Image restoration is an important technique to deal with the degradation of the image. This paper presents an efficient and trusty denoising scheme, which combines the convolutional neural network (CNN) technique with the traditional variational model, to offer interpretable and high quality reconstructions. In this scheme, CNN, which has proven effectiveness in feature extraction tasks, is adopted to obtain the designed edge features from the noisy images, to be the prior of the reconstruction through an edge regularization. In the proposed denoising model, the total variation (TV) regularization is also adopted for its superior performance in allowing the sharp edges. The solution of the proposed model is obtained by using the Bregman splitting method, with the existence and the uniqueness of the solution also analyzed in this paper. Extensive experiments show that the two regularizations combined in the proposed model are able to fix the staircasing defects effectively and retrieve the fine textures in the recovered images as well, which outperforms the state-of-the-art interpretable denoising methods. Moreover, the proposed edge regularization can be easily extended into other kinds of noise or other restoration tasks, which implies the strong adaptivity of the proposed scheme.

图像恢复是处理图像质量下降的重要技术。本文提出了一种有效且可信赖的降噪方案，该方案将卷积神经网络（CNN）技术与传统变分模型相结合，以提供可解释的高质量重构。在该方案中，采用在特征提取任务中被证明有效的CNN来从噪声图像中获取设计的边缘特征，从而成为通过边缘正则化进行重建的先决条件。在所提出的去噪模型中，由于其在允许尖锐边缘方面的优越性能，还采用了总变化（TV）正则化。利用Bregman分裂方法获得了所提出模型的解，并分析了该解的存在性和唯一性。大量的实验表明，在所提出的模型中结合的两个正则化方法能够有效地修复楼梯缺陷，并且还可以在恢复的图像中检索出细微的纹理，这优于最新的可解释降噪方法。此外，所提出的边缘正则化可以容易地扩展到其他类型的噪声或其他恢复任务中，这意味着所提出的方案具有很强的适应性。