号处理,多年来经过了仔细研究。尽管非常简单,但它仍然用于诸如BM3D等最先进的“传统”去除无效算法的关键部分。然而,由于几年以来,深共振神经网络(CNN)的表现超过了传统神经网络,降低了信号处理方法的吸引力。在本文中,我们证明DCT denoiser可以被视为浅浅显的CNN,因此其原始线性变换可以通过梯度下降来调整,从而大大改进其性能。这导致产生了一个完全可解释的CNN,称为DCT2net。为了处理DCT和DCT2net所引出的剩余文物,建议将这两种方法所能提供的最好办法结合起来的原始混合解决办法;DCT2net被选为非静止图像处理,而DCT对平滑度的补补补。对人造图像的实验表明,人造热度图像显示二层DCTM3是比快速的DM3级算法。