To improve the speed of image reconstruction based on fan-beam Filtered Back Projection (FBP), a new optimized fast reconstruction method was proposed for polar back-projection algorithm. According to the symmetry feature of trigonometric function, the preprocessing projection datum were back-projected on the polar coordinates at the same time. During the back-projection data coordinate transformation, the computation of bilinear interpolation could be reduced by using the symmetry of the pixel position parameters. The experimental result shows that, compared with the traditional convolution back-projection algorithm, the speed of reconstruction can be improved more than eight times by the proposed method without sacrificing image quality. The new method is also applicable to 3D cone-beam reconstruction, and can be extended to multilayer spiral three-dimensional reconstruction.
In Positron Emission Tomography (PET) computed imaging, traditional iterative algorithms have the problem of details loss and fuzzy object edges. A high quality Median Prior (MP) reconstruction algorithm based on correlation coefficient and Forward-And-Backward (FAB) diffusion was proposed to solve the problem in this paper. Firstly, a characteristic factor called correlation coefficient was introduced to represent the image local gray information. Then through combining the correlation coefficient and forward-and-backward diffusion model, a new model was made up. Secondly, considering that the forward-and-backward diffusion model has the advantages of dealing with background and edge separately, the proposed model was applied to Maximum A Posterior (MAP) reconstruction algorithm of the median prior distribution, thus a median prior reconstruction algorithm based on forward-and-backward diffusion was obtained. The simulation results show that, the new algorithm can remove the image noise while preserving object edges well. The Signal-to-Noise Ratio (SNR) and Root Mean Squared Error (RMSE) also show visually the improvement of the reconstructed image quality.
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.