Research On The Signal Reconstruction Algorithms Based On Sparse And Low-rank Priors

According to the theory of Compressed Sensing,the sparse exists in the redundant data.How to make reasonable and full use of the redundant data,to reconstruct the original data from a small amount of observations or from highly corrupted measurements,has become an improtant research project in image prcocessing,machine learning and many other fields.Because they can make full use of the sparse and low-rank characteristics of data,Compressed Sensing signal reconstruction and low-rank matrix reconstruction have attracted much attention in signal reconstruction research area and achieved certain research results.However,the current studies did not make full use of the inherent structure information,and the reconstruction models and algorithms still need to be further completed.Therefore,this dissertation studied on the signal reconstruction algorithms based on the sparse and low-rank priors in order to effectively perceive the sparse nature of redundant data via structure priors,such as sparse and low-rank characteristics,and improve the quality of signal reconstruction.The main work and innovations of the dissertation are outlined as follows:?1?Truncated l_2,1-norm regularization and reweightedl_2,1-norm regularization constraints were designed based on the support detection method,and then the reconstruction models of block sparse signals were constructed based on truncated basis pursuit and truncated reweighted basis pursuit,and the corresponding recovery algorithms of block sparse signals were proposed.The proposed algorithms can return enough number of correct detections via support detecting from inexact reconstruction,which guarantees the correct block sparse signals reconstruction.Experimental results demonstrate that block sparse signals can be recovered from very limited observations or measured data,and the requirement of fast decaying property in the common plain sparse signal recovery is not necessary any longer.Besides,the proposed algorithms have better adaptability to the measurement dimension,sparse and noise,and exhibit good robustness.?2?Instead of the nuclear norm minimization,the low-rank matrix recovery model was constructed via the truncated nuclear norm minimization.To reduce the computational complexity and improve the computation efficiency,the fast iterative algorithm that independent of the rank was proposed to solve the optimization problem.The proposed algorithm uses the soft threshold method to estimate the rank of low-rank matrix at each iteration.Moreover,the convergence analysis of the proposed algorithm was presented.The experimental results on synthetic data,background modeling and removing shadows from face images show that the proposed algorithm reduces the reconstruction error and ensures the efficiency,and can accurately adapt dynamic change of scene.The results validate both effectiveness and robustness of the proposed algorithm.?3?The matrix formed of the nonlocal similar patches has the low-rank property.The weighted Schatten p-norm is used as low-rank constraint of the matrix.Based on this,the compressed sensing image reconstruction model was constructed based on weighted Schatten p-norm,and the compressed sensing image reconstruction algorithm jointly using sparse and low-rank priors was proposed via the alternate minimization method.To seek the optimal solution of the model,the proposed algorithm contains the solution of the low-rank matrix and the reconstruction of image.Additionally,these two steps are carried out alternately.Moreover,the weighted values are updated adaptively by the designed strategy.The experimental results on nature images and MRI images indicate that the proposed algorithm not only improves the quality of reconstruction image,but also reserves the detail of image,such as the texture and edge.