| As an important carrier of information storage and transmission,image is also an important way for human to perceive information.However,images are often polluted by noise due to various factors.In recent years,in order to recover the real information of images as much as possible,the low-rank matrix restoration model has shown good performance.On the other hand,with the development of deep learning,researchers have found that the trained model is prone to interference from adversarial noise.Studies show that if adversarial noise can be removed from the input image,the robustness of the neural network can be effectively improved.This paper mainly focuses on the optimization of traditional low-rank matrix restoration model,the removal of salt-and-pepper noise and the application of adversarial noise,so as to improve the robustness of the deep neural network model.Specific research contents include the following three aspects:(1)Sparse representation theory can represent or extract the main features of image well,and it has a good effect on image denoising.Low-rank group sparse coding(LR-GSC)takes group as unit and combines the advantages of image local sparsity and non-local autocorrelation to achieve good results for Gaussian noise removal,but can not effectively remove sparse large noise.In addition,when the noise density is high,since each image patch contains these noisy pixels,the acquisition of similar patches is affected,resulting in a large difference between similar patches.In this paper,an improved sparse loud noise removal model based on low-rank group sparse coding is proposed,which is called smooth double-weighted low-rank group sparse coding(SDWLR-GSC)model.In addition to using the non-local self-similarity prior conditions of the image,the model maintains the low-rank of the coefficient of the similar blocks when constructing the similar blocks,and at the same time imposes the low rank constraint on the whole of the reconstructed similar patches.In addition,the TV regularization term was incorporated into the model to ensure the structural smoothness of the image denoising.The experimental results show that when the image is polluted by salt and pepper noise,it has a better recovery effect.(2)The rank minimization problem in low-rank matrix restoration algorithm is often solved by approximating the rank function by nuclear norm.In this paper,for images with complex semantic structures at different spatial scales,the nuclear norm can not provide an effective approximation of original rank function,a low-rank matrix restoration method based on TV and smooth nuclear norm is proposed.On the one hand,this method uses smooth nuclear norm instead of nuclear norm as the non-convex approximation of matrix rank function,so as to approximate the rank function better.On the other hand,the TV regular term is introduced to avoid excessive smoothness of the restored image.Experimental results show that compared with the existing low-rank matrix restoration algorithms,this method has a better effect on image restoration,and the recovery efficiency is significantly improved.(3)Aiming at the problem that the deep neural network model is prone to noise interference,this paper takes advantage of the good performance of the low-rank matrix restoration model in image reconstruction and applies it to improve the robustness of the deep neural network,and proposes an adversarial example defense method based on smooth nuclear norm low-rank matrix restoration.Firstly,some pixels in the noisy image are randomly discarded,and then smooth nuclear norm low-rank matrix is used to inpaint the incomplete image.It not only destroys the adversarial structure of noise,but also enhances the global information effectively.In order to test the effectiveness of the algorithm,we conducted experiments on MNIST,CIFAR-10 and SVHN datasets,and the results show that compared with the existing defense methods,the proposed method has certain defense capability against black box attacks. |
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