Image Compressive Sensing Reconstruction Method Based On Nonlocal Low-rank Regularization

Compressive sensing(CS)theory which relies on the sparsity or compressibility of the nat-ural signals breaks the limitation of the traditional Nyquist sampling theory,and demonstrates that a signal could be accurately reconstructed from far fewer measurements than suggested by the Nyquist sampling theory.As a novel signal acquisition theory,it opened a new research area of information technology.As one of the crucial issues,the reconstruction algorithm plays a key role in the application of CS and affects its practical usage.How to design a reconstruc-tion algorithm with low complexity and high recovery accuracy to recover the signal has been a research focus.Under this background,the dissertation has deeply studied the image CS re-construction methods in order to find accurate and robust reconstruction algorithms.The main contributions and innovations of the dissertation are as follows.(1)Truncated schatten-p norm regularization based CS model.Based on the nonlocal low-rank property prior,in the reconstruction procedure,how to solve the resulting rank regu-larization problem which is known as an NP-hard problem is critical to the recovery results.We propose a truncated schatten-p norm regularization based image CS recovery method.Truncat-ed schatten-p norm regularization,which is used as a surrogate for the rank function to exploit the benefits of both schatten-p norm and truncated nuclear norm,has been proposed toward better exploiting low-rank property in CS recovery.We have developed an efficient iterative scheme based on the alternating direction method of multipliers(ADMM)to solve the result-ing nonconvex optimization problem.Extended experiment results indicate that the proposed CS reconstruction method has a better improvement in terms of objective criterion and visual fidelity over other related nonlocal low-rank regularization based reconstruction methods.(2)Nonlocal low-rank tensor regularization based CS model.In the process of reconstruc-tion,almost all the image CS reconstruction methods cannot preserve the original geometrical structure of image patches and ignores the relationship between pixels because it deals with the vector form of image patches and the matrix form of patch groups for simplicity.We propose a nonlocal low-rank tensor regularization approach toward exploiting the original structural information of image patches and nonlocal low-rank property of similar patches,and regu-larizing the ranks of tensors grouped by similar patches are low.We also exploit schatten-p norm as a nonconvex relaxation for tensor rank.At last,we utilize ADMM to solve the non-convex optimization model.Some experimental results demonstrate that the consideration of patch structural information is helpful to improve the reconstruction quality in edge and texture areas.Comparing with other related reconstruction methods,this proposed algorithm signifi-cantly improves the Peak Signal-to-Noise Rate.(3)Block sparsity and nonlocal low-rank regularization based CS model.It has been demonstrated that,without knowing the sparsity basis,blind compressive sensing(BCS)can achieve similar results with those CS methods which rely on prior knowledge of the sparsity basis.BCS is closer to the real application environment.However,BCS still suffers from two problems when it is applied to images.First,compared with block-based sparsity,the global image sparsity ignores the local image features.Second,since BCS only exploits the weaker prior than CS and ignores the other useful priors,the sampling rate on an image required by BCS is still very high in practice.We firstly propose a novel blind compressive sensing method based on block sparsity and nonlocal low-rank property priors in the original images to further reduce the sampling rate.Experimental results have demonstrated that the proposed algorithm can significantly reduce the sampling rate without sacrificing the quality of the reconstructed image.(4)Half-quadratic function and weighted schatten-p norm based CS model.Since noise is an inevitable factor in real-world applications,designing robust image recovery technologies is crucial to the application of CS system.However,current CS approaches rarely take noise into consideration or only consider the noise generated in the process of transmission.When the original image is corrupted by noise,especially non-Gaussian noise,due to the natural or artificial factors,almost all the CS approaches will break down.In this paper,we propose a m-estimator based robust image CS approach to recover the original clean images from the compressed measurements of their corrupted versions.We simultaneously conduct reconstruct-ing and denoising in a unified framework.We also take use of weighted schatten-p norm to better exploiting the nonlocal low-rank property.In addition,we have developed an efficient iterative scheme based on half-quadratic theory and ADMM to solve the resulting nonconvex optimization problem.Experimental results have shown that the proposed algorithm can accu-rately recover the clean images when the original images are corrupted by impulsive noise.