基于通用迭代收缩阈值算法的多光谱生物发光断层成像
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摘要
生物发光断层成像(bioluminescence tomography, BLT)是一种高灵敏非侵入式光学分子成像模态,但近红外光在生物组织中传输的复杂性及表面测量信息的有限性,对BLT光源重建算法提出了较高要求.本文提出了一种基于通用迭代收缩阈值(general iterative shrinkage and threshold,GIST)的BLT重建算法,采用非凸平滑剪切绝对偏差(smoothly clipped absolute deviation, SCAD)惩罚项,并通过迭代求解对非凸惩罚项有解析解的邻近算子问题来获得优化结果.此外,重建中也结合了多光谱测量和收缩可行域策略以降低逆问题的不适定性.为评估该算法的光源定位及多光源辨识能力,本文设计了多组仿真和物理仿体实验,并将GIST与几个典型稀疏重建算法进行了对比.实验结果表明GIST算法在不同光源深度和间隔距离的实验中在中心定位误差方面有较大优势.
Bioluminescence tomography(BLT) is a noninvasive optical molecular imaging modality with high sensitivity. The complexity of near-infrared light transmission in biological tissues and the limitation of measurable information place a higher demand on BLT source reconstruction algorithms. In this paper, we present a reconstruction algorithm based on general iterative shrinkage and threshold(GIST), which uses a non-convex smoothly clipped absolute deviation function as the penalty term, and solves a proximal operator problem that has a closed-form solution for the penalty. In addition, we utilize multispectral measurements and an iteratively shrinking permissible region strategy to address the ill-posedness of the BLT inverse problem. To investigate the source location and multi-source resolution abilities of the proposed method, we perform comparisons between three typical sparse reconstruction algorithms based on several groups of simulations and phantom experiments.The reconstruction results demonstrate great advantages of the proposed GIST algorithm in terms of source location accuracy in all considered source settings with different source depths and separations.
Bioluminescence tomography(BLT) is a noninvasive optical molecular imaging modality with high sensitivity. The complexity of near-infrared light transmission in biological tissues and the limitation of measurable information place a higher demand on BLT source reconstruction algorithms. In this paper, we present a reconstruction algorithm based on general iterative shrinkage and threshold(GIST), which uses a non-convex smoothly clipped absolute deviation function as the penalty term, and solves a proximal operator problem that has a closed-form solution for the penalty. In addition, we utilize multispectral measurements and an iteratively shrinking permissible region strategy to address the ill-posedness of the BLT inverse problem. To investigate the source location and multi-source resolution abilities of the proposed method, we perform comparisons between three typical sparse reconstruction algorithms based on several groups of simulations and phantom experiments.The reconstruction results demonstrate great advantages of the proposed GIST algorithm in terms of source location accuracy in all considered source settings with different source depths and separations.
引文
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32 Hansen P C,O’Leary D P.The use of the L-curve in the regularization of discrete ill-posed problems.SIAM J Sci Comput,1993,14:1487-1503
33 Alexandrakis G,Rannou F R,Chatziioannou A F.Tomographic bioluminescence imaging by use of a combined opticalPET(OPET)system:a computer simulation feasibility study.Phys Med Biol,2005,50:4225-4241
34 Pekar J,Patterson M S.Fabrication and characterization of phantoms with tissue-like optical properties from 500 to700 nm.Med Laser Appl,2010,25:147-153
2 Cong W,Wang G,Kumar D,et al.Practical reconstruction method for bioluminescence tomography.Opt Express,2005,13:6756
3 Gu X,Zhang Q,Larcom L,et al.Three-dimensional bioluminescence tomography with model-based reconstruction.Opt Express,2004,12:3996-4000
4 Zhang B,Wang K K H,Yu J,et al.Bioluminescence tomography-guided radiation therapy for preclinical research.Int J Radiat Oncology Biol Phys,2016,94:1144-1153
5 Mollard S,Fanciullino R,Giacometti S,et al.In vivo bioluminescence tomography for monitoring breast tumor growth and metastatic spreading:comparative study and mathematical modeling.Sci Rep,2016,6:36173
6 Guggenheim J A,Basevi H R A,Styles I B,et al.Bioluminescence tomography improves quantitative accuracy for pre-clinical imaging.In:Proceedings of Society of Photo-Optical Instrumentation Engineers(SPIE),Munich,2013.1-6
