Research On Image Denoising Algorithm Based On Low-rank Matrix Restoration

Low-rank matrix recovery(LRMR)refers to the method that can automatically identify the damaged elements of a matrix and recover the original matrix.It generalizes the sparse representation of the vector sample to the low-rank case of the matrix,and has become an important way to obtain and represent data after the sparse representation(SR).The low-rank matrix recovery method is generally based on structural groups and optimization of sparse representations.The data matrix is first expressed as the sum of the low-rank matrix and the noise matrix,and then the low-rank matrix is restored by solving the nuclear norm optimization problem.The premise of low-rank matrix recovery is that the original matrix is low-rank or approximately low-rank.Low-rank matrix recovery can be used to recover images because similar patches matrices formed by similar patches of clean images have low-rank properties.Based on the existing low-rank matrix recovery algorithm,this paper proposes improved image denoising algorithms by improving the inadequacies of the existing algorithm,and compares the improved algorithms with the existing state-of-the-art denoising algorithm to prove the proposed algorithms achieves better denoising performance.The specific research work has the following aspects:(1)The low-rank representation(LRR)model uses the nuclear norm to estimate nonzero singular values,while all singular values are treated equally and they shrunk by the same amount when solving the nuclear norm minimization problem,which usually leads the obtained result to be a suboptimal solution of the original rank minimization problem.To solve this problem,in this paper a parameterized nonconvex penalty function is used to estimate nonzero singular value,and then the low rank representation model is improved.The nonconvex penalty function can determine the contraction value according to the practical meaning of each singular value when solving the minimization problem,which makes it estimate the nonzero singular value more accurately than the nuclear norm.The experimental results show that the improved algorithm achieves better denoising performance.(2)In order to improve the region smoothness and edge structure of the restored image and avoid the visible artifacts in image denoising,in this paper total variation(TV)norm is incorporated into the existing low rank representation model.And then a new low-rank matrix recovery algorithm for image denoising is developed,called the total variation low rank representation(TVLRR)model.The TV norm can effectively maintain the image edge and enhance the smoothness of the region,which can significantly improve the quality of restored image.The experimental results demonstrate the effectiveness of the proposed algorithm in image denoising.(3)The higher the noise intensity is,the more complex the noise image structure becomes,and then the similar patches matrix has higher rank and the error of the matrix is more dense.Therefore,the algorithm will easily confuse the image details with noise when denoising,which makes the restored image too smooth or producing visible artifacts.In order to solve this problem and further improve the denoising performance of the algorithm with high noise intensity,the parameterized nonconvex penalty function is employed to estimate nonzero singular values.Meanwhile using the ability of Total Variation(TV)norm to preserve image edge information and enhance the smoothness of image region,an enhanced low-rank representation image denoising algorithm is proposed,and the corresponding model is solved by an alternating minimization method.Exploiting the nonlocal self-similarity prior inherent in the image,the proposed algorithm can effectively find and remove noise,while enhancing the structure and area smoothness,which improves the quality of the restored image.Experimental results indicate that the proposed algorithm achieves a competitive denoising performance,especially for high-intensity noise,in comparison with state-of-the-art algorithms in terms of objective evaluation and visual effect.