Research On Spectral CT Image Reconstruction Algorithm Based On Tensor Analysis

The X-ray spectral computed tomography（CT）technique based on photon-counting detectors exhibits significant advantages over traditional XCT technology in acquiring spectral information and accurately characterizing material compositions,which holds vital significance for the novel advancements in applications such as biomedical imaging,security inspections,and non-destructive testing within academic realms.However,the narrow energy spectrum channel and limited photon count of spectral CT result in significant noise in the projection data,making the reconstructed image quality susceptible to noise and artifacts,which affects the practical application of spectral CT technology.Traditional reconstruction methods only focus on the correlation of single channel image,neglecting the relationship between multi-channel images,which affects the restoration of image structure.In order to capture the correlation feature of images between energy channels and improve reconstruction accuracy,reconstruction algorithms based on tensor models have been proposed.Although current algorithms have achieved better results,the feature representation of spectral image correlation is still insufficient,and there are still shortcomings in noise suppression,artifact removal,and image structure restoration of spectral images,which affect image quality and subsequent material decomposition.Therefore,on the basis of existing reconstruction algorithms,this article focuses on further exploring the correlation representation of images within the single channel spatial domain and between the multi-channel spectral domains of the energy spectral,and conducts research on energy spectral CT image reconstruction algorithms based on tensor analysis to make the energy spectral CT reconstruction algorithm more accurate and effective.The principal research issues of this paper are as following:（1）To address the problem of losing image edges and details in sparse view reconstruction using tensor dictionary learning,a reconstruction algorithm based on enhanced constrained tensor dictionary learning is proposed.This algorithm first utilizes the advantage of tensor dictionary learning to fully explore the correlation between various channels of CT energy spectral images;Secondly,combining the high signal-to-noise ratio characteristics of full spectral images and the advantage of image gradient L₀ norm to protect image edges,an integrated regularization term is designed to further enhance sparsity constraints in the single channel image domain.The algorithm’s performance was verified on both simulated and physical mouse datasets.The results of the experiment demonstrate that the algorithm is capable of proficiently conserving image edge attributes and subtle structures,while repressing image noise and improving the quality of reconstructed images.（2）To address the problem that the quality of images reconstructed by tensor dictionary algorithm depends heavily on the trained tensor dictionary samples,and it is difficult to obtain high quality pre-trained global tensor dictionary in practice,a total generalized variational（TGV）tensor decomposition energy spectral CT reconstruction algorithm is proposed.In the process of constructing tensor volumes,this algorithm utilizes non local similarity features of images to construct fourth order tensor volumes,and uses CP（Canonical Polyadic）tensor decomposition instead of pre-trained tensor dictionaries to further explore the inter channel correlation of images;Simultaneously,introducing the TGV regularization term to characterize spatial sparsity features,the use of higher-order derivatives can better adapt to different image structures and noise levels.The algorithm’s performance was assessed using simulated and real mouse datasets.The experimental results demonstrate that the proposed algorithm could effectively suppress noise and artifacts,while restoring image small structures.（3）To address the problem of Tucker and CP tensor decomposition algorithms not being able to achieve low rank and sparsity unification in tensor space simultaneously,a spectral CT image reconstruction algorithm combining KBR（Kronecker Basis Representation）tensor decomposition and total variation（TV）is proposed.This algorithm utilizes KBR tensor decomposition to simultaneously explore the low rank and sparsity of third-order image tensors,unifying the sparsity metric of tensor space.The introduction of TV regularization in the single channel image domain can effectively suppress artifacts caused by image block aggregation during tensor decomposition,and further improve image quality without excessively increasing algorithm runtime.The algorithm’s effectiveness was assessed through simulated and real mouse datasets.The experimental results demonstrate that the proposed algorithm could better restore the image structures,while effectively suppressing artifacts and noise.