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.

中文翻译：

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DCT2net：用于图像去噪的可解释浅层 CNN

这项工作解决了从图像中去除噪声的问题，重点是著名的 DCT 图像去噪算法。后者源于信号处理，多年来得到了很好的研究。虽然非常简单，但它仍然用于最先进的“传统”去噪算法（如 BM3D）的关键部分。然而，几年以来，深度卷积神经网络 (CNN) 的表现优于传统网络，使得信号处理方法的吸引力降低。在本文中，我们证明了 DCT 降噪器可以看作是一个浅层 CNN，因此它的原始线性变换可以以监督的方式通过梯度下降进行调整，从而显着提高其性能。这催生了一个完全可解释的 CNN，称为 DCT2net。为了处理由 DCT2net 引起的剩余工件，DCT 和 DCT2net 之间的原始混合解决方案结合了这两种方法所能提供的最佳解决方案；选择 DCT2net 来处理非平稳图像块，而 DCT 最适合用于分段平滑块。人工噪声图像的实验表明，两层 DCT2net 提供了与 BM3D 相当的结果，并且与由十多个层组成的 DnCNN 算法一样快。