基于时域光信息的近红外光学成像
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摘要
利用时域辐射传输方程,模拟了脉冲激光在弥散介质内的传输。利用广义Guess-Markov随机场模型,构建了正则化项,克服了反问题的病态特性。将步长加速法与序列二次规划算法相结合来求解反问题,构建了一种不依赖初值的光学成像算法,重建了二维弥散介质内的吸收系数和散射系数的分布,并模拟了癌变生物组织的近红外光学成像。研究结果表明,所提算法能够较好地解决初值依赖性问题且具备高精度,重建得到的图像能够清晰地分辨出介质内部的结构。
The time-domain radiative transfer equation is used to simulate the propagation of pulsed laser in dispersive medium. The generalized Guess-Markov random field model is adopted to establish a regularization term and thus the ill-posed property of an inverse problem is overcome. The inverse problem is solved by the step acceleration method combined with the sequential quadratic programming algorithm. An optical imaging algorithm which does not rely on the initial values is proposed to reconstruct the distributions of absorption and scattering coefficients in the two-dimensional dispersive medium. The near-infrared optical imaging of the cancerous biological tissues is simulated. The research results show that the proposed algorithm can not only relatively well solve the initial value dependent problem, but also possesses high accuracy. The reconstructed images can show the inner structures of medium clearly.
The time-domain radiative transfer equation is used to simulate the propagation of pulsed laser in dispersive medium. The generalized Guess-Markov random field model is adopted to establish a regularization term and thus the ill-posed property of an inverse problem is overcome. The inverse problem is solved by the step acceleration method combined with the sequential quadratic programming algorithm. An optical imaging algorithm which does not rely on the initial values is proposed to reconstruct the distributions of absorption and scattering coefficients in the two-dimensional dispersive medium. The near-infrared optical imaging of the cancerous biological tissues is simulated. The research results show that the proposed algorithm can not only relatively well solve the initial value dependent problem, but also possesses high accuracy. The reconstructed images can show the inner structures of medium clearly.
引文
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[29] Soni S,Tyagi H,Taylor R A,et al.Investigation on nanoparticle distribution for thermal ablation of a tumour subjected to nanoparticle assisted thermal therapy[J].Journal of Thermal Biology,2014,43:70-80.
[30] Germer C T,Roggan A,Ritz J P,et al.Optical properties of native and coagulated human liver tissue and liver metastases in the near infrared range[J].Lasers in Surgery and Medicine,1998,23(4):194-203.
[2] Joshi A,Rasmussen J C,Sevick-Muraca E M,et al.Radiative transport-based frequency-domain fluorescence tomography[J].Physics in Medicine and Biology,2008,53(8):2069-2088.
[3] Zhao S Q,Li L.Numerical investigation of phase change during thermal ablation of gold films induced by femtosecond laser[J].Acta Optica Sinica,2015,35(12):1214001.赵士强,李凌.飞秒脉冲激光烧蚀金膜的相变传热研究[J].光学学报,2015,35(12):1214001.
[4] Zhang F J,Chen B Q,Zhao S Z,et al.Noninvasive determination of tissue optical properties based on radiative transfer theory[J].Optics & Laser Technology,2004,36(5):353-359.
[5] Tian Q J,Li Z,Chang S T,et al.Measurement method of infrared radiometric characteristics for high-temperature small targets[J].Acta Optica Sinica,2017,37(10):1012004.田棋杰,李周,常松涛,等.高温小目标红外辐射特性测量方法[J].光学学报,2017,37(10):1012004.
[6] Lin X M.Research on small target detecting algorithm based on IR imaging[J].Aero Weaponry,2014(3):12-15,39.蔺向明.基于红外成像的小目标检测技术研究[J].航空兵器,2014(3):12-15,39.
[7] Li H J.Investigation of pulse thermography sensitivity for CFRP delamination in aero-space industry[J].Acta Optica Sinica,2011,31(s1):s100112.李慧娟.航空CFRP中分层缺陷的脉冲红外检测精度研究[J].光学学报,2011,31(s1):s100112.
[8] Wang Z,Zhang Y W,Yu Y,et al.Depth test of pipeline defects by active thermal excitation and infrared thermography[J].Acta Optica Sinica,2018,38(9):0912003.王卓,张云伟,喻勇,等.主动热激励式红外热成像管道缺陷深度检测[J].光学学报,2018,38(9):0912003.
[9] Abdoulaev G S,Hielscher A H.Three-dimensional optical tomography with the equation of radiative transfer[J].Journal of Electronic Imaging,2003,12(4):594-601.
[10] Klose A D,Hielscher A H.Optical tomography with the equation of radiative transfer[J].International Journal of Numerical Methods for Heat & Fluid Flow,2008,18(3/4):443-464.
