Research On Limited-angle CT Reconstruction Algorithm Based On Image Gradient L₀ Norm

Computed tomography(CT)is a commonly used non-destructive testing technique.In the practical application of CT,due to the limitation of X-ray radiation dose or the requirement of large-scale object,only limited-angle projection data of testing object can be acquired.For example,when we conduct a CT detection on an aluminum conductor composite core wire that has been installed in a high-voltage network,because the wire itself cannot be rotated,scanning in a full-angle range cannot be achieved,and ultimately only limited-angle projection data can be obtained.When the projection data is complete,that is to say the projection is full-angle,both iterative and analytical algorithms can reconstruct images of high quality.When the projection data is incomplete,that is,the projection data is less than 180°,the existing analytical algorithm and iterative algorithm are not good enough to reconstruct the image,and cannot accurately provide guidance for CT detection.Therefore,it is of great important application value to study a better limited-angle CT reconstruction algorithm.Regarding the problem of limited-angle projections CT reconstruction,we mainly study from two aspects in this paper:First,the reconstruction algorithm based on the image gradient L₀ norm optimization;Second,improving the reconstruction optimization algorithm based on the image gradient L₀ norm.The research content has the following three specific points:(1)We analyzed and compared the advantages and disadvantages of the optimized reconstruction algorithm based on the image gradient L₀ and L₁ norm.From the theoretical and practical aspects of reconstructed image quality,we analyzed and tested the advantages and disadvantages of the reconstruction algorithm on the SART algorithm and the additional norm regularization reconstruction algorithm,and used to solve the limited-angle CT reconstruction problem of carbon fiber composite core wires.Then the effectiveness of the algorithm based on the image gradient L₀ norm was verified.(2)We proposed an optimization algorithm based on image gradient L₀ norm and singular value decomposition(SART+L₀+SVD).For the parameters of the SART+L₀algorithm in limited-angle projection reconstruction,it is difficult to balance the details and structure.First,we use the sparseness of the image to maintain the edge of the image,that is,the L₀ norm of the image gradient;second,we also use the low rank of the image singular value decomposition and kernel norm minimization to better protect the image structure features.The simulation data and actual CT data experiments show that the algorithm can effectively reduce the reconstructed image artifacts and restore the image edge contour to a certain extent.(3)We proposed a super-pixel guided L₀ norm optimization algorithm(SLIC+L₀).In the optimization process of SART+L₀ algorithm,the optimization parameters of the L₀norm are globally unchanged.When the parameter is large,it is easy to cause the loss of details,and when the parameter is too small,the finite angle artifact cannot be eliminated.For the problem of improper image smoothing caused by the global invariance of the L₀norm smoothing parameters,the simple linear iterative clustering super-pixel segmentation algorithm(SLIC)is used to perform super-pixel segmentation on the image,and the logarithmic transformation is used for image enhancement,and then adaptively determine the L₀ norm pixel smoothing parameter based on structural similarity,so that the L₀ norm achieves an appropriate balance between detail maintenance and contour restoration.It can effectively balance the image details and edges protection.Experiments show that the algorithm can effectively restore the image outline and maintain details.