Research On The Algorithm Of Cone-beam X-ray Luminescence Computed Tomography Imaging Based On Simplified Spherical Harmonic Approximation And Sparse Regularization

Molecular imaging technique has the potential to accurately localize and quantify the three dimensional(3D)distribution of optical agents in vivo.X-ray luminescence computed tomography(XLCT)has been one of the most important techniques of molecular imaging.XLCT is realized by X-ray-excitable probes and optical imaging system based on micro-CT.Its advantages of XLCT are manifested in the avoidance of a significant background noise and the ability of imaging deeper tissue.As an emerging technique of XLCT,cone-beam X-ray luminescence computed tomography(CB-XLCT)can decrease the scanning time and fully utilize the X-ray dose by using a cone beam X-ray source,thus it is expected to be a powerful tool for image-guided radiotherapy.In this thesis,researches on further improving the image quality of CB-XLCT for early detection of small tumor in preclinical research are conducted.Specifically,the system prototype,photon-transportation model,imaging strategies and reconstruction algorithms have been investigated to solve the problem of fast CB-XLCT imaging.The main contributions of thesis are listed as follows:1)We presented a comparative analysis between pencil-beam XLCT and cone-beam XLCT which are the two principal types of XLCT system.Respective performance indexes such as the excitation scheme,scanning costs,efficiency of reconstruction,spatial resolving capacity and reconstruction costs are compared and analyzed in detail.Three groups of contrast experiments have been designed:the scanning cost of pencil-beam XLCT is 436s but the cone-beam XLCT's is only 10s.In the experiment with single target,the reconstruction cost and location error of pencil-beam XLCT are 82.57s and 0.47mm,the cone-beam XLCT's are 172.63s and 1.59mm;In the two group experiments with double targets which edge distances are 1mm and 0.5mm respectively,for the pencil-beam XLCT,the reconstruction results are accurate and the location error are less than 0.8mm,but the location error of the cone-beam XLCT both reach 1.7mm or so for the double targets which edge distance is 1mm,and can not make correct separation when edge distance is reduced to 0.5mm.Experimental results demonstrate that:compared with the cone-beam XLCT,the pencil-beam XLCT has better performance in location accuracy,spatial resolving and reconstruction costs,due to its "excitation priors",but has obviously poor capability on the cost of system scanning.The contribution of this work is to provide a valuable reference to researchers for appropriate XLCT system selection or designing in preclinical research.2)We presented a systematic comparison between the common-used Monte Carlo model and simplified spherical harmonics(SPN)model.The performance of the two methods was evaluated over several main spectrums using a known XLCT material.We designed both a global measurement based on the cosine similarity and a locally-averaged relative error,to quantitatively assess these methods.The results show that the SP3 could reach a good balance between the modeling accuracy and computational efficiency for all of the tested emission spectrums.Besides,the SP1(which is equivalent to the diffusion equation(DE))can be a reasonable alternative model for emission wavelength over 692nm.In vivo experiment further demonstrates the reconstruction performance of the SP3 and DE.This study would provide a valuable guidance for modeling the photon-transportation in CB-XLCT imaging.3)Since the CB-XLCT imaging suffers from a severe ill-posed problem.In order to solve the problem efficiently,a sparse non-convex Lp(0<p<1)regularization was utilized for the efficient reconstruction for early detection of small tumor in CB-XLCT imaging.Specifically,we transformed the non-convex optimization problem into iteratively reweighted scheme based on the L1 regularization.Further,an iteratively reweighted split augmented lagrangian shrinkage algorithm(IRW_SALSA-Lp)was proposed to efficiently solve the non-convex Lp(0<p<1)model.We studied eight different non-convex p-values(1/16,1/8,1/4,3/8,1/2,5/8,3/4,7/8)in both 3D digital mouse experiments and in vivo experiments.The results demonstrate that the proposed nonconvex methods outperform L2 and L1 regularization in accurately recovering sparse targets in CB-XLCT.And among all the non-convex p-values,our Lp(1/4<p<1/2)methods give the best performance.4)Since single-view data reconstruction is a key issue of CB-XLCT imaging and promotes the study of dynamic XLCT imaging effectively.However,it suffers from serious ill-posedness in the inverse problem.In order to solve the problem efficiently,a multi-spectrum strategy is adopted to relieve the ill-posedness of reconstruction.The method is based on the third-order simplified spherical harmonics approximation model.Then,an orthogonal Laplacianfaces-based method is proposed to reduce the large computational burden without quality degradation.Both simulated data and in vivo experimental data were used to demonstrate the efficiency and robustness of the proposed method.The results indicate that the proposed method can produce better reconstruction in terms of both location and quantitative recovering,and it is computational efficiently.This makes it a practical and promising method for single-view CB-XLCT imaging.5)Since the columns of system matrix used for CB-XLCT imaging tend to be highly coherent,which means L1 minimization may not produce the sparsest solution.In order to solve the problem efficiently,we proposed a novel reconstruction method by minimization of the difference of L1 and L2 norms.To solve the non-convex L1-2 minimization problem,an iterative method based on the difference of convex algorithm(DCA)is presented.In each DCA iteration,the update of solution involves an L1 minimization subproblem,which is solved by the alternating direction method of multipliers with an adaptive penalty.We investigated the performance of the proposed method with both simulated data and in vivo experimental data.The results demonstrate that the DCA for L1-2 minimization outperforms the representative algorithms for L1,L2,L1/2 and L0 when the system matrix is highly coherent.