Image Reconstruction Techniques For X-ray Spectral Computed Tomography

X-ray Computed tomography（XCT）can reconstruct the internal image of an object by measuring the information of passing x-ray.However,the conventional XCT not only has disadvantages in tissue contrast and spatial resolution,but also it fails to provide quantitative analysis results and discriminate the materials.To avoid these limitations,the spectral CT emerges and attracts increasing attentions.A typical spectral CT system can collect several projections from different energy windows by employing a photon counting detector（PCD）.The spectral CT has a great potential in improving spatial resolution,enhancing material discrimination ability and providing quantitative results.However,the limited photons within the narrow energy window can result in severe noise,energy response inconsistency and so on within the spectral CT projections.Therefore,how to reconstruct high-quality image from low-quality X-ray spectral CT projection becomes a big challenge.To reconstruct high-quality reconstructed images,it is necessary to explore the correlation of projections among different energy channels and other hidden image features.According to the theory of X-ray spectral CT and further combining compressed sensing with tensor analysis theory,this work aims to formulate X-ray spectral CT optimization reconstruction model.The main research works can be summarized as follows:（1）According to the characteristics and challenges of X-ray spectral CT,the image reconstruction is introduced.First,to address the image reconstruction issue,the prior knowledge is introduced into the fundamental image reconstruction model to improve image quality.Then,the total variation,tensor dictionary learning and tensor factorization theories are introduced,which can lay a solid theoretical foundation for this dissertation.Finally,the image quality evaluation indexes of the reconstructed image were summarized.（2）Joint image gradient L₀-norm and tensor dictionary learning（L₀TDL）method was proposed X-ray spectral CT image reconstruction.There are the difficulties for tensor dictionary learning based image reconstructed method in the case of low-dose,especially in image edge preservation,features loss,etc.Considering image gradient L₀-norm has the advantages in image edge and feature extraction,it is appropriate to formulate the image gradient L₀-norm minimization with tensor dictionary method for low-dose X-ray spectral CT image reconstruction.The L₀TDL not only can characterize the correlation between different energy channels,but also it can encode the sparsity of single energy-channel.The benefits are to reduce low-dose artifacts and further achieve the goal of obtaining high-quality images.Both numerical simulation and preclinical real dataset experiments validate the effectiveness of L₀TDL method.The experiment results demonstrate that the L₀TDL can protect image edge and feature recovery in low-dose case.（3）The image reconstruction based on spatial-spectral cube matching frame（SSCMF）was studied in this dissertation.On one hand,the L₀TDL model contains many parameters and its results mainly depends on the image quality used in the training process of tensor dictionary learning.On the other hand,the analysis of X-ray spectral CT image feature demonstrates that non-local image similarity is also image feature for X-ray spectral CT image.To avoid the limitation of L₀TDL and further explore image non-local similarity,the SSCMF model is formulated.First,the cube matching frame（CMF）regularization was extracted by utilizing the tensor theory to interpret the BM4D denoising algorithm.Then,the proposed CMF regularization was proposed to characterize non-local similarity of X-ray spectral CT image,generating the SSCMF image reconstruction method.The experiments on numerical simulation and clinical real datasets validate the outperformance by comparing with other competitors.The experiment results demonstrate the SSCMF can more easily obtain higher quality reconstructed image in the full dose case.（4）The image reconstruction based on non-local low-rank cube tensor factorization（NLCTF）was studied in this dissertation.The SSCMF was implemented by grouping the non-local similar spatial-spectral cubes and then operating the two-step filtering（hard-thresholding filtering and collaborating filtering）on each formulated group.However,on one hand,the size of extracted spatial-spectral cube is too small to encode the low-rank property of the group.On the other hand,the two-step filtering in the SSCMF cannot address with group well so that the finer image features and structures missing.Here,to fully explore the non-local similarity,the tensor factorization was employed to further explore the image feature for X-ray spectral CT and generated the NLCTF reconstruction method.The NLCTF can use the tensor factorization to dig the correlation and compensation of high-low energy channels.In addition,the formulated 3^rd-order low-rank tensor by clustering up the image non-local similar cubes can fully encode image non-local similarity.All of these can lead to the high-quality reconstructed image.Both numerical simulation and preclinical real dataset experiments validate the effectiveness of the NLCTF method.The experiment results demonstrate that the NLCTF can obtain higher quality images than other the-state-of-art methods in low-dose case.In summary,this dissertation focuses on the research of the image reconstruction methods for X-ray spectral CT.According to the theories of tensor dictionary learning,image gradient and tensor analysis,this dissertation gradually constructed L₀TDL,SSCMF and NLCTF algorithms,and their effectiveness were validated by numeric simulation and preclinical real datasets.