A new denoising algorithm, Adaptive Total Generalized Variation (ATGV), was proposed for removing streak artifacts within the reconstructed image of low-dose Computed Tomography (CT). Considering the shortage that the traditional Total Generalized Variation (TGV) would blur the edge details, the intuitionistic fuzzy entropy which can distinguish the smooth and detail regions was introduced into the TGV algorithm. Different areas of the image were processed with different denoising intensities. As a result, the image details could be well preserved. Firstly, the Filtered Back Projection (FBP) algorithm was used to obtain a reconstructed image. Secondly, the edge indicator function based on intuitive fuzzy entropy was applied to improve the TGV algorithm. Finally, the new algorithm was employed to reduce the noise in the reconstructed image. The simulations of the low-dose CT image reconstruction for the Shepp-Logan model and the thorax phantom were used to test the effectiveness of the proposed algorithm. The experimental results show that the proposed algorithm has the smaller values of the Normalized Mean Square Distance (NMSD) and Normalized Average Absolute Distance (NAAD) in the two experiment images, compared with the Total Variation (TV) algorithm and TGV algorithm. Meanwhile, the two experiment images processed with the new method can obtain high Peak Signal-to-Noise Ratios (PSNR) of 26.90 dB and 44.58 dB, respectively. So the proposed algorithm can effectively preserve image details and edges, while reducing streak artifacts.

Concerning the serious recession problems of the low-dose Computed Tomography (CT) reconstruction images, a low-dose CT reconstruction method of MLEM based on non-locality and variable exponent was presented. Considering the traditional anisotropic diffusion noise reduction is insufficient, variable exponent which could effectively compromise between heat conduction and anisotropic diffusion P-M models, and the similarity function which could detect the edge and details instead of gradient were applied to the traditional anisotropic diffusion, so as to achieve the desired effect. In each iteration, firstly, the basic MLEM algorithm was used to reconstruct the low-dose projection data. And then the diffusion function was improved by the non-local similarity measure, variable index and fuzzy mathematics theory, and the improved anisotropic diffusion was used to denoise the reconstructed image. Finally median filter was used to eliminate impulse noise points in the image. The experimental results show the proposed algorithm has a smaller numerical value than OS-PLS (Ordered Subsets-Penalized Least Squares), OS-PML-OSL (Ordered Subsets-Penalized Maximum Likelihood-One Step Late), and the algorithm based on the traditional PM, in the variance of Mean Absolute Error (MAE), and Normalized Mean Square Distance (NMSD), especially its Signal-to-Noise Ratio (SNR) is up to 10.52. This algorithm can effectively eliminate the bar of artifacts, and can keep image edges and details information better.

Concerning the contradiction between edge-preserving and noise-suppressing in the process of image denoising, a patch similarity anisotropic diffusion algorithm based on variable exponent for image denoising was proposed. The algorithm combined adaptive Perona-Malik (PM) model based on variable exponent for image denoising and the idea of patch similarity, constructed a new edge indicator and a new diffusion coefficient function. The traditional anisotropic diffusion algorithms for image denoising based on the intensity similarity of each single pixel (or gradient information) to detect edge cannot effectively preserve weak edges and details such as texture. However, the proposed algorithm can preserve more detail information while removing the noise, since the algorithm utilizes the intensity similarity of neighbor pixels. The simulation results show that, compared with the traditional image denoising algorithms based on Partial Differential Equation (PDE), the proposed algorithm improves Signal-to-Noise ratio (SNR) and Peak-Signal-to-Noise Ratio (PSNR) to 16.602480dB and 31.284672dB respectively, and enhances anti-noise capability. At the same time, the filtered image preserves more detail features such as weak edges and textures and has good visual effects. Therefore, the algorithm achieves a good balance between noise reduction and edge maintenance.