Research On Greedy Image Reconstruction Algorithms Based On Blind Sparsity

In the era of high-intelligentization,informatization and digitization,the amount of data that we need to be processed is increasing rapidly.In addition,the requirement on data processing efficiency and speed becomes urgent.However,the traditional Nyquist sampling theorem has entered the bottleneck.The introduction of compressed sensing makes up for the deficiencies of the Nyquist sampling theorem,which makes full use of the sparsity or compressibility of the signal,compresses the data at the same time of sampling,and finally performs low-rank reconstruction with a small amount of measurements.The reconstruction algorithm is an important part of the compressed sensing theory,and its principle is to recover the original signal from less measurements than the original signal dimension.Based on the research of traditional greedy reconstruction algorithms,this thesis improves the existing algorithms and proposes a blind sparsity greedy image reconstruction algorithm based on the sparse representation of overcomplete dictionary.The main work and innovation of the thesis are as follows:(1)The greedy reconstruction algorithms based on sparse representation of discrete wavelet are studied.In order to solve the problem that sparse representation of discrete wavelet sparse representation is not flexible and can not guarantee the sparseness of signals under the sparsity basis,the overcomplete dictionary trained by the K-Means singular value decomposition as a sparsity basis is used,and compared it with the sparsity basis for the discrete wavelet transform and MOD overcomplete dictionary respectively.(2)Based on the shortcoming that OMP algorithm only choose one atom for each atom selection stage.The thesis analyses the ROMP with regularization method,the gOMP with generalized thought and the CoSaMP and SP algorithm with backtracking idea.Firstly,the relationship between the exact reconstruction probability,the sparsity and the number of measurements are studied.Secondly,this thesis uses OMP,ROMP,gOMP and CoSaMP four greedy reconstruction algorithms to reconstruct original signal respectively at the compression ratio of 0.3,0.4,0.5,0.6,0.7.Finally,the advantages and disadvantages of each reconstruction algorithm are analyzed respectively using the three indexes of peak signal-to-noise ratio,relative error and reconstruction time of the reconstructed image.(3)The reconstruction algorithm of KSVD Regularized Adaptive Matching Pursuit ispresented.The sparsity basis of the algorithm is an overcomplete dictionary trained by K-SVD algorithm,and the reconstruction algorithm is based on the SAMP algorithm which can realize the reconstruction of blind sparse images and ROMP algorithm can realize the second selection of atoms.Therefore,the algorithm can realize the accurate reconstruction of blind sparse images,and the experiments show that the proposed KSVD-RAMP algorithm improves the peak signal-to-noise ratio nearly 2 dB ~ 6 dB than that based on the discrete wavelet sparse representation of the RAMP algorithm.(4)This thesis proposes a generalized Sparse Adaptive Matching Pursuit algorithm,which added the idea of "generalized" to sparse adaptive matching pursuit algorithm.By designing the dual-threshold decide whether to stop the iteration and whether to change the number of atom selection,the sparsity of the original signal is continuously approached to realize the accurate reconstruction of the blind sparse image.After a large number of experiments show that this algorithm is superior to the traditional greedy reconstruction algorithms such as MP,OMP,ROMP,SAMP and gOMP both in visual impression and objective evaluation index.