Median Prior (MP) reconstruction algorithm combined with nonlocal means fuzzy diffusion and extended neighborhood bilateral filter was proposed to reduce the streak artifacts in low-dose Computed Tomography (CT) reconstruction. In the new algorithm, the nonlocal means fuzzy diffusion method was used to improve the median of the prior distribution Maximum A Posterior (MAP) reconstruction algorithm at first, which reduced the noise in the reconstruction image; then, the bilateral filtering method based on the expended neighborhood was applied to preserve the edges and details of the reconstruction image and improve the Signal-to-Noise Ratio (SNR). 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 method has the smaller values of the Normalized Mean Square Distance (NMSD) and Mean Absolute Error (MAE) and the highest SNR (10.20 dB and 15.51 dB, respectively) in the two experiment images, compared with Filtered Back Projection (FBP), Median Root Prior (MRP), NonLocal Mean MP (NLMMP) and NonLocal Mean Bilateral Filter MP (NLMBFMP) algorithms. The experimental results show that the proposed reconstruction algorithm can reduce noise while keeping the edges and details of the image, which improves the deterioration problem of the low-dose CT image and obtains the image with higher SNR and quality.

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.