7 Wang G,Li Y,Jiang M.Uniqueness theorems in bioluminescence tomography.Med Phys,2004,31:2289-2299
8 Jiang M,He D.Mathematical problems of joint reconstruction for biomedical multi-modality imaging techniques.Sci Sin Math,2016,46:571-577[姜明,何迪.多模态生物医学成像联合重建的数学问题.中国科学:数学,2016,46:571-577]
9 Chaudhari A J,Darvas F,Bading J R,et al.Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging.Phys Med Biol,2005,50:5421-5441
10 Dehghani H,Davis S C,Jiang S,et al.Spectrally resolved bioluminescence optical tomography.Opt Lett,2006,31:365-367
11 Cong A X,Wang G.Multispectral bioluminescence tomography:methodology and simulation.Int J Biomed Imag,2006,2006:1-7
12 Feng J,Jia K,Yan G,et al.An optimal permissible source region strategy for multispectral bioluminescence tomography.Opt Express,2008,16:15640
13 Naser M A,Patterson M S.Bioluminescence tomography using eigenvectors expansion and iterative solution for the optimized permissible source region.Biomed Opt Express,2011,2:3179-3192
14 Naser M A,Patterson M S.Improved bioluminescence and fluorescence reconstruction algorithms using diffuse optical tomography,normalized data,and optimized selection of the permissible source region.Biomed Opt Express,2011,2:169
15 Beck A,Teboulle M.A fast iterative shrinkage-thresholding algorithm for linear inverse problems.SIAM J Imag Sci,2009,2:183-202
16 Gao Y,Wang K,Jiang S,et al.Bioluminescence tomography based on Gaussian weighted laplace prior regularization for in vivo morphological imaging of glioma.IEEE Trans Med Imag,2017,36:2343-2354
17 Yu J,Zhang B,Iordachita I I,et al.Systematic study of target localization for bioluminescence tomography guided radiation therapy.Med Phys,2016,43:2619-2629
18 Liu Y N,Yu J J,Qin X W,et al.The split bregman iteration algorithm for bioluminescence tomography.Sci Sin Inform,2014,44:284-294[刘亚楠,余景景,秦晓伟,等.Split Bregman迭代算法生物发光断层成像.中国科学:信息科学,2014,44:284-294]
19 He X,Liang J,Wang X,et al.Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method.Opt Express,2010,18:24825
20 Xu Z B,Chang X Y,Xu F M,et al.L1/2regularization:a thresholding representation theory and a fast solver.IEEETrans Neural Netw Learning Syst,2012,23:1013-1027
21 Yukawa M,Amari S I.?p-regularized least squares(0
23 Guo H,Yu J,He X,et al.Improved sparse reconstruction for fluorescence molecular tomography with L1/2regularization.Biomed Opt Express,2015,6:1648-1664
24 Okawa S,Hoshi Y,Yamada Y.Improvement of image quality of time-domain diffuse optical tomography with lp sparsity regularization.Biomed Opt Express,2011,2:3334-3348
25 Fan J,Li R.Variable selection via nonconcave penalized likelihood and its oracle properties.J Am Stat Assoc,2001,96:1348-1360
26 Wang H,Li R,Tsai C L.Tuning parameter selectors for the smoothly clipped absolute deviation method.Biometrika,2007,94:553-568
27 Mehranian A,Rad H S,Rahmim A,et al.Smoothly clipped absolute deviation(SCAD)regularization for compressed sensing MRI using an augmented Lagrangian scheme.Magn Reson Imag,2013,31:1399-1411
28 Gong P H,Zhang C S,Lu Z S,et al.A general iterative shrinkage and thresholding algorithm for non-convex regularized optimization problems.In:Proceedings of the 30th International Conference on Machine Learning,Atlanta,2013.37-45
29 Zhang C H,Zhang T.A general theory of concave regularization for high-dimensional sparse estimation problems.Stat Sci,2012,27:576-593
30 Barzilai J,Borwein J M.Two-point step size gradient methods.IMA J Numer Anal,1988,8:141-148
31 Yang Y,Wang K K H,Eslami S,et al.Systematic calibration of an integrated x-ray and optical tomography system for preclinical radiation research.Med Phys,2015,42:1710-1720
32 Hansen P C,O’Leary D P.The use of the L-curve in the regularization of discrete ill-posed problems.SIAM J Sci Comput,1993,14:1487-1503
33 Alexandrakis G,Rannou F R,Chatziioannou A F.Tomographic bioluminescence imaging by use of a combined opticalPET(OPET)system:a computer simulation feasibility study.Phys Med Biol,2005,50:4225-4241
34 Pekar J,Patterson M S.Fabrication and characterization of phantoms with tissue-like optical properties from 500 to700 nm.Med Laser Appl,2010,25:147-153