Computed Tomography Image Reconstruction With Incomplete Projection Data

Computed tomography(CT)technology can present the detailed information of the internal structure of the detected object without damage and image overlap,which is widely used in medical image diagnosis and industrial non-destructive testing.X-ray CT image reconstruction is the process that the detected object is penetrated by X-ray and the internal fault information of the detected object is reconstructed by using the projection data collected from multiple scanning angles.It is the key technology of CT imaging.The construction and practicability of CT image reconstruction model are affected by the completeness of projection data.CT imaging application in medicine and industry,it is often encountered to the problem of incomplete projection reconstruction.For example,due to the limitation of reducing scanning and imaging time,object geometry and low radiation dose,it is impossible to collect complete projection data.When large-scale objects or objects that only need to display part of the area need to be imaged,only truncated projections can be obtained;When the imaging conditions are limited,only part of the projection data of the object can be obtained.In view of the lack of different projection data caused by specific CT imaging problems,how to design an appropriate reconstruction model and algorithm to meet the actual reconstruction needs is an important research direction of CT incomplete projection reconstruction,which has certain theoretical significance and practical value.This paper focuses on the reconstruction of incomplete projection CT,that is,the internal problem of projection truncation and the finite angle reconstruction.The main research work is as follows:1.A fast global-local CT reconstruction method based on selective directional total variation(SDTV)was proposed.In the process of CT global image reconstruction,the high-quality imaging speed is slower than that of analytical method due to the large amount of projection data and the calculation amount of iterative algorithm.In this paper,a local reconstruction method of region of interest(ROI)is proposed to solve the problem.However,in practical application,the ROI region of the tested object may be unknown before reconstruction.To solve this problem,a global local imaging strategy is proposed to find the ROI position.In this imaging strategy,aiming at the problem that the projection corresponding to the ROI region with random position also has randomness,this paper proposes a calculation method to obtain the truncated projection of the local ROI region in the global projection.Finally,the p value in the L_p norm model based on directional total variation(DTV)is fixed,resulting in the model can not well adjust and change the edge details,which may lead to the problem of over-smoothing of local edges.Therefore,this paper proposes an algorithm to adaptively select the p value according to the estimated gradient amplitude of image pixels,so as to reduce the local edge over-smoothing phenomenon and obtain high-quality local reconstructed images.Experimental results show that the proposed method is more than ten times faster than the global algorithm in imaging speed and higher than ART and POCS-TVM algorithms in reconstruction quality.2.Nonlocal low-rank and prior image-based reconstruction in a wavelet tight frame using limited-angle projection data was proposed.In the limited-angle projection reconstruction,the missing angle of continuous scanning will lead to the incomplete projection data,and solving to the corresponding equation has serious ill posedness.Moreover,in the direction of missing projection data,the reconstructed image has edge artifacts and blurred details.In order to solve the problem of limited angle artifacts,the wavelet coefficients and the nonlocal low-rank approximation of the image block are used to enhance the sparse representation and constraints of the image,so as to effectively suppress the limited-angle artifacts.For edge detail blur,the prior image which is very similar to the image to be reconstructed,whose high frequency information is used to restore edge detail.By combining the above methods,a new reconstruction model from limited-angle projection based on nonlocal low-rank and prior image in a wavelet tight frame is proposed.3.Because the equation corresponding to the above model is seriously ill-posed,in order to optimize the solution results and increase the stability of the algorithm,this paper proposes to use variable separation and alternative direction method of multipliers(ADMM)to transform the original reconstruction problem into an optimization problem with multiple subproblems solved alternately for efficient solution.Compared with SART,POCS-TVM and PICCS algorithms,the reconstruction results of numerical simulation and actual projection data show that the proposed algorithm can better suppress the limited-angle artifacts and noise,and also can better restore the image details.4.The effects of parameters,noise and nonlocal low-rank sparse regularization on the reconstruction results are discussed.In this paper,there are many parameters that affect the results in the limited-angle projection reconstruction algorithm.Through many experiments,the parameters corresponding to the experimental data are given,but the influence of each parameter on the reconstruction result is not explained in detail.In order to further study the factors that affect the reconstruction results,this paper first analyzes the influence of three parameters on the edge of the reconstructed object.Through the comparison of the reconstructed image and the quantitative index,the different degrees of influence on the edge of the object are determined.Secondly,three groups of limited-angle projections with different noise levels are designed for reconstruction,and the results show that the proposed reconstruction model is stable for high noise projection.Finally,the l₀ norm sparse regularization and nonlocal low-rank sparse regularization are compared and analyzed.The experimental results show that the algorithm with nonlocal low-rank sparse regularization has better reconstruction effect than with l₀ norm sparse regularization.