Image Reconstruction Models And Algorithms For Exterior Problem Of CT

Computed Tomography(CT)is an important imaging technology in medical imaging and nondestructive testing.In practical applications,due to the influence of scanning environment,X-ray energy,detector size,object size and other factors,the collected projection data may be incomplete.As a typical incomplete projection reconstruction problem,the exterior problem of CT usually occurs when the collected projection data can only pass through the external ring region of the object.The exterior problem have important applications in industrial CT.For example,the size of the object is so large that x-ray beam cannot cover it completely,the density of the central part of the object is so high that x-rays cannot pass through,and there is fluid flowing inside the large-diameter tube.In the above case,if the regions of interest(ROI)are only located in the external area of the object(defects in the outer wall of the online pipeline,tooth defects of large gear,etc.),the exterior problem of CT can provide a feasible detection scheme.Based on the previous research results,two main characteristics of the exterior problem are described.On the one hand,due to the missing projection data pointing to the inside of the object,the edges along the angular direction can be easily reconstructed,while the edges along the radial direction are difficult to be reconstructed.Serious artifacts are distributed along the radial direction.On the other hand,the missing projection data is different for each point of the object.Due to the missing projection data,the exterior problem of CT is a serious ill-posed inverse problem,so how to suppress the artifacts distributed along the radial direction in the exterior problem is a difficult and core problem.First,we study the two-dimensional exterior problems of CT with fan beam scanning geometry.Due to the missing projection data pointing to the inside of the object,artifacts will be presented in the reconstructed image,especially near the radial edges.Due to the influence of beam hardening,the artifacts in reconstructed images will cause uneven distribution of gray levels.Since the edge information of the image has important reference value for further image analysis and measurement,we consider to combine the image reconstruction algorithm with the image segmentation algorithm,and introduce the image segmentation step in the process of image reconstruction to gradually correct the edges of the reconstructed image.Many studies have shown that RSF(Region Scalable Fitting)can effectively segment images with intensity inhomogeneity.Therefore,we develop a method combining traditional TV(Total Variation)image reconstruction algorithm with RSF image segmentation algorithm(TV-RSF)to preserve edges and suppress artifacts.In this method,a segmentation algorithm(RSF)is introduced after a certain iterative reconstruction step to segment and determine the edges of the image,so as to gradually correct the edges of the image and suppress artifacts.Simulated and real projection data experiments show that our method can effectively reduce the artifacts caused by missing projection data and beam hardening.Second,although the above TV-RSF method can reduce artifacts,the reconstruction results are highly dependent on the accuracy of image segmentation.Hence,the above method has great limitations in practical applications.In order to better deal with the ill-posedness of the exterior problem and better suppress the artifacts along the radial direction,we study the reconstruction algorithms base on the regularization method.According to the characteristics of the artifact distribution in the exterior problem with fan beam geometry,a new regularization term,namely WDTV(weighted directional total variation),which conforms to the characteristics of the artifact distribution in the exterior problem is proposed.Different from the traditional regularization terms,such as the commonly used TV regularization term,the WDTV regularization term has the following characteristics: 1)In order to suppress the artifacts along the radial direction,we choose the radial and angular direction instead of x and y direction in traditional TV to calculate the discrete directional differences.2)In order to enhance the edge response along the radial direction,we introduce two weight parameters in WDTV for discrete differences along radial and angular direction,respectively.The edge response along both directions is controlled by selecting different weight parameters.3)WDTV of the image can be used to describe the sparsity of the gradient modulus of the image,which makes the reconstructed image tend to be an approximate piecewise constant image.Based on the above characteristics of WDTV,we introduce it into the reconstruction model and propose an algorithm of SART+WDTV minimization to solve the reconstruction model.The experimental results of simulated and real projection data show that our reconstruction model and algorithm can suppress radial artifacts and preserve edges better.Third,with the continuous development of CT technology,3D(Three dimensional)cone beam CT has been widely used because of its short scan time,high precision and low radiation dose.In practical applications,the exterior problem of cone beam CT has more prominent practical value.So we study the reconstruction algorithm for the exterior problem of cone beam CT with circular scanning geometry(ECCBCT).According to the experimental analysis,in the ECCBCT,the artifacts in reconstructed images are mainly distributed along the radial,angular and z direction,which correspond to the three directions of cylindrical coordinates.Therefore,based on the idea of previous WDTV,a reconstruction model based on three dimensional WDTV(3D-WDTV)in cylindrical coordinates is developed.We choose radial,angular and z direction to calculate the discrete directional differences,and then set different weight parameters to control the edge response along three different directions.In order to further illustrate our model,we prove that our model is convex,and the algorithm implementation is convenient.In addition,the relation between our model and the traditional TV model is proved.By comparing the differences between our model and the traditional TV model,the effectiveness of our model can be further illustrated.Simulated results show that our model and algorithm are superior in suppressing artifacts.Finally,in WDTV based models,the selection of weight parameters has a great impact on the reconstruction results.The desired reconstruction results can be obtained with appropriate weight parameters.However,improper selection of weighting parameters will introduce serious additional artifacts and reduce the quality of reconstructed images.Generally speaking,the manual selection of weight parameters is subjective and time-consuming.Therefore,we propose a reconstruction model based on weighted polar total variation(WPTV),and verify it on the exterior problem of CT with 2D fan beam geometry.The main difference between WPTV and WDTV lies in that: in WPTV,the weight parameters along radial and angular direction at each point are related to the polar radius and the missing angular range of projection data at that point.Hence the weight parameter of each point is different.In WDTV,the weight parameters are fixed values selected artificially for each point.Therefore,WPTV can better reflect the characteristics of the exterior problem.At the same time,based on WPTV,we give a weight parameter selection scheme.Further,since both WPTV and WDTV will introduce additional streak artifacts in the smoothed area of the image,we use the prior image and the reconstructed image of WPTV for fusion to achieve the purpose of suppressing additional artifacts.Numerical experiments verify the advantages of our proposed model and algorithm in suppressing artifacts and preserving radial edges.