Image Compressive Sensing Reconstruction Based On Total Variation And Nonlocal Low Rank Prior

As a new signal theory,compressive sensing breaks the traditional Nyquist sampling theorem restrictions on the sampling rate of the signal.Based on the sparsity or compressibility of the signal,low speed compressive sampling and accurate reconstruction of the signal can be realized simultaneously.Compressive sensing usually includes compressive measurement of signal and optimal reconstruction based on sparse prior.How to use sparse prior to enhance the quality of image compressive sensing is now an important issue focused on by both the academic and industry.Nonlocal similarity of images has attracted great attention in the traditional image restoration applications.How to apply it to image compressive sensing reconstruction,to improve the quality of image reconstruction,has become a hot issue for researchers in domestic and foreign.Based on deeply analyzing image restoration algorithms proposed using local and nonlocal sparse models,and low rank approximation of image similar patches group,this thesis discussed in detail image compressive sensing reconstruction by collaborative regularization combining the total variation and low rank.The main works of this paper are as follows:(1)An image restoration method based on nonlocal low rank model is studied.Traditional nonlocal prior models are usually based on the fixed sparse domain filtering of each self similar blocks,which are lack of adaptability to different self similar structure features and ignoring some subtle differences within self similar structures.By utilizing the structural similarity between nonlocal similarity image blocks,each group of similar image blocks extracted are firstly rearranged into a column vector and formed a two dimensional data matrix,and processed by the improved low rank approximation technique,then the restored image is obtained by average.A large number of comparative experiments verify the effectiveness of the nonlocal adaptive low rank model in improving the performance of image denoising.(2)An image compressive sensing reconstruction algorithm based on collaborative constraints of image local sparse and non local low rank prior is proposed.On the basis of further research on the collaborative sparse reconstruction algorithm which combine the gradient sparse and nonlocal sparse prior,aiming at problem that the collaborative sparse reconstruction algorithm with nonlocal sparse domain filtering cannot adequately exploit the nonlocal similarity in images,the nonlocal adaptive low rank approximation algorithm is used to replace the nonlocal sparse domain filtering,and the multi variable optimization is solved by using alternating direction multiplier method.Experimental results show that,when using the peak signal noise ratio,structure similarity and subjective visual effect to measure the quality of the reconstructed image,the reconstructed image quality of proposed image compressive sensing reconstruction algorithm which combined with total variation and nonlocal adaptive low rank prior has been greatly improved.