Research On Ultra-limited Angles Computed Tomography Sampling Condition And Image Reconstruction Algorithm

Computed Tomography(CT)has been widely used in medicine,industry,security inspection,national defense and other fields because of its non-destructive,fast and perspective characteristics.CT image reconstruction is one of the key technologies of CT imaging system,which uses X-ray projection data penetrating through the object at different sampling angles to generate the internal structure image of the object.However,due to the constraints of radiation dose,system scanning geometry and other factors,projection data can only be collected by imaging systems in the range of less than 180 degrees in many practical applications.And the missing projection data in the continuous angle range will lead to singularity in the solution,namely the limited angles(or limited views)problem,which has been a hot and difficult point in CT imaging technology.Aiming at the ultra-limited angles reconstruction problem when the sampling angle range is less than 90 degrees,this paper focuses on the analysis of sampling conditions for exact reconstruction,the inpainting of missing angle projection data,and the image reconstruction based on the estimated projection.The main research results are as follows:1.A sampling condition analysis algorithm based on alternating direction method of multipliers(ADMM)is proposed.Aiming at the computational bottleneck problem in the analysis of limited angle exact reconstruction sampling conditions,this paper transform the necessary and sufficient conditions of the of the total variation(TV)minimization reconstruction model into a linearly constrained convex optimization problem.The algorithm transforms the original problem into an optimization problem in which the two sub-problems are solved alternately.The two subproblems can be efficiently solved by strategies such as matrix Cholesky decomposition.The solution is used to determine whether the solution of the TV minimization model is unique under different sampling conditions,and then the quantitative analysis results of the sampling conditions are obtained.The experimental results show that the proposed method reduces the computation time of sampling condition analysis by about 47%,extends the analysis scale of accurate reconstruction sampling condition,and provides theoretical guidance for the system design and reconstruction algorithm research in practical applications.2.An ultra-limited angles sinogram inpainting method based on generative adversarial networks(GAN)is proposed.In ultra-limited angles CT reconstruction,the truncated artifacts caused by the missing of large-scale consecutive projections seriously affect the reconstruction quality.Aiming at this problem,this paper deeply mined the characteristics of data distribution in sinogram domain in the ultra-limited angles problem and fully utilized the sine of each voxel in the sinogram.The modified U-Net generator and the patch discriminator are designed under the conditional GAN(CGAN)framework.At the same time,in order to further enhance the learning of the sinogram details,we introduce a back-projection module with the ability of backpropagation to achieve the joint optimization of sinogram and image domains.The experimental results show that the sinogram inpainting errors of the proposed method is reduced by about 50% compared with that of the simple patch discriminator based GAN(patch-GAN).This method can effectively fill the missing projection data in the ultra-limited angles problem,and can significantly suppress truncated artifacts caused by the large-scale continuous missing projection data in real CT scans.3.A joint sinogram-image dual-domain regularization algorithm based on estimated sinogram for ultra-limited angles reconstruction is proposed.In order to make full use of the advantage of SI-GAN in inpainting missing projection and suppressing truncated artifacts in ultra-limited angles problem,the joint sinogram-image reconstruction model is established.For purpose of suppressing the influence of errors between estimated and real sinograms,a dual-domain joint regularization reconstruction algorithm based on block matching and TV minimization is designed by using convex set projection method and alternating minimization technique.The experimental results show that this method can improve the quality of ultra-limited angles reconstruction by mining sparse information in both image and sinogram domains sufficiently,using the inpainting effect of restored projection and the fidelity effect of original projection.Compared with the typical TV minimization reconstruction algorithm,the proposed algorithm has obvious advantages in image detail recovery and artifact suppression.