Line Integral Based Cone-beam CT Deblurring Research

In recent years,cone-beam CT has played an important role in micro-structure imaging due to its high acquisition speed and good image isotropy.The key to micro-structure imaging of cone-beam CT lies on the imaging quality of the edge of the micro-structure.The spatial resolution of the cone-beam CT is susceptible to blurring effects,including soft tissue-cavity edge blurring and high-contrast calcification structure blurring.Therefore,the blurring effect of cone-beam CT becomes a key problem to be solved in micro-structure imaging.The blurring effect of cone-beam CT mainly comes from non-ideal physical factors including finite focal spot size of X-ray source,the resolution of the flat panel detector,and the photon spreading effect in scintillator.Due to the complexity of the above factors,it is difficult for the projection domain deblurring algorithm to completely and accurately model the blurring effect of the entire system.The constructed model is more complex and difficult to solve.In contrast,the mathematical model of image domain deblurring algorithm is concise,and the convolution kernel can be easily obtained by methods such as experimental measurement and model-based estimation.For the three-dimensional reconstruction,the image domain deblurring method performs three-dimensional convolution which leads to higher computational complexity.And such methods belong to the image post-processing method.Before applying the image deblurring,it is necessary to perform three-dimensional CT reconstruction.Thus,it is difficult to be directly incorporated into the data acquisition process.For the above problems of projection domain and the image domain,we propose a method of line integral based cone-beam CT deblurring,which performs deconvolution on line integral domain to improve the spatial resolution of CT images.Firstly,logarithmic transformation is applied to the original projection to obtain line integral data.Then,we establish a deconvolution model based on the system point spread function in the line integral.This includes data fidelity terms that guarantee data integrity conditions and regularization terms that control noise level.The convolution kernel comes from the point spread function of the imaging system and uses a rotationally symmetric single-parameter Gaussian function as the model.Finally,a three-dimensional analytical reconstruction is applied to the deconvolved line integral data to obtain high-resolution CT images.Proposed method is essentially equivalent to the image domain deblurring method.In practice,it performs two-dimensional deconvolution to line integral data.Therefore,proposed method has advantages in computational efficiency.Since the model establishes in line integration domain,it is simple to add the deblurring operation to data acquisition process and directly obtains the recovered data.The image deconvolution problem usually leads to large scale of computation due to the large matrix generated by the three-dimensional images.The conventional convex optimization algorithm is less efficient in solving such problems.In this paper,the Chambolle-Pock algorithm is selected to solve the large matrix problem of the system.Instead of solving a linear system involving a large matrix,we only need to perform a multiplication by the large matrix at each iteration through the Chambolle-Pock algorithm,which also has a faster convergence speed.Total variation has the property of maintaining a sharp edge of the structure and was chosen as a regularization term of the objective function to achieve balance between noise and spatial resolution.In this paper,proposed method was verified in simulation data,physical phantom data and experimental mouse data,which was compared with three-dimensional image domain deconvolution method in terms of spatial resolution,noise distribution and calculation time.The experimental results show that the two-dimensional line integral domain deblurring and the three-dimensional image domain deblurring approach have close performance in enhancing spatial resolution of CT images,but the two-dimensional line integral model has greater advantages in computational efficiency.In simulation study,compared with the original CT image,the spatial resolution of the two-dimensional model increased by approximately 21.4%,the three-dimensional model increased by approximately 14.1%,and the calculation time of two-dimensional model was 4.6%of the three-dimensional model.In the physical model study,the spatial resolution of the two-dimensional model increased by about 25.9%,the three-dimensional model increased by about 22.2%,and the calculation time of two-dimensional model was 4.4%of the three-dimensional model.In the experimental mouse study,the spatial resolution of the two-dimensional model increased by approximately 12.5%,the three-dimensional model increased by approximately 13.9%,and the calculation time of two-dimensional model was 4.9%of the three-dimensional model.Overall,both the line integral domain and image domain deblurring method achieve close performance in spatial resolution improvement,but the computational efficiency of the former is 20 times more efficient than the latter one.