[11] Chu M,Vishwanath K,Klose A D,et al.Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations[J].Physics in Medicine and Biology,2009,54(8):2493-2509.
[12] Zhou X Q,Wang Q,Fan Y,et al.Fast reconstruction scheme of diffuse optical tomography for dense sampling dataset[J].Acta Optica Sinica,2013,33(4):0417001.周晓青,王倩,范颖,等.面向大数据量的扩散光层析成像快速重建算法[J].光学学报,2013,33(4):0417001.
[13] Balima O,Favennec Y,Boulanger J,et al.Optical tomography with the discontinuous Galerkin formulation of the radiative transfer equation in frequency domain[J].Journal of Quantitative Spectroscopy and Radiative Transfer,2012,113(10):805-814.
[14] Kim H K,Hielscher A H.A PDE-constrained SQP algorithm for optical tomography based on the frequency-domain equation of radiative transfer[J].Inverse Problems,2009,25(1):015010.
[15] Kim H K,Charette A.A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer[J].Journal of Quantitative Spectroscopy and Radiative Transfer,2007,104(1):24-39.
[16] Bu P,Wang X Z,Osami S.Fourier-domain optical coherence tomography based on sinusoidal phase modulation[J].Acta Optica Sinica,2007,27(8):1470-1474.步鹏,王向朝,佐佐木修己.正弦相位调制的频域光学相干层析成像[J].光学学报,2007,27(8):1470-1474.
[17] Ren K,Bal G,Hielscher A H.Frequency domain optical tomography based on the equation of radiative transfer[J].SIAM Journal on Scientific Computing,2006,28(4):1463-1489.
[18] Yu J J,Liu J L.Simulation of bioluminescence tomography based on nonconvex L1-2 regularization[J].Chinese Journal of Lasers,2018,45(4):0407006.余景景,刘佳乐.基于非凸L1-2正则化的生物发光断层成像仿真研究[J].中国激光,2018,45(4):0407006.
[19] Klose A D,Hielscher A H.Optical tomography using the time-independent equation of radiative transfer:Part 2:inverse model[J].Journal of Quantitative Spectroscopy and Radiative Transfer,2002,72(5):715-732.
[20] Marin M,Asllanaj F,Maillet D.Sensitivity analysis to optical properties of biological tissues subjected to a short-pulsed laser using the time-dependent radiative transfer equation[J].Journal of Quantitative Spectroscopy and Radiative Transfer,2014,133:117-127.
[21] Qiao Y B,Qi H,Chen Q,et al.An efficient and robust reconstruction method for optical tomography with the time-domain radiative transfer equation[J].Optics and Lasers in Engineering,2015,78:155-164.
[22] Wang S G.Inversed transient radiative transfer in one-dimensional non-homogeneous media[J].Infrared and Laser Engineering,2013,42(8):2012-2016.王圣刚.一维非均匀介质中的瞬态辐射反问题[J].红外与激光工程,2013,42(8):2012-2016.
[23] Klose A D.The forward and inverse problem in tissue optics based on the radiative transfer equation:A brief review[J].Journal of Quantitative Spectroscopy and Radiative Transfer,2010,111(11):1852-1853.
[24] Boulanger J,Balima O,Charette A.Refractive index imaging from radiative transfer equation-based reconstruction algorithm:Fundamentals[J].Journal of Quantitative Spectroscopy and Radiative Transfer,2011,112(7):1222-1228.
[25] Su T S,Peng W J,Zhou Z Y,et al.The computation principle and algorithm program design of optimization[M].Changsha:The National University of Defense Technology Press,2002:83-86.粟塔山,彭维杰,周作益,等.最优化计算原理与算法程序设计[M].长沙:国防科技大学出版社,2002:83-86.
[26] Ye J C,Webb K J,Bouman C A,et al.Optical diffusion tomography by iterative-coordinate-descent optimization in a Bayesian framework[J].Journal of the Optical Society of America A,1999,16(10):2400-2412.
[27] Powell M J D.The convergence of variable metric methods for non-linearly constrained optimization calculations[M].Amsterdam:Elsevier,1978:27-63.
[28] Zhang B.Photothermal signal simulation for laser-irradiated semi-transparent media and its inverse problems[D].Harbin:Harbin Institute of Technology,2014:121-132.张彪.激光作用下半透明介质光热信息模拟及反问题研究[D].哈尔滨:哈尔滨工业大学,2014:121-132.
[29] Soni S,Tyagi H,Taylor R A,et al.Investigation on nanoparticle distribution for thermal ablation of a tumour subjected to nanoparticle assisted thermal therapy[J].Journal of Thermal Biology,2014,43:70-80.
[30] Germer C T,Roggan A,Ritz J P,et al.Optical properties of native and coagulated human liver tissue and liver metastases in the near infrared range[J].Lasers in Surgery and Medicine,1998,23(4):194-203.