Computed Tomography Image Reconstruction With Incomplete Projection Data

Computed tomography(CT)technique has played an indispensable role in a wide range of applications such as medical imaging and industrial nondestructive testing since it was invented.CT image reconstruction is the core foundation of CT imaging,which is a process of obtaining inner tomographic images of the object from the transmission X-ray projections.The completeness of projection data is a key factor for the practical design of image reconstruction algorithms.When the projection data acquired is complete,the development of reconstruction theories and methods is comparatively comprehensive,and a high quality reconstructed image is easy to be obtained.However,when the projection data is incomplete,traditional reconstruction methods easily introduce serious artifacts in the reconstructed images and the realization of high accuracy reconstruction remains a big challenge.Image reconstruction from incomplete projection data,also called incomplete data image reconstruction,has been a long-standing research hotspot in the fields of CT.In many medical and industrial applications,the problems of incomplete projection data are not uncommon,such as the loss of inner projections caused by impenetrable metal objects,sparse view sampling for radiation dose reduction,and limited view sampling due to geometric constraint scanning.Research on image reconstruction from incomplete projection data has both theoretical and engineering significance.This dissertation focuses on the image reconstruction in three different incomplete data cases which suffer exterior problem,sparse-view problem and limited-angle problem,respectively.The main achievements are as follows:1.A projection completion method based on both radon and spatial domain regularization is proposed.Estimation and restoration of the missing data from neighboring projections is the most widely used approach for metal artifact reduction(MAR).Conventional projection completion methods only employ the information of radon domain and often result in several artifacts in the reconstructed images.To solve this problem,this paper proposes a novel projection completion method that not only considers the prior of the projection but also exploits the prior of the image to be reconstructed.A projection restoration model with prior exploitation for radon and spatial domain is demonstrated and then efficiently solved by Chambolle-Pock optimization approach.The results of both numerical simulation and actual CT data indicate that the proposed method exhibits reasonable performance and outperforms the conventional methods when applied to metal artifact reduction problems.With the prior exploitation in the spatial domain,the unwanted artifacts in the reconstructed image could be obviously reduced,and the recovered part of projection could be more accurate.2.An iterative MAR approach with unmatched projector/backprojector pairs is proposed.Conventional iterative MAR methods easily introduce new artifacts around metal implants in practical CT applications.To solve this problem,an iterative strategy utilizing unmatched projector/backprojector pairs is proposed.Based on the analysis of the physics and math prelateship of imaging model,we conclude that the above mentioned phenomenon is caused by the data inconsistency in practical data acquisition.Then,a ramp filter is introduced into the back-projection procedure to restrain the inconsistency components in low frequencies and generate more reliable images of the regions around metals with convergence guarantee.Experimental results of both numerical simulation and actual CT data show that the proposed method is able to effectively remove streak metal artifacts,as well as improving image quality around the metal objects.In particular,the method demonstrates clear improvement over some mainstream MAR algorithms.3.A total generalized p-variation regularization-based sparse-view CT image reconstruction algorithm is proposed.Total generalized variation(TGV)regularization-based image reconstruction,which shows a favorable performance in edge preservation,is a practical useful method that handles sparse-views problems in CT image reconstruction.However,conventional TGV regularization employs L1-based form,which is not the most direct measure of sparsity.In this study,we propose a total generalized p-variation(TGpV)regularization model to improve the sparsity exploitation of TGV and offer efficient solutions to few-view CT image reconstruction problems.To solve the nonconvex optimization problem of the TGpV minimization model,an efficient iterative algorithm based on variable splitting and alternating minimization method is presented.All of the resulting subproblems decoupled by variable splitting admit explicit solutions by applying generalized p-shrinkage mapping and proximal point method.Experimental results of both numerical simulation and actual CT data show that the proposed method can accurately reconstruct sharp edges and smoothly varying image regions from insufficient data.In particular,the proposed method shows considerable advantages over the standard TGV-based algorithm.4.An Euler's elastica-based image reconstruction algorithm is proposed to solve the limited-angle problem.In the case of limited-angle problem,the reconstruction can be treated as an inverse problem that is inherently ill-posed and the reconstructed image often suffers severe blurs in the missing directions.To solve this problem,we firstly considered the visual connectivity of the objects and found that the isophotes in the specific missing directions are easy to be multiplex and broken.Based on this analysis,a curvature-driven Euler's elastica regularization model is introduced to compensate the broken gaps and recover the details with continuous smooth isophotes,and then keep the edge information without undesirable distortions.The proposed model is solved via augmented Lagrangian method and alternating minimization scheme by minimizing the subproblems alternately.Experimental results of both numerical simulation and actual CT data show that the proposed method is able to effectively preserve edge and recover details,as well as achieving a better image quality for limited-angle CT image reconstruction.5.A deep convolutional neural network-based limited-angle artifacts suppression method is proposed.Iterative reconstruction is the main approach to reconstruct images from limited-angle projections,but its cost is high and its application is limited.This paper proposed an 'analytical reconstruction plus post-processing' strategy for solving limited-angle problem.Based on the analysis of limited-angle artifacts in Filtered Backprojection FBP reconstructions,a deep convolutional neural network is introduced to reduce the specific artifacts and recover true details.An end-to-end mapping between FBP and artifact-free images is learned by data-driven method,and implicit features involving artifacts are extracted and suppressed via nonlinear mapping.The experimental results indicate that the proposed method show a stable and prospective performance on artifact reduction and detail recovery for limited-angle tomography.In particular,the presented strategy is a non-iterative approach which could be integrated into practical applications immediately with little increase in computation.The findings in this study enable a more effective approach for improving the image quality of reconstruction results from limited projection data and will have a high value for practical applications.