Research On Image Restoration Method Based On Nuclear Norm Minimization

Vision is one of the most important ways for human beings to observe,perceive and understand the outside world,and vision-based technologies are widely employed in industry,medicine,remote sensing,and other fields,where the performance of these applications depends on image quality.High-quality images have higher resolution,sharper image texture and clearer image details,and thus these images have superior visual form.Although image imaging technology tends to mature,the quality of image is poor since it is affected by objective factors in image acquisition and transmission process,such as acquisition device,imaging technology,meteorological conditions,human interference,and so on.Therefore,it is vital to reproduce the high-quality image from its low-quality image with the aid of image restoration technology,which can effectively promote the visual perception of the image and subsequently facilitate the understanding and analyzing of image content.However,image restoration is a classical ill-posed inverse problem,which is a hard problem to be settled.Therefore,image restoration is still challenging.Generally,image restoration is divided into two categories: model-based methods and learning-based methods.Among these methods,learning-based methods rely heavily on external image data,and have complex model structure and strict requirements for computational resources.Thus,the application scenarios of such methods are limited.Compared with learning-based methods,model-based methods are more complex.But,combined with specific optimization algorithms,it can be effectively optimized to ensure the model performance.Therefore,model-based method is now one of the hot topics in image restoration research,which has a broad application prospect and is the research focus of this paper.In this paper,we conduct the research work of image restoration from two aspects: image nonlocal self-similarity and low-rank nature,and take the Super Resolution(SR)and Image Denoising(ID)tasks as the research objects.The main contents and contributions of this research are as follows:(1)Nowadays,imaging technology of natural images is becoming more and more popular,but the image resolution is low due to the restriction of objective factors like imaging equipment,imaging environment,external noise,etc.To solve this problem,we propose the probability model of image super-resolution reconstruction,which is based on maximum a posterior and nonlocal low-rank prior.Firstly,we extract image patches from the single low-resolution image,and then reshape them into high-dimensional tensor to construct a patch-based matrix.Then,the maximum a posteriori is adopted to model the image super-resolution reconstruction problem,where the parameters are fitted by Gaussian distribution and Gibbs distribution,respectively.With the nonlocal self-similarity of images being explored,the nonlocal low-rank prior is used to regularize the image reconstruction process.Finally,each high-resolution image patch is recovered from known low-resolution image patches.The restored high-resolution image patch is embedded into the intermediate image matrix patch by patch,and then the result image is generated,wherein we set the numerical constant to truncate the smaller singular values to weaken the noisy impact on the result image.Experimental results on public image datasets,Set5,Set14,BSD100,and Urban100,show that compared with 12 advanced algorithms,the proposed algorithm not only achieves superior quantitative indexes in the simulation experiments of SR task,but also can effectively maintain image texture and preserve image details,which has desirable visual perception.(2)To recover the high-quality image from its degraded version,image restoration methods based on low-rank prior usually solve a matrix low-rank approximation problem via the nuclear norm minimization.However,most approaches handle the matrix singular values individually and thus ignore the inherent correlation among singular values.To address this problem,we propose a novel probability-inducing nuclear norm minimization(PINNM)algorithm,where the intrinsic correlation among singular values of a matrix is explored.Firstly,we extract several overlapped image patches from the input image and convert them into patch tensors.According to the patch-based low-rank model,nonlocal self-similarity of natural images can be exploited to construct the matrix based on the similar image patches.Secondly,the proposed algorithm adopts maximum a posterior to model the inherent correlation among singular values,and then derives the probabilityinducing estimator of desired singular values,where the amplitude of singular values is used to truncate the smaller values.Finally,to reproduce the image details lost in restoration process,the recovered intermediate image is employed to improve the quality of desired image by residual cascade scheme.In this paper,the proposed model is evaluated on SR and ID tasks,respectively.Experimental results demonstrate that our approach outperforms most advanced approaches both quantitatively and qualitatively.The first approach uses the nonlocal low-rank prior to constraint the image reconstruction process,and adopts low-rank truncation to suppress noise.However,with the increase of image texture and detail,it will become more difficult for this approach to reproduce image details.In addition,a fixed value designed for low-rank truncation ignores the difference among the input images.To improve the reconstruction and generalization performance of the first method,the second method truncates smaller singular values through the amplitude of singular values.Besides,it can improve the image quality by using residual cascade scheme to preserve the image detail,which is expanded into ID task.