Research On Low-rank Denoising Method Combined With Noise Energy Distribution Estimation

With the popularity of digital photography products and the rapid development of the Internet,people are increasingly using images and videos to record their work and life.This development brings a high demand for image quality.Image denoising as an important approach to improve image quality is the most basic part of the image processing.It is an important foundation for subsequent processing,understanding,and analysis operations and has a wide range of application needs in various fields such as daily life,industrial production,media,and technology.The low-rank problem of matrices has always been an important issue in the field of matrix analysis,its research and applications have a long history.In recent years,with the rise of research on the nonlocal property of natural images,traditional local denoising models have been overturned.More and more experts and scholars began to use the nonlocal self-similarity(NSS)of natural images for research.They used the high redundancy of similar block information to find breakthroughs and achieved a number of research results.The low-rank based denoising method is an important branch based on the nonlocal theory which exhibits strong strength in the field of image denoising.The nonlocal self-similarity property of natural images has shown great potential in various image tasks.For a noisy image,the group matrix is constructed by similarity patches whose noise-free version has distinct low-rank property.Therefore,it is an effective method to solve the denoising problem by low-rank approximation.It is found that the singular values of the noise-free matrix can reflect the energy distribution of real information in the SVD domain,and the improved denoising results can be obtained by using the real energy distribution.A series of noisy images are obtained by adding different levels of noise into the noise-free image.There is a specific functional relationship between the singular values of the noisy images,which can be used to construct the singular values of the noise-free image.Based on the above research and theory,we improve the denoising method based on the low-rank model in this paper.Firstly,we estimate the energy distribution of noise of group matrix in the SVD domain using the energy characteristics of the image with different noise level.The energy of the noise is shrunk to obtain the energy distribution of the true signal.Then,based on the optimal energy compaction property of SVD,the low-rank property of matrix is constrained in the SVD domain to obtain the low-rank approximation of matrix.Meanwhile,we expand the search region for image area with less redundant information to guarantee the low-rank of the group matrix.What's more,an iterative back projection method is used in this paper to suppress residual noise.A fast noise standard deviation estimation approach,targeted at the back projection process,is proposed to effectively optimize the denoising results during the iteration.At the experimental stage,the paper uses synthetic images and natural images as experimental objects.The analysis of the experimental results shows that noise can be effectively reduced by the proposed algorithm.In addition,compared with the denoising results of other representative algorithms,this proposed algorithm not only improves the objective quantitative data but also maintains the detailed information on subjective visual effects.In addition,the proposed algorithm achieves a good balance between denoising effect and running time.