The deep unfolding network (DUN) provides an efficient framework for image restoration. It consists of a regularization module and a data fitting module. In existing DUN models, it is common to directly use a deep convolution neural network (DCNN) as the regularization module, and perform data fitting before regularization in each iteration/stage. In this work, we present a DUN by incorporating a new regularization module, and putting the regularization module before the data fitting module. The proposed regularization model is deducted by using the regularization by denoing (RED) and plugging in it a newly designed DCNN. For the data fitting module, we use the closed-form solution with Faster Fourier Transform (FFT). The resulted DRED-DUN model has some major advantages. First, the regularization model inherits the flexibility of learned image-adaptive and interpretability of RED. Second, the DRED-DUN model is an end-to-end trainable DUN, which learns the regularization network and other parameters jointly, thus leads to better restoration performance than the plug-and-play framework. Third, extensive experiments show that, our proposed model significantly outperforms the-state-of-the-art model-based methods and learning based methods in terms of PSNR indexes as well as the visual effects. In particular, our method has much better capability in recovering salient image components such as edges and small scale textures.

Weight decay (WD) is a fundamental and practical regularization technique in improving generalization of current deep learning models. However, it is observed that the WD does not work effectively for an adaptive optimization algorithm (such as Adam), as it works for SGD. Specifically, the solution found by Adam with the WD often generalizes unsatisfactorily. Though efforts have been made to mitigate this issue, the reason for such deficiency is still vague. In this article, we first show that when using the Adam optimizer, the weight norm increases very fast along with the training procedure, which is in contrast to SGD where the weight norm increases relatively slower and tends to converge. The fast increase of weight norm is adverse to WD; in consequence, the Adam optimizer will lose efficacy in finding solution that generalizes well. To resolve this problem, we propose to tailor Adam by introducing a regularization term on the adaptive learning rate, such that it is friendly to WD. Meanwhile, we introduce first moment on the WD to further enhance the regularization effect. We show that the proposed method is able to find solution with small norm and generalizes better than SGD. We test the proposed method on general image classification and fine-grained image classification tasks with different networks. Experimental results on all these cases substantiate the effectiveness of the proposed method in help improving the generalization. Specifically, the proposed method improves the test accuracy of Adam by a large margin and even improves the performance of SGD by $0.84\%$ on CIFAR 10 and $1.03 \%$ on CIFAR 100 with ResNet-50. The code of this article is public available at xxx.

Multiplicative speckle noise removal is a challenging task in image processing. Motivated by the performance of anisotropic diffusion in additive noise removal and the structure of the standard deviation of a compressed speckle noisy image, we address this problem with anisotropic diffusion theories. Firstly, an anisotropic diffusion model based on image statistics, including information on the gradient of the image, gray levels, and noise standard deviation of the image, is proposed. Although the proposed model can effectively remove multiplicative speckle noise, it does not consider the noise at the edge during the denoising process. Hence, we decompose the divergence term in order to make the diffusion at the edge occur along the boundaries rather than perpendicular to the boundaries, and improve the model to meet our requirements. Secondly, the iteration stopping criteria based on kurtosis and correlation in view of the lack of ground truth in real image experiments, is proposed. The optimal values of the parameters in the model are obtained by learning. To improve the denoising effect, post-processing is performed. Finally, the simulation results show that the proposed model can effectively remove the speckle noise and retain minute details of the images for the real ultrasound and RGB color images.