Research On Image Reconstruction Algorithms For Incomplete Projection CT Based On Compressed Sensing

Computed Tomography(CT)is widely used in rail transit equipment testing,automotive key components testing,industrial non-destructive testing,medical services and diagnosis and other fields.However,more and more attention has been paid to the harm of X-ray radiation to human body and the surrounding environment.In order to reduce the harm of X-ray radiation to human body,CT system for medical diagnosis is increasing to consider reducing radiation doses.In industrial CT inspection,half-covered projection,sparse angle and limited angle projection have to be faced sometimes.In the above cases,it is inevitable to face the problem of CT image reconstruction with incomplete projection.For incomplete projection,it is generally unable to meet the requirements of Shannon Sampling Theorem.Therefore,due to the appearance of aliasing artifacts,it is impossible to reconstruct CT images with high quality.Compressed Sensing(CS)theory is helpful for CT image reconstruction using the sparsity of the image as prior knowledge,which can obviously improve the reconstruction quality of incomplete projection CT images.Based on CS theory,Total Variation(TV)minimization and Dictionary Learning(DL)regular sparse constraints,this dissertation studies the model and improvement method of CT image reconstruction with incomplete projection for the above-mentioned incomplete projection reconstruction problem.The main innovative works are as follows:(1)There are situations in industrial CT examination that the whole cross-section of the scanned object can not completely cover the field of view(FOV).The FOV half-covered projection CT iterative reconstruction is proposed to meet the need of detecting larger size objects with relatively smaller size detector.In order to solve this problem under the condition of incomplete projection CT image reconstruction,and based on the CS technology,the regular optimization reconstruction model of CT imaging,which is under the L1-norm of image pixels and TV constraint at the same time,is introduced,and a solution of SB-TVM algorithm is proposed.The numerical simulation of Shepp-Logan image results show that for half-covered sparse projection CT image reconstruction,the proposed SB-TVM algorithm has advantages for better reconstruction quality with less iterations when compared with that of the existing Algebraic Reconstruction Techniques(ART)algorithm and the L1-norm of image pixels constraint reconstruction algorithm(Split Bregman method).The four evaluation metrics including the Root-Mean-Square-Error(RMSE),the Mean-Absolute-Error(MAE),the Peak-Signal-to-Noise-Ratio(PSNR),the Residuals,also show that the reconstuciton quality for SB-TVM is much better than the corresponding ones of ART and Split Bregman.(2)Reconstructed images from CT using ART and Simultaneous ART(SART)algorithms often suffer from obvious artefacts when only sparse and limited-angle projections data are available.Using the good ability of dictionary learning in image feature extraction and signal sparse representation,a iterative reconstruction algorithm ART-DL-L1 is proposed to overcome the aforementioned limitations.This algorithm is based on an L1 norm constraint of DL,combined with ART.An alternate iterative solving strategy based on "ART first,then adaptive DL" is suggested,.For both noisy projection of 360° sparse data and limited-angle data of 120°,simulation reconstruction results from the Shepp-Logan image obtained using ART-DL-L1 appear to be better than those obtained using the SART and TV algorithms,as well as better than the cutting-edge ART-DL-L2 algorithm.Five evaluation metrics corresponding to RMSE,MAE,PSNR,Residuals and the Structural SIMilarity index(SSIM)are adopted to estimate the reconstruction effect.The results suggest that the five metrics obtained using ART-DL-L1 outperform those obtained using the other three algorithms.The impacts of various-sized patches played in the DL part for ART-DL-L1 are considered in the simulations,and the patch size for best-reconstructed image quality is identified in the case as 25(5x5).The proposed ART-DL-L1 algorithm might reduce artefacts from incomplete projection and suppress noise in the projection data.(3)To improve image reconstruction quality of sparse and limited angle projection CT,a novel reconstruction algorithm ART-DL-Lp based on DL is developed and tested.An Lp norm dictionary learning term is suitable for regular term of objective function for CT image reconstruction.This is helpful for solving the objective function by combining the ART algorithm.The alternate solving strategy of the algorithm of "ART first,then the adaptive DL" is provided.The impact on reconstruction results of ART-DL-Lp at different p values(0<p<1)is also considered.For both noisy projection data of 360° sparse and limited-angle of 150°,the digital experiments show that ART-DL-Lp is superior to those of ART,SART,and ART-DL-L2.The objective evaluation metrics of RMSE,MAE,PSNR,Residuals and SSIM are all better than those of the contrasted three algorithms.In both incomplete projection situations,smaller p-value of ART-DL-Lp algorithm induces more close reconstructed images to the original image and better five objective evaluation metrics.The reconstruction efficiency of the proposed ART-DL-Lp for CT imaging to noisy incomplete projections outperforms ART,SART and ART-DL-L2 algorithms,and lower p-value results in better reconstruction effects.(4)Based on TV and DL respectively constrained by L2,L1 and Lp(0<p<1)norm,three CT image reconstruction algorithms TV-DL-L2,TV-DL-L1 and TV-DL-Lp are proposed respectively by combining the two regularization methods,and a step-by-step alternating solution strategy of "TV part first,then the adaptive DL part" is presented.For noisy projection data,the reconstruction effects of the algorithm TV-DL-L2 for three kind of limited-angle projection cases,150 °,120 °,and 90 °,are verified by simulation reconstruction.The reconstructed images of the algorithm TV-DL-L2 are compared with those of ART,SART and TV.The quality of the reconstructed image of the algorithm TV-DL-L2 is better than that of the comparative objects for the incomlete projection data.For the above three projection cases,the five quantitative evaluation indexes of the algorithm are all better than the corresponding evaluation indexes of ART,SART and TV algorithms.The simulation reconstruction respectively verified the reconstruction effects of TV-DL-L1 and TV-DL-Lp algorithms on 360° and 150° noise-containing projection data.The reconstruction results of the algorithms TV-DL-L1 and TV-DL-Lp are compared with those of TV and TV-DL-L2 algorithms.The quantitative analysis results also show that the reconstruction quality of the TV-DL-L1 and TV-DL-Lp algorithms on the Shepp-Logan outperform those of TV and TV-DL-L2.The proposed TV-DL-L2,TV-DL-L1,and TV-DL-Lp based on TV and dictionary learning combined regularization improve the quality of incomplete projection CT image reconstruction.Aiming at the insufficiency of incomplete projection reconstruction in CT imaging,the six algorithms,including SB-TVM,ART-DL-L1,ART-DL-Lp,TV-DL-L2,TV-DL-L1 and TV-DL-Lp,are proposed.The simulation results show that the reconstructed image quality of each proposed algorithm outperforms the contrast algorithms.The quantitative evaluation metrics of the reconstructed image exceed the corresponding result obtained by the comparison algorithms.The proposed algorithms achieve the effect of improving the quality of CT image for incomplete projection.