Research On CT Reconstruction Algorithms For Incomplete Projection Data

Computerized Tomography(CT)is known as a technology used for non-destructive testing.In CT,a set of projection data at different angles of an object is measured,from which a 2D or 3D image visualizing the structures of obj ect is reconstructed.CT has been widely used in many fields such as medical diagnosis,industrial inspection,and security check,because it produces a cross-sectional image with relatively high time and space resolutions,and can easily be visualized in 2D or 3D.In many imaging situations,however,due to consideration of X-ray dose and physical restrictions occurring in each scanning environment or the object,measured projection data is not complete,which means that the data does not satisfy the condition of accurate image reconstruction.Therefore,for many years,accurate CT image reconstruction from various incomplete projection data has been one of popular research topics in CT community.In this thesis,we focus on the development of image reconstruction algorithms from various incomplete projection data.These include low-dose CT,few-view CT,and limited-angle CT situations.When performing image reconstruction from the incomplete projection data,quality of reconstructed image and computational cost of image reconstruction are very important.The main contributions of our thesis can be summarized as follows:1.It is well-known that accurate reconstructions are difficult from the projection data obtained in the low-dose and few-view CT.In these cases,analytical reconstruction methods such as Filtered Back-Projection(FBP)perform image reconstruction very fast,but cannot obtain good reconstructions.On the other hand,iterative reconstruction methods can achieve better image quality,but they are time-consuming because of the necessity of a number of iterations.To combine the merits of analytical methods and iterative methods,we proposed a fast iterative reconstruction algorithm for fan-beam scanning geometries,including standard fan-beam full scan,short-scan,and super-short-scan source trajectories.This algorithm covers both the low-dose and few-view CT cases.Our proposed algorithm employs a preconditioning matrix constructed based on fan-beam FBP method,which is able to accelerate the iteration of commonly used fisrt-order primal-dual algorithms.The above-mentioned different fan-beam scanning geometries require different FBP methods.Therefore,for each fan-beam geometry,we designed different preconditioning matrices by using the different FBP methods.Our proposed algorithm converges to the exact solution minimizing the cost function very fast.In our experiments,the convergence speed was more than 2.5 times faster compared to some standard fast iterative reconstruction methods such as Fast Iterative Shrinkage-Thresholding Algorithm(FISTA).In addition,our proposed algorithm possesses an easily parallelizable structure,thereby the reconstruction process can be further accelerated by using parallel computing environments such as Graphical Processing Unit(GPU).2.Cone-beam CT can directly reconstruct a 3D image of object.Cone-beam CT has many advantages such as faster scanning speed,isotropic spatial resolution,and efficient utilization of X-ray power.Therefore,it has been widely used in medical and industrial fields for many years.However,image reconstruction in cone-beam CT is much more complicated compared to those in 2-D parallel-beam and fan-beam CT.Furthermore,computation cost required for image reconstruction becomes much higher.Therefore,cone-beam CT requires faster iterative algorithms.In this thesis,by using the fact that approximate analytical reconstruction algorithms need much simpler computations than the iterative reconstruction,we proposed a fast iterative algorithm for cone-beam CT with the circular source trajectory.In this algorithm,we use analytical FDK(Feldkamp,Davis,Kress)algorithm to design a preconditioning matrix to accelerate the iterative reconstruction.This algorithm covers both the low-dose and few-view CT situations.Our proposed algorithm performs better than the other competitive algorithms in our experiments,and the convergence speed of our algorithm is much faster.In addition,by using a GPU,we can further accelerate the reconstruction process because our algorithm is easily parallelizable.3.For the limited-angle CT reconstruction,we proposed a fast iterative reconstruction algorithm based on anisotropic total variation(TV).This algorithm also covers both the low-dose and few-view CT situations,and it can be applied to the parallel-beam,fan-beam,and cone-beam scanning geometries.The ordinary TV utilizes only image sparsity in the gradient domain for regularization.In comparison,the anisotropic TV not only utilizes the image sparsity,but also utilizes information on angular range of measuring projection data to design the regularization term.From this modification,the anisotropic TV achieve better performance in the limited-angle CT reconstruction.By combining the anisotropic TV with our fast iterative algorithm mentioned above,our proposed algorithm is able to achieve better reconstruction compared to the other competitive methods,and reconstructed images suffer from less image artifact appearing in the limited-angle CT.4.To utilize prior information on the image sparsity in a more successful way,we proposed an iterative reconstruction algorithm based on the reweighted anisotropic TV for the limited-angle CT.Although the L0 norm is the most direct measure to evaluate the sparsity,we cannot exactly minimize the L0 norm cost due to its nonconvex nature.Therefore,in most previous studies,the L1 norm is used as a substitute because it can be minimized by using a class of standard convex optimization techniques.The reweighting technique assigns different weights to each term of the L1 norm cost function,which results in a better approximation of the L0 norm cost.We incorporated the reweighting technique into the anisotropic TV,and the resulting algorithm not only utilizes the image sparsity for the regularization more efficiently,but also utilizes information on the angular range of measuring projection data.Compared with the other standard TV reconstruction methods,our proposed algorithm is able to reconstruct better images.The quantitative measures such as root mean square error of the reconstruction image obtained by our algorithm was 20%smaller than the other standard TV methods,and the computational cost was reduced by at least 7%.