基于SQP算法的弥散介质辐射物性场重建
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摘要
介质的辐射物性的参数测量在高温火焰燃烧诊断、无损检测、生物医学成像等领域有着广泛的应用。传统的直接测量方法得到的大多是测量试件的等效物性,精确的测量通常需要通过反演的方法得到。利用时域辐射传输方程模拟脉冲激光在弥散介质内的传输,求解介质边界的透反射信号。采用序列二次规划(sequential quadratic programming,SQP)算法求解反问题,重建了二维弥散介质内的吸收系数和散射系数分布。利用广义的高斯-马尔科夫随机场模型构建正则化项,加入目标函数中以克服反问题的病态特性。同时使用OpenMP并行计算技术对部分代码做了并行化处理,从而大大减少了重建时间。重建结果表明基于SQP算法能够很好地重建出吸收系数和散射系数的分布。
The measurement of radiative properties for disperse media has a broad application in high temperature flame combustion diagnosis,nondestructive testing,biomedical imaging and other related fields.Traditional direct measurement methods are mostly to measure the equivalent properties of the specimen,while precise measurements usually need to be obtained by inversion method.Transporttheroy-based reconstruction algorithm can effectively overcome this problem,however,it has a high computational burden and often slowly converging.Therefore,methods that have high accurate and low computation burden are desirable.In this paper,time-domain radiative transfer equation was applied to simulate the photon propagation of the pulse laser in disperse media and then to obtain abundant transmission and reflection signals of media boundary.Sequential quadratic programming algorithm was introduced to inverse the distribution of absorption and scattering coefficient of two-dimensional disperse media.The generalized Gaussian Markov random fields(GGMRF)model was adopted as regularization term to overcome the ill-posed nature of the inverse problem.Simultaneously,to reduce the computation time,the openMP parallel technology is applied to the part of the codes.The reconstruction results show that the SQP algorithm is a promising method to well reconstruct the distribution of absorption andscattering coefficient of two-dimensional disperse media.
The measurement of radiative properties for disperse media has a broad application in high temperature flame combustion diagnosis,nondestructive testing,biomedical imaging and other related fields.Traditional direct measurement methods are mostly to measure the equivalent properties of the specimen,while precise measurements usually need to be obtained by inversion method.Transporttheroy-based reconstruction algorithm can effectively overcome this problem,however,it has a high computational burden and often slowly converging.Therefore,methods that have high accurate and low computation burden are desirable.In this paper,time-domain radiative transfer equation was applied to simulate the photon propagation of the pulse laser in disperse media and then to obtain abundant transmission and reflection signals of media boundary.Sequential quadratic programming algorithm was introduced to inverse the distribution of absorption and scattering coefficient of two-dimensional disperse media.The generalized Gaussian Markov random fields(GGMRF)model was adopted as regularization term to overcome the ill-posed nature of the inverse problem.Simultaneously,to reduce the computation time,the openMP parallel technology is applied to the part of the codes.The reconstruction results show that the SQP algorithm is a promising method to well reconstruct the distribution of absorption andscattering coefficient of two-dimensional disperse media.
引文
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[16]QUAN H,GUO Z.Fast 3-D optical imaging with transient fluorescence signals[J].Optics Express,2004,12(3):449-457.
[17]BOULANGER J,CHARETTE A.Numerical developments for short-pulsed near infra-red laser spectroscopy[J].Journal of Quantitative Spectroscopy&Radiative Transfer,2005,91(3):297-318.
[18]ZIRAK R,KHADEMI M.An efficient method for model refinement in diffuse optical tomography[J].Optics Communications,2007,279(2):273-284.
[19]QIAO Y B,QI H,CHEN Q,et al.Multi-start iterative reconstruction of the radiative parameter distributions in participating media based on the transient radiative transfer equation[J].Optics Communications,2015,351:75-84.
[20]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.
[21]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&Radiative Transfer,2007,104(1):24-39.
[22]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.
[23]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.
[24]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&Radiative Transfer,2012,113(10):805-814.
[25]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&Radiative Transfer,2010,111(11):1852-1853.
[26]GUAN J,FANG S,GUO C.Optical tomography reconstruction algorithm based on the radiative transfer equation considering refractive index[J].Computerized Medical Imaging and Graphics,2013,37(3):256-262.
[27]QI H,QIAO Y B,SUN S C,et al.Image reconstruction of two-dimensional highly scattering inhomogeneous medium using MAP-based estimation[J].Mathematical Problems in Engineering,2015,2015:1-9.
[28]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&Radiative Transfer,2014,133:117-127.
[29]QIAO Y B,QI H,CHEN Q,et al.An efficient and robust reconstruction method for optical tomography with the timedomain radiative transfer equation[J].Optics and Lasers in Engineering,2016,78:155-164.
