Research On Regularization Methods For XCT Reconstruction From Variable Truncation (VT) Data And Sparse Angle Data

X-ray computed tomography?XCT?technique has been widely used in medicine and diagnosis,industry detection,material analysis,etc,because of its ability to reconstruct the inner structure of object noninvasively.In practice,due to the limitations of experi-mental equipments,measurement conditions,user needs and other factors,the projection data we usually collect is incomplete.Problems related to this type of data are called incomplete projection data problems?or incomplete data problems?.Reconstructing im-ages from incomplete projection data is an important problem in XCT reconstruction,and it is also one of the research hotspots in this field.This thesis mainly studies two types of incomplete data problems:VT?data??variable truncation?data??problem and sparse angle problem.On the one hand,VT problem derives from in-suit x-ray CT?ISXCT?imaging.Due to the influence of equipments,the x-ray beam is partially or completely occluded in some projection directions,which will cause the loss of projection data.Because the missing projection data changes in different projection directions,this data is called variable truncation data.The image reconstructed from VT data often suffers from severe artifacts.On the other hand,in medical diagnosis,in order to reduce the harm of x-ray radiation to patients,reducing the radiation dose is an effective method.It can be achieved by reducing the projection angles?sparse angle sampling?.This method reduces the radiation to patients and also shortens the scanning time,but it often leads to severe reconstruction artifacts.Therefore,studying both VT problem and sparse angle problem have important application value and social significance.Since the regularization method is an effective method to study the problem of incom-plete projection data,this thesis will study the regularization reconstruction models and algorithms for these two problems.In view of the difficulty of parameter determination,this thesis proposes a background estimation method for estimating artifact strength.The estimated artifact strength is used to design the selection of regularization parameters.Therefore,this thesis proposes an adaptive sparse representation VT data reconstruction model?ASVT?,and uses ADMM?Alternating Direction Multiplier Method?method to solve this modelFor the sparse angle problem,this thesis studies a non-convex regularization method based on L₁-?L₂.Due to the outstanding sparse expression ability of L₁-L₂ regu-larization,and better image edge retention ability of TV?total variation?method,this thesis proposes an improved model?LGTV?based on both the new gradient operator and L₁-?L₂ regularization after defining a generalized gradient operator and studying related properties of it.This thesis employ ADMM method to solve LGTV model,this method decomposes the primal problem into several subproblems which can be solved by methods such as proximity point method,fast Fourier transform,etcIn order to illustrate the effectiveness of the proposed models,a comparative experi-ment is conducted for the ASVT method and the LGTV method respectively.Numerical experimental results and quantitative indicators such as structural similarity,etc,indicate that the ASVT method not only suppresses the artifacts generated by the VT data,but also overcomes the weak edges generated by the TV method;the LGTV method is better than TV based L₁-L₂ method in removing noise,and retains more image details than this method.