CT Reconstruction Algorithm Based On Low Rank Constraint

Computed tomography(CT)has developed rapidly in clinical medical diagnosis,and the research of CT reconstruction algorithm has achieved satisfactory results.However,with the further development of CT reconstruction technology,the high dose of CT makes the cancer risk of CT become a problem that can not be ignored,which makes reducing the radiation dose of CT become a hot issue to be solved urgently.In order to reduce the injury caused by high radiation dose,the researchers introduced compression sensing(CS)theory to reduce the sampling time of the signal with the help of random projection at a lower sampling frequency than Nyquist Shannon sampling frequency.However,although the current hospital CT image reconstruction algorithm can recover the high quality image,the algorithm requires high completeness of projection data,which requires more radiation dose in scanning,which will cause harm to patients.Although the CT image reconstruction algorithm based on compression perception can reconstruct CT image with less projection data,it can not be applied in the actual medical diagnosis because of its long operation time,image artifact and weak denoising ability.This thiese will focus on the reconstruction of low-dose CT projection data,aiming at improving the quality of CT image reconstruction algorithm based on compression perception.The purpose of this thiese is to study the algorithm of CT image reconstruction based on low rank constraints,the main contents are as follows:(1)Based on the theory of compression perception,sparse representation and low rank matrix restoration,the thiese studies the problems of artifact and projection data in traditional CT image reconstruction algorithm.A new algorithm based on low rank matrix restoration(LRC CT)is proposed.Firstly,the initial value of the image is estimated.At the same time,the image block is grouped by using the self similarity of natural image,and the non local self similarity priori of image signal is established.Singular value threshold is adopted,SVT)is used to solve the L1 norm regularization problem and approach the image matrix with low rank.Then,a new algorithm based on low rank constraint is proposed to improve the quality of CT image reconstruction.The experimental results of ideal data and noisy data show that compared with the contrast algorithm,this thiese can effectively remove artifacts and obtain better CT images.(2)Based on the finite difference theory and the related knowledge of gradient descent method,a non local TV regularized CT image reconstruction algorithm based on low rank constraint(tvlrc)is proposed to solve the problems of fuzzy detail organization and over smooth edge in the current CT image reconstruction algorithm.Based on the LRC CT algorithm model,TV regularization constraints are applied to low rank matrix,and the objective function is solved by singular value threshold method,algebraic iteration method,alternate multiplier algorithm and other optimization algorithms.The experimental results show that tvlrc can effectively suppress the artifact and the edge over smooth problem under incomplete projection data compared with the contrast algorithm,and further improve the quality of CT image reconstruction.