Research On Back Projection Optimization Algorithm Based On Low Rank Matrix Recovery Theory

CT reconstruction technology has been widely applied in the industrial field,and it can carry out tomographic imaging research on the internal structure of industrial equipment.Traditional CT imaging requires the beam to be rotated and scanned within a range of 180 degrees to obtain complete projection data,and the detection environment is highly demanded.However,in practical applications,severe noise interference,energy scattering interference,and incomplete projection are often accompanied by various situations,so that CT image data contains a large amount of noise and artifacts.How to remove noise and eliminate artifacts to truly restore image organization has become a hot spot in the field of CT reconstruction applications,and it is of great significance for non-destructive testing of industrial equipment.In this thesis,the in-depth study of industrial CT image denoising and artifact correction is carried out.Based on the physical nature of image denoising and CT reconstruction,an improved Weighted Nuclear Norm Minimization(WNNM)algorithm is proposed by appropriate mathematical theory derivation.Backprojection reconstruction of industrial CT is performed using an improved weighted nuclear norm minimization algorithm.Aiming at the problem of industrial CT tomographic image denoising,this paper proposes a method based on Mallet transform and Sobel operator to estimate the noise variance for WNNM noise reduction,and the derivation formula of the weight in objective function is given based on the singular value perturbation theory to give.The WNNM algorithm uses the image non-local self-similarity to perform low-rank matrix recovery operations.After noise reduction,not only the image details,edges and texture structures are well preserved,but also the image ambiguity is small after noise reduction.However,the WNNM algorithm assumes that the magnitude of the noise variance in the image is known when denoising,and sets the noise variance parameter and the weight in the objective function according to the subjective experience of the individual,which is theoretically incomplete.Aiming at this problem,this paper proposes an improved WNNM algorithm for estimating the variance of noise in advance.The simulation results show that the proposed signal-to-noise ratio is higher after noise reduction..In view of the artifact correction problem caused by noise in industrial CT images,this thesis applies the improved WNNM combined with Fan-Beam Back Projection algorithm to reconstruct industrial CT images.Firstly,based on the WNNM method,the noise interference of the wide-beam industrial CT scan projection data is reduced,and the data contamination problem is solved from the root;Then,the noise-reduced and coordinate-converted projection data is convoluted with the convolution kernel.And the equal-angle angular Fan-Beam Back Projection reconstructed image formula is deduced after noise reduction processing.Through simulation experiments,it can be seen from the reconstructed image results and the calculated mean square error that the image reconstruction effect of this algorithm is better than the filtered back projection algorithm.