| With the advent of information age,the demand for image information processing is getting higher and higher.The traditional image processing method based on Nyquist sampling theorem can not meet the demand of image processing in today’s society because of the disadvantages of redundant data and high sampling cost.In the process of using Compressed Sensing(CS)algorithm to sample the signal,a frequency far lower than Nyquist sampling theorem can be used,and the original signal can be successfully recovered by reconstruction algorithm.CS algorithm greatly reduces the requirement of storage capacity and has become a hotspot of image information processing.Aiming at the shortcomings of image CS algorithm,such as lack of details and long reconstruction time,a fast and efficient CS algorithm applied to two-dimensional images was proposed on the basis of in-depth study of multi-scale geometric transformation and semi-tensor product operation.The main research contents and innovations are as follows:(1)To address the problem of poor image reconstruction quality,we conduct a study on the multi-scale geometric transform,apply the Non-Subsampled Contourlet Transform(NSCT)to the CS algorithm and propose an image CS algorithm(NSCT-IRLS)based on Iterative Reweighted Least Square(IRLS)and NSCT.After sparse transformation of 2d image signals by NSCT,random Gaussian matrix is used as measurement matrix to carry out linear projection of sparse signals,and IRLS algorithm is used to reconstruct the image.The gray scale and color natural image,medical image and remote sensing image are compressed and reconstructed.In order to verify the anti-jamming ability of the algorithm,random Gaussian noise with standard deviation of 5,10 and 15 was added to the image.Simulation results show that with the sampling rate in the range of 0.1～0.6,the proposed algorithm improves the image reconstruction quality compared with existing algorithms.Especially when the sampling rate is low,the improvement of image reconstruction quality is more obvious.When the sampling rate is 0.1,the Peak Signal to Noise Ratio(PSNR)obtained by image reconstruction is improved by 0.9～5.5 d B compared with existing algorithms.After the noise is inserted into the image,the image reconstructed by this algorithm still has a higher PSNR than the existing algorithm.When the sampling rate is 0.3and the random noise with standard deviation of 5 is added,the PSNR of reconstructed gray image decreases by 0.029-0.143 d B only.(2)To address the problems of large memory consumption,long reconstruction time and low reconstruction speed in CS reconstruction process,the semi-tensor product compressed sensing model(EIG-STP)based on eigenvalue decomposition is proposed.The original image was sparsely transformed by NSCT to obtain sparse signals,and then the measurement matrix was decomposed by eigenvalues to obtain the optimization measurement matrix with lower column correlation.Then the optimization measurement matrix with mismatched matrix dimensions and sparse signals were calculated by semitensor product.Finally,the projection matrix was reconstructed by IRLS algorithm.The size of measurement matrix is reduced in proportion,and the quality and reconstruction time of reconstructed images are compared.The simulation results show that the PSNR of reconstructed images is basically unchanged while the reconstruction time is greatly reduced when the size of measurement matrix decreases proportionally.When the resolution of the image is 1024*1024 and the number of rows and columns of the measurement matrix is reduced by 32 times,the reconstruction time is reduced by 24.138-119.37 times,which greatly improves the real-time performance of the algorithm. |
