结合平滑l_0范数和可行区域的有限投影荧光分子断层成像
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摘要
有限投影荧光分子断层成像(FMT)可以以较短的数据采集时间在动物体内快速重建出荧光目标的三维分布。然而,由于较少的投影数据使得有限投影FMT具有严重的病态性。为了降低FMT重建的病态性并提高重建速度,考虑到FMT中光源稀疏分布的特性,提出了一种结合平滑l0范数(SL0)和可行区域的有限投影FMT重建方法,采用一种基于SL0的FMT重建方法,利用一个连续函数来逼近l_0范数,以实现快速求解,同时将可行区域作为有效的先验信息,以提高重建精度。数字鼠模型的重建结果表明,在3、6、9个激发点下,重建图像的位置误差都小于1mm,重建时间缩短,3个激发点下的重建时间为8s。物理实验的重建结果进一步表明了该方法在实际FMT重建上的可行性。
Limited-projection fluorescence molecular tomography(FMT)allows rapid reconstruction of threedimensional distribution of fluorescent targets in animals through shorter data acquisition times.However,due to less projection data,the limited-projection FMT undergoes severe ill condition.In order to reduce the ill condition of FMT reconstruction and improve the reconstruction speed,we propose a reconstruction method for limitedprojection FMT.Considering the characteristics of the sparse distribution of the target of FMT,this method combines with smoothed l0 norm and feasible region of prior information.A continuous function approximates the smoothed l_0 norm,which improved the calculation speed.And the feasible region of the prior information improves the precision of the recovered results.The reconstruction results of digital mouse model show that the position error of the reconstructed image is less than 1 mm at 3,6 and 9 excitation points and the reconstruction time is shortened,and the reconstruction time under the 3 excitation points is 8 s.The reconstruction result of physical phantom further verifies the feasibility of this method in practical FMT applications.
Limited-projection fluorescence molecular tomography(FMT)allows rapid reconstruction of threedimensional distribution of fluorescent targets in animals through shorter data acquisition times.However,due to less projection data,the limited-projection FMT undergoes severe ill condition.In order to reduce the ill condition of FMT reconstruction and improve the reconstruction speed,we propose a reconstruction method for limitedprojection FMT.Considering the characteristics of the sparse distribution of the target of FMT,this method combines with smoothed l0 norm and feasible region of prior information.A continuous function approximates the smoothed l_0 norm,which improved the calculation speed.And the feasible region of the prior information improves the precision of the recovered results.The reconstruction results of digital mouse model show that the position error of the reconstructed image is less than 1 mm at 3,6 and 9 excitation points and the reconstruction time is shortened,and the reconstruction time under the 3 excitation points is 8 s.The reconstruction result of physical phantom further verifies the feasibility of this method in practical FMT applications.
引文
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[13]Xue Z W,Ma X B,Zhang Q,et al.Adaptive regularized method based on homotopy for sparse fluorescence tomography[J].Applied Optics,2013,52(11):2374-2384.
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[15]Yi H J,Zhang X,Peng J Y,et al.Reconstruction for limited-projection fluorescence molecular tomography based on a double-mesh strategy[J].BioMed Research International,2016,2016:5682851.
[16]Mohimani H,Babaie-Zadeh M,Jutten C,et al.Afast approach for overcomplete sparse decomposition based on smoothed l0 norm[J].IEEE Transactions on Signal Processing,2009,57(1):289-301.
[17]Guo H B,Hou Y Q,He X W,et al.Adaptive hp finite element method for fluorescence molecular tomography with simplified spherical harmonics approximation[J].Journal of Innovative Optical Health Sciences,2014,7(2):1350057.
[18]Dong F,Hou Y Q,Yu J J,et al.Fluorescence molecular tomography via greedy method combined with region-shrinking strategy[J].Laser&Optoelectronics Progress,2016,53(1):011701.董芳,侯榆青,余景景,等.结合区域收缩和贪婪策略的荧光分子断层成像[J].激光与光电子学进展,2016,53(1):011701.
