A Study On Image Restoration And Reconstruction Based On Sparse Regularization

In recent years, under the framework of compressed sensing (CS), a great deal of progress has been made for the study of image restoration and image reconstruction based on sparsity. Studies on CS theory unveil that if the signals satisfy the restricted isometry property (RIP) to some degrees, there is a high possibility to recover the orginal signal when the requirement specified by the Nyquist-Shannon sampling theorem cannot be satisfied. The l0-norm is an optimal choice to describe the sparsity of the signal. However, the model based on the l0-norm regularization is not derivable. It has been demonstrated that the l1-norm can play the same role as the l0-norm under certain conditions. In adittion, the TV norm can be considered as the l1-norm in the field of image process.Based on the modification of the sparae regularization terms, in this dissertation, we conduct the study of their application in the image restoration and low dose Computed Tomographt (CT) image reconstruction. Specifically, the works of image restoration are presented as follows:(1) A local and non local induced double sparsity based image restoration algorithm (L-NL) is proposed. The proposed algorithm makes full use of the advantage of the TV model and inverse filtering model, and also contains the essence of non local means filtering algorithm. To weaken the influencers of the nosie and improve the behavior of the inverse filtering, we remodel the inverse filtering model into an unconstrainted optimization model, and replace the degraded image varable by its denoised version by non local means. To improve the computational speed of non local means, a correlation based strategy for the acceleration of non-local means filtering algorithm is proposed. However, under this condition, the image restored by inverse filtering is still unsatisfied. The resion is that the algorithm of non local means cannot completely restore the previous counterpart and maybe induced method noise. Consequently, we combined the remodeled inverse filtering model and TV model and propose the local and non local induced double sparsity based image restoration algorithm (L-NL). Plenty of experiments are performed to verify the performance of the proposed algorithm. Based on the objective evaluation index of Peak Signal to Noise Ratio (PSNR) and Structural Similarly Index Measurement (SSIM) together with the visual effects, quantitative and qualitative results show the superiority of the proposed algorithm.(2) We further propose a local and dictionary representation induced double sparsity based image restoration algorithm (L-DR). The proposed method can be considered as a modified version of the above proposed L-NL method. We first filtered the degraded image by an adaptive learned dictionary, which is learned by the methd of orthogonal matching pursuit (OMP) and K-singular value decomposition (K-SVD). The inverse filtering model and TV model are then remodeled to propose a local and dictionary representation induced double sparsity based image restoration algorithm (L-DR). To verify the performance of the proposed algorithm, lots of experiments are conducted. Based on the objective evaluation index of PSNR and SSIM together with the visual effects, quantitative and qualitative results show the superiority of the proposed algorithm.The works of image reconstruction are presented as follows:(1) The algorithm of sparse-view X-ray CT reconstruction with Gamma regularization is proposed. Through the analysis of inherent relation among the classical sparse regularization modeles, such as l2-norm regularization,l1-norm regularization and l0-norm regularization, we firstly propose a universal sparse regularization model through introducing a regularization kernel function. Combining the Gamma statistical model and the proposed universal model, we propose the Gamma regularization based sparse-view X-ray CT reconstruction model, which fills the gap between the l0-norm regularization and the l1-norm regularization. Therefore, it is also called the fractional norm regularization. The Gamma regularization can adjust its parameters to adapt different reconstruction task. To evaluate the performance of the proposed algorithm, we perform experiments on the simulated Modified Shepp-Logan (MSL) and Non-Uniform Rational B-Splines Based Cardiac-Torso (NCAT) phantom together with the real clinical data. Compared to l2-norm and l1-norm regularization, and based on the objective evaluation index of PSNR and the visual effects, quantitative and qualitative results show the superiority of the proposed algorithm.(2) We further propose an adaptive Gamma regularization based low dose CT reconstruction algorithm. Combining weighted least square model established according to the analysis of the property of noise within the low dose projection data and previous proposed Gamma regularization model, we propose the Weighted Least Squares (WLS) model based on the Gamma regularization. To adaptively set the two parameters in the Gamma model, which paly a great role in the reconsreuction task, we firstly analyze their relation, and find that their contributaion devoted to making the Gamma regulation term approaching the l0-norm is opposite. Therefore, fixed variable methodonly is employed. We then accomplish the setting of the parametesr in terms of their rates. The performance of our proposed algorithm is evaluated on simulated MSL and NACT phantoms and Catphon 600 physical phantom data. Compaied to other methods, and according to the objective evaluation index of PSNR, SNR, and SSIM together with the visual effects, quantitative and qualitative results show the superiority of the proposed algorithm.