[30]SAQUIB S S,HANSON K M,CUNNINGHAM G S.Model-based image reconstruction from time-resolved diffusion data[J].Proc.SPIE,1997,3034:369-380.
[2]HERNANDEZ R,BALLESTER J.Flame imaging as a diagnostic tool for industrial combustion[J].Combustion and Flame,2008,155(3):509-528.
[3]CLARK M R,MCCANN D M,FORDE M C.Application of infrared thermography to the non-destructive testing of concrete and masonry bridges[J].Ndt.&E.International,2003,36(4):265-275.
[4]HYUN K K,ANDREAS H H.A PDE-constrained SQP algorithm for optical tomography based on the frequencydomain equation of radiative transfer[J].Inverse Problems,2009,25:1-20.
[5]罗剑峰.镜漫反射下多层吸收散射性介质内的瞬态耦合换热[D].哈尔滨:哈尔滨工业大学,2002.LUO J F.Transient coupled heat transfer in multi-layer absorbing-scattering composite with specular and diffuse reflection properties[D].Harbin:Harbin Institute of Technology,2002.
[6]LIU D,YAN J H,WANG F,et al.Inverse radiation analysis of simultaneous estimation of temperature field and radiative properties in a two-dimensional participating medium[J].International Journal of Heat and Mass Transfer,2010,53(21):4474-4481.
[7]MORJ J.The Levenberg-Marquardt algorithm:implementation and theory[J].Lecture Notes in Mathematics,1977,630:105-116.
[8]CHAN R H,NG M K.Conjugate gradient methods for toeplitz systems[J].Siam Review,1996,38:427-482.
[9]田娜.偏微分方程反问题数值解研究和应用[D].无锡:江南大学,2012.TIAN N.Numerical methods for the PDE-based inverse problems and applications[D].Wuxi:Jiangnan University,2012.
[10]江爱朋.大规模简约空间SQP算法及其在过程优化系统中的应用[D].杭州:浙江大学,2005.JIANG A P.Research on large-scale reduced space SQP algorithm and its application to process systems[D].Hangzhou:Zhejiang University,2005.
[11]石国春.关于序列二次规划算法求解非线性规划反问题的研究[D].兰州:兰州大学,2009.SHI G C.Research on algorithm of sequential quadratic programming for nonlinear programming problems[D].Lanzhou:Lanzhou University,2009.
[12]TARVAINEN T,COX B T,KAIPIO J P,et al.Reconstructing absorption and scattering distributions in quantitative photoacoustic tomography[J].Inverse Problems,2012,28(8):1067-1079.
[13]KLOSE A D,HIELSCHER A H.Optical tomography using the time-independent equation of radiative transfer(Ⅱ):Inverse model[J].Journal of Quantitative Spectroscopy&Radiative Transfer,2002,72(5):715-732.
[14]GASSAN S A,ANDREAS H H.Three-dimensional optical tomography with the equation of radiative transfer[J].Journal of Electronic Imaging,2003,12(4):594-601.
[15]ELALOUFI R,CARMINATI R,GREFFET J J.Timedependent transport through scattering media:from radiative transfer to diffusion[J].Journal of Optics A:Pure and Applied Optics,2002,4(5):S103-S108.
[16]QUAN H,GUO Z.Fast 3-D optical imaging with transient fluorescence signals[J].Optics Express,2004,12(3):449-457.
[17]BOULANGER J,CHARETTE A.Numerical developments for short-pulsed near infra-red laser spectroscopy[J].Journal of Quantitative Spectroscopy&Radiative Transfer,2005,91(3):297-318.
[18]ZIRAK R,KHADEMI M.An efficient method for model refinement in diffuse optical tomography[J].Optics Communications,2007,279(2):273-284.
[19]QIAO Y B,QI H,CHEN Q,et al.Multi-start iterative reconstruction of the radiative parameter distributions in participating media based on the transient radiative transfer equation[J].Optics Communications,2015,351:75-84.
[20]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.
[21]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&Radiative Transfer,2007,104(1):24-39.
[22]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.
[23]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.
[24]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&Radiative Transfer,2012,113(10):805-814.
[25]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&Radiative Transfer,2010,111(11):1852-1853.
[26]GUAN J,FANG S,GUO C.Optical tomography reconstruction algorithm based on the radiative transfer equation considering refractive index[J].Computerized Medical Imaging and Graphics,2013,37(3):256-262.
[27]QI H,QIAO Y B,SUN S C,et al.Image reconstruction of two-dimensional highly scattering inhomogeneous medium using MAP-based estimation[J].Mathematical Problems in Engineering,2015,2015:1-9.
[28]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&Radiative Transfer,2014,133:117-127.
[29]QIAO Y B,QI H,CHEN Q,et al.An efficient and robust reconstruction method for optical tomography with the timedomain radiative transfer equation[J].Optics and Lasers in Engineering,2016,78:155-164.
[30]SAQUIB S S,HANSON K M,CUNNINGHAