Research On Image Block Compressive Sensing Technology Based On Overcomplete Dictionary

Along with the information era,people have enhancing demands on digital information.However,according to Shannon Nyqvist sampling theorem,the sampling frequency of signals should be twice as the signal bandwidth so as to recover the primary signals losslessly.The increasingly common appliance of high bandwidth has been posed great pressure to signal transmission and storage.Compressed sensing technology,by the means of space conversion,will combine signal sampling and compression,transform signal sampling to information sampling,so that signal sampling would no longer rely on the bandwidth of signal,and high bandwidth sampling would be realized.That will greatly reduce the pressure of hardware equipment during its sample transmission and storage,as well as do favor to higher frequency sampling.CS(Compressed Sensing)theory is mainly composed of sparse representation,the restricted isometry property of measurement matrix and the relevant non-linear reconstruction algorithm.Sparse representation is the foundation and precondition of CS,its focal point is the design of sparse dictionary.The selection of sparse dictionary has determined the degree of signal sparsity and the efficiency of sparse representation.The design and optimization of measurement matrix is a pivotal step of CS,which serving as a link of the former step and latter step,its measured value restores the important effective information of the signals,so that the primary signals could be recovered by reconstruction algorithm.Block Compressed Sensing(BCS),based on the information-rich feature of images,processes compressed sensing to image by dividing it into small size blocks.This will greatly reduce the storage space and processing time of compressed sampling,for the reason that the information which the small size blocks bring is much less than it in the primary image.This theory,based on the research of overcomplete dictionary training and optimization of measurement matrix correlation,is mainly divided into the following aspects,namely:1.It is found that different image blocks possess similarity after the image being divided.Supposing that image blocks with similarity be organized and trained by the same dictionary,the adaptivity of these image blocks would be enhanced to the same dictionary that will lead to better accuracy of image presentation by dictionary,as well as shorter time for accumulation.This thesis,based on the theory of grey relational analysis and variance,proposed the dictionary training which is based upon image blocks with joint action of grey relational analysis and variance.This method could help to classify image blocks respectively by their external and internal characteristics.Using K-SVD algorithm as dictionary training method,image blocks of the same kind will be trained with the same dictionary,while those of different kinds will be trained with different dictionary atom in order to possess better adaptivity of dictionary towards the image blocks of the same kind.According to the simulation result,this method has done favor to reducing dictionary training time effectively,as well as enhancing the precision of dictionary presentation of images.2.Non-linear correlation of measurement matrix directly affect the minimum measured value of reconstruction and the execution efficiency of reconstruction algorithm.Optimizing random measurement matrix which based on correlation,will do favor to enhance the property of measurement matrix and get better result after its compressed sensing process.This thesis,based on the relation of condition number,singular value and correlation,proposed an optimized design of uncorrelated property.Remained the sum of singular value of measurement matrix,optimized its correlation by the means of formulating distribution formula of adaptivity and mean value.The simulation result has shown that in the same time of measurement and reconstruction,image reconstruction precision had been improved obviously.3.After combining dictionary training which based on grey relation and variance,as well as optimization design of measurement matrix based on incoherence,measurement matrix correlation and sparse dictionary adaptivity had gained some kind of improvement.By the representation of Greedy algorithm,namely,orthogonal mathing pursuit(OMP),different methods had been used to verify the effect towards PSNR of compressed sensing.The simulation results have shown that comparing with the primary algorithm,the optimized algorithm led to better PSNR values.