Research On Fast Image Reconstruction Algorithms For Low-Dose Spectral CT

Computed tomography(CT)imaging has become one of the indispensable imaging technologies in medical diagnosis.With the continuous development of medicine,it is more and more difficult for conventional CT to meet clinical needs,especially in composition analysis and functional analysis.As an upgrade of conventional CT,spectral CT has the advantages of component analysis and functional analysis,and is gaining more and more extensive clinical application and attention.However,spectral CT imaging requires the acquisition of two sets of X-ray projections,resulting in patients receiving twice the radiation dose of conventional CT.In addition,the existing spectral CT reconstruction algorithm has a problem that takes too long.High radiation dose will increase the probability of disease in the patient's body and endanger the health of the patient;time-consuming reconstruction will increase the patient's waiting time and delay the diagnosis and treatment of the disease.Therefore,the study of fast image reconstruction algorithms for low-dose spectral CT has important clinical significance.Sparse view projection is one of the main methods to achieve low dose scanning.This dissertation focuses on the difficulties and key points of fast image reconstruction algorithms for low-dose spectral CT,and has achieved the following achievements:(1)Aiming at the problem that the projection domain basic material decomposition algorithm based on the lookup table is time-consuming,a linear acceleration algorithm and a plane acceleration algorithm are proposed.These two algorithms use the straight line and plane approximation to look up the table data respectively,and transform the process of matching the optimal estimation value of the base material decomposition coefficient projection into the process of calculating the estimated value through the line equation or the plane equation.The experimental results show that the two algorithms can improve the matching rate of the best estimated value of the base material decomposition coefficient projection by more than 100 times.At the same time,the projection estimates of the base material decomposition coefficients obtained by the two algorithms are the same as the projection estimates of the base material decomposition coefficients obtained by the current look-up table method.(2)Aiming at the problem that the data fitting process of the projection domain basic material decomposition algorithm based on data fitting is time-consuming and the portability of the fitting coefficient is poor,an iterative algorithm for fitting the basic material decomposition coefficient projection and the high-low energy projection relationship is proposed.The algorithm constructs an appropriate surrogate function by using the convexity of the relationship between the basic material decomposition coefficient projection and the high-low energy projection.Through the optimization of the surrogate function,the best estimation value of the base material decomposition coefficient projection is calculated iteratively.The experimental results show that the proposed algorithm can obtain high-precision projection estimation value of the base material decomposition coefficient projection.Moreover,the time consumed by the algorithm is on the same order of magnitude as the linear acceleration algorithm proposed in this paper.Furthermore,the algorithm does not need to calculate the fit factor.(3)Aiming at the problem that the existing reconstruction algorithms for low-dose decomposition coefficient image is time-consuming,a new image reconstruction algorithm is proposed.The objective function of the algorithm consists of a least squares function and a total variational regular term.In order to improve the reconstruction speed,according to the characteristics of the least squares function and the total variational regularization term,two methods for constructing the separable quadratic substitution function is proposed respectively.Wherein,the proposed quasi-tangent method is currently the only method for constructing separable quadratic substitution function for total variation.The experimental results show that the quality of the basic material decomposition coefficient image reconstructed by the proposed reconstruction algorithm is the same as the quality of the basic material decomposition coefficient image reconstructed by the existing reconstruction algorithm,and the reconstruction consumption time is only 1/10 of the existing algorithm,which greatly improves the reconstruction speed.This reconstruction algorithm is only suitable for the case where the high and low energy projection data are in the same direction.(4)Aiming at the problem that the existing direct reconstruction algorithm has high scanning dose and slow reconstruction speed,a new algorithm for directly reconstructing the basic material decomposition coefficient image is proposed.The objective function of the algorithm consists of a maximum likelihood function and a total variational regular term.This objective function is very complex and cannot be solved directly.In order to optimize the objective function,quasi-Taylor series method is proposed to reconstruct the separable quadratic substitution function of the maximum likelihood function,and the proposed quasi-tangent method was applied to reconstruct the separable quadratic substitution function of the total variational regular term.The experimental results show that the proposed algorithm can directly reconstruct high-quality basic material decomposition coefficient images with sparse and different-direction high-and low-energy projection data,and the reconstruction time is only 1/6 of the existing algorithm.The proposed algorithm is suitable for the case where the high and low energy projection data are in different direction.Compared with the existing similar algorithms,firstly,the proposed algorithm can reconstruct high-quality images by using sparse projection,which greatly reduces the radiation dose of patients;secondly,it has high parallelism and simple calculation process,which can greatly improve the reconstruction speed.In addition,the proposed quasi-Taylor series method provides a new method to construct a separable quadratic substitution function of convex function substitution function for convex functions.By means of the above research,fast reconstruction algorithms for low-dose spectral CT is proposed for both the same-direction and different-direction high-and low-energy projections.These algorithms can reduce the dose of X-ray radiation that patients are exposed to and reduce the waiting time of patients,which has important clinical value,economic value and social significance.