[2]Vonwil D,Christensen J,Fischer S,et al.Validation of fluorescence molecular tomography/micro-CT multimodal imaging in vivo in rats[J].Molecular Imaging and Biology,2014,16(3):350-361.
[3]Bai J,Xu Z.Fluorescence molecular tomography[M].Berlin Heidelberg:Springer,2013:185-216.
[4]Hou Y Q,Jing M Y,He X W,et al.Fluorescence molecular tomography using a stochastic variant of alternating direction method of multipliers[J].Acta Optica Sinica,2017,37(7):0717001.侯榆青,金明阳,贺小伟,等.基于随机变量交替方向乘子法的荧光分子断层成像[J].光学学报,2017,37(7):0717001.
[5]Zhang X,Yi H J,Hou Y Q,et al.Fast reconstruction in fluorescence molecular tomography based on locality preserving projection[J].Acta Optica Sinica,2016,36(7):0717001.张旭,易黄建,侯榆青,等.基于局部保留投影的荧光分子断层成像快速重建[J].光学学报,2016,36(7):0717001.
[6]He Y,Cao X,Liu F,et al.Influence of limitedprojection on fluorescence molecular tomography[J].Journal of Innovation in Optical Health Science,2012,5(3):1250020.
[7]Radrich K,Mohajerani P,Bussemer J,et al.Limited-projection-angle hybrid fluorescence molecular tomography of multiple molecules[J].Journal of Biomedical Optics,2014,19(4):046016.
[8]Radrich K,Ale A,Ermolayev V,et al.Improving limited-projection-angle fluorescence molecular tomography using a co-registered X-ray computed tomography scan[J].Journal of Biomedical Optics,2012,17(12):126011.
[9]Xu Z,Bai J.Analysis of finite-element-based methods for reducing the ill-posedness in the reconstruction of fluorescence molecular tomography[J].Progress in Natural Science,2009,19(4):501-509.
[10]Han D,Tian J,Liu K,et al.Sparsity-promoting tomographic fluorescence imaging with simplified spherical harmonics approximation[J].IEEETransactions on Biomedical Engineering,2010,57(10):2564-2567.
[11]Nu1ez M Z,Arias F X,Carlos A M C.Comparative analysis of sparse signal reconstruction algorithms for compressed sensing[C/OL].Twelfth LACCEI Latin American and Caribbean Conference for Engineering and Technology,2014.https://www.researchgate.net/publication/264121234_Comparative_Analysis_of_Sparse_Signal_Reconstruction_Algorithms_for_Compressed_Sensing.
[12]He X W,Liang J M,Wang X R,et al.Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method[J].Optics Express,2010,18(24):24825-24821.
[13]Xue Z W,Ma X B,Zhang Q,et al.Adaptive regularized method based on homotopy for sparse fluorescence tomography[J].Applied Optics,2013,52(11):2374-2384.
[14]Liu X,Yan Z Z,Lu H B.Performance evaluation of apriori information on reconstruction of fluorescence molecular tomography[J].IEEE Access,2015,3:64-72.
[15]Yi H J,Zhang X,Peng J Y,et al.Reconstruction for limited-projection fluorescence molecular tomography based on a double-mesh strategy[J].BioMed Research International,2016,2016:5682851.
[16]Mohimani H,Babaie-Zadeh M,Jutten C,et al.Afast approach for overcomplete sparse decomposition based on smoothed l0 norm[J].IEEE Transactions on Signal Processing,2009,57(1):289-301.
[17]Guo H B,Hou Y Q,He X W,et al.Adaptive hp finite element method for fluorescence molecular tomography with simplified spherical harmonics approximation[J].Journal of Innovative Optical Health Sciences,2014,7(2):1350057.
[18]Dong F,Hou Y Q,Yu J J,et al.Fluorescence molecular tomography via greedy method combined with region-shrinking strategy[J].Laser&Optoelectronics Progress,2016,53(1):011701.董芳,侯榆青,余景景,等.结合区域收缩和贪婪策略的荧光分子断层成像[J].激光与光电子学进展,2016,53(1):011701.
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