Research On Low Rank Property Based Compressive Sensing Reconstruction

Currently,almost all traditional compression sampling methods are based on the Nyquist sampling theory which notes that the sampling rate must be more than twice of the signal bandwidth in order to achieve accurate reconstruction.When the amount of data increases,there will be too many sampling points to proeess and transmit.The emergence of compressive sensing theory breaks the limitation of traditional sampling theorem.It has noted that if the signal is sparse or compressible in some transform space,the signal can be sampled at a low sampling rate less than the Nyquist Sampling Theorem required with a special observation matrix and can be reconstructed in high precision.In compressive sensing theory,the reconstruction algorithim is one of the key points.Therefore,this paper focus on the research of reconstruction method which makes the best of low rank prior and nonlocal prior to improve the reconstruction quality of images and videos.The study is significant to the field of image processing and applications of compressive sensing.This paper first introduced the background and significance of our research and current situation and development trend of compressive sensing.And then,we summarized the common image sparse representation,common measurement matrix and under common optimization reconstruction algorithms in the framework of compressive sensing theory.Furthermore,we described the application of low rank matrix in images.On this basis,we put forward the new reconstruction method using low rank matrix.Considering the nonlocal similarity of remote sensing images,a compressive sensing reconstruction method based on nonlocal similarity and low rank matrix is proposed in this paper.It first clusters the nonlocal similar blocks to get a matrix with low rank,and then reconstructs the images using the constraints of low rank and minimum total variation.A new joint block matching method based on Euclidean distance and structural similarity is developed,which makes the matching result more accurate.We use standard test images and remote sensing images for simulation experiment,the experimental results show that the proposed method can obtain high quality reconstructed image,and peak signal-to-noise ratio and structural similarity index are promoted.In the temporal compressive sensing,based on the background ot the video signal has low rank feature,we present an adaptive reconstruction algorithm for temporal compressive sensing.In temporal compressive sensing,the single observed image which is used to reconstruct the original multiple images is the sum of multiple exposure coding frames.It has improved the temporal resolution of video,and solved the problem of constraint between video temporal and spatial resolution.Inter-frame correlation is used to segment the video into background and moving objects.For the background,we use low rank matrix reconstruction method,while for the moving objects,we first match three-dimensional similar blocks,and then use low rank matrix and the minimun total variation constraints to solve the restoration problem.The simulation experiment results show that the proposed method can obtain better reconstruction quality.