Research On Limited Angular CT Sampling Condition Analysis And Reconstruction Algorithms Based On Sparsity Optimization

Computed tomography utilizes X-ray attenuation information from different angles to obtain the attenuation characteristic profile of scanned object via reconstruction algorithms,which can perspective imaging of the internal structure of the scanned object without destruction.CT has been widely applied into medical diagnosis,industrial non-destructive testing and safety inspection areas.However,in certain applications,the scanning angular is restricted within 180? because of the X-ray radiation dose,exposure time,and the geometric settings of the imaging system.The deficiency of projection data in some specific angular causes serious image artifacts.Recently,reconstruction from limited angles becomes the hotspots and difficulties of CT imaging.The study of limited angular CT has important theory significance and practical value.In this paper,studies around the limited angular CT problems have been carried out,such as the quantitative analysis of the exact reconstruction sampling condition,artifacts suppression of spatial domain,and inpainting of the deficient projection data.The exact reconstruction sampling conditions are quantified based on the analysis of the CT imaging system matric.Two methods are designed from the aspects of image correction in spatial domain and data extrapolation in radon domain,in order to solve the image distortion caused by the deficiency of continuous angular projection data.1.Few previous studies have mentioned a quantitative notion of the scanning angular range and projection number for limited angular exact reconstruction.In this paper,an exact reconstruction sampling condition for limited angular problem is studied by verifying the uniqueness of solution in total variation(TV)minimization model.Uniqueness is tested by solving a convex optimization problem derived from the sufficient and necessary condition of solution uniqueness.Through this method,the sufficient sampling numbers of exact reconstruction at different scanning angular range are quantified for different phantoms and fixed geometrical parameter in the limited angular problem.By narrowing the scanning angular range,the lowest bounds of the scanning range corresponding to different phantoms are presented,to which extent the exact reconstruction cannot be obtained once the projection angular is narrowed.The proposed method provides a preliminary theoretical basis for designing novel imaging system and evaluating the performance of reconstruction algorithm.2.The formation of artifacts caused by lack of continuous projection data severely disturbs the reconstruction image.To address this problem,this paper uses the idea of regional enhancement of the true values and suppression of illusory artifacts outside the region to develop an efficient iterative algorithm.In this algorithm,the segmentation approach is introduced to distinguish the region of different image knowledge and generate the support mask of the image.A new regularization term,which contains the support knowledge to enhance the true values of the image,is incorporated into the objective function of TV minimization model.Then,the proposed optimization model is solved by variable splitting and the alternating direction method efficiently.A compensation approach is also designed to extract useful information from initial projections and thus reduce false segmentation result.The experimental results indicated that,when inspect some industrial components e.g.aero-engine blade that contains irregular inner structure and lacks specimen penetration in some specific directions,the proposed algorithm is able to suppress illusory artifacts caused by the deficiency in valid data and produce high-quality inner and edge information than the other reconstruction methods.This will contribute wider applications of CT techniques in the area of industrial non-destructive testing.3.Most of limited angle reconstruction algorithms dose not fully study the sparse prior knowledge of radon domains.Conventional methods that only exploit sparsity priors of spatial domains often fail to provide images with satisfying quality when projection suffers from serious data deficiency and various noises.This paper develops an adaptive simultaneous spatial and radon domain regularization reconstruction model based on TV and data driven tight frame for limited angle CT reconstruction.Data driven tight frame regularization aims at exploiting sparsity priors of a sinogram,and it can be adaptively learned from projections to provide optimal sparse approximations in radon domains.Experiments were performed on the medical image that contains lots of complex texture and tissues information.The results demonstrate that the proposed algorithm shows better performance in detail preservation and sinogram inpainting than those with only spatial domain regularization,which helps to improve the image quality in limited angular CT problem.