Improved Optimization Method For Constrained CT Reconstruction

X-ray Computed Tomography（CT）uses X-ray sources to scan objects in different directions and accurately reconstruct the interior structure of objects.The purpose of CT imaging is to reconstruct the interior structure details of object without damage.CT scanning has the advantages of fast and nondestructive,and has been widely used in industrial engineering,medical diagnosis,aerospace and other fields.CT image reconstruction is an important step in CT imaging,that is,the process from projection data to reconstruct CT image.For fan-beam CT scanning,the projection data need at least180°+fan-angle to achieve accurate reconstruction conditions.This means that the scanning system or object rotates at least 180°+fan angle around the rotation center.Classical filtered back projection（FBP）and simultaneous algebraic reconstruction technique（SART）reconstruction algorithms can effectively reconstruct high quality images when the projection data is complete.However,due to the damage of X-ray radiation,the limitation of scanning environment and the requirement of scanning time,the obtained projection data may not meet the conditions of accurate reconstruction.When the rotation angle is less than 180°+fan angle,it is called the limited-angle CT problem.Limited-angle CT has a wide range of applications,such as medical imaging,C-arm CT,dental CT and so on.For industrial products such as large diameter pipes or gears,X-ray may not be able to penetrate the central area,or there may be fluid in the pipes with large diameter in service,which may affect the accurate collection of projection data in the central area.Howerer,we are more concerned about the exterior situation of the object.For example,whether there are defects in the pipe wall of large pipes,whether there are cracks in the gear teeth of large gears,etc.This creates an exterior CT problem.Because exterior CT lacks X-ray projection data of the central area,it can only reconstruct images of the outer area of the scanned object.In view of the above incomplete CT reconstruction such as limited-angle and exterior CT problems,it is of great significance to develop advanced CT image reconstruction models and algorithms in order to reconstruct high-quality CT images.The main research contents of this thesis are listed as follows:Firstly,an exterior CT regularization reconstruction algorithm based on wavelet transform and L₀ quasi norm is proposed to reduce noise and artifacts in reconstructed images.Due to the different truncation methods of exterior CT projection data,there is no X-ray passing through the center of the object,so the reconstructed image obtained by the traditional image reconstruction algorithm will have artifacts and noise.Artifacts are mainly distributed along the radial edge of the image,resulting in blurred edges of the image.In this paper,we introduce B-spline compact wavelet framework and use L₀ quasi norm to constrain the sparsity of coefficients after image wavelet transform.The multi-scale property of wavelet transform can better describe the sparsity of image,and the constraint of L₀ quasi norm on wavelet coefficient can remove artifacts and noise while preserving image edge.In this paper,ADMM algorithm is used to solve the regularization problem.Second,the L₀ quasi norm of the coefficients after wavelet transform can be used as the regular term of exterior CT to reduce the artifacts of reconstructed images.However,the wavelet decomposition of two-dimensional image is multi-scale decomposition along the x and y directions of the image,without considering the characteristics of exterior CT scanning mode and the distribution characteristics of exterior CT image artifacts.In order to suppress the artifacts of exterior CT and reconstruct clear images,an exterior CT image reconstruction algorithm based on polar anisotropic relative total variation（ARTV）is proposed in this paper.During the solving process,the exterior CT image is transformed into polar coordinate representation by polar coordinate transformation.Therefore,the edges of CT images distributed along the radial and tangential directions are along the polar angle and diameters of the polar coordinates respectively,and then the ARTV of the image in polar coordinates is used as the regular term to constrain the image to reduce the artifacts near the radial edge of the image.The windowed inherent total variation（WIV）in ARTV can be regarded as the weight of windowed total variation（WTV）,which makes ARTV adaptive to suppress noise and image artifacts and protect image edges.Since the distribution direction of exterior CT artifacts is not uniform,different weights are added to the polar angle and diameters of polar coordinates to ensure the quality of reconstructed images.Then,a limited-angle CT reconstruction algorithm based on total variation and prior image guidance（TVPI-G）is proposed for limited-angle CT image reconstruction,and solved by iterative method.In each iteration,our algorithm first performs a TV step（including SART and TV）to obtain the initial reconstructed image.Then,the results of TV iteration are combined with prior images to form intermediate results.Finally,we modify the intermediate results with the guided image filtering（GIF）,which take the result of TV as the guided image.Finally,we use simulated multi-source X-ray CT to realize the projection data acquisition of limited-angle CT,and use the limited-angle projection data to reconstruct the image.We propose average image induced relative total variation（Aii-RTV）for limited-angle spectral CT reconstruction.Firstly,the limited-angle spectral projection data are weighted averaged.Then the RTV reconstruction algorithm is used to reconstruct the average image using average projection data.Finally,the limited-angle projection data of each energy channel are reconstructed to obtain energy spectral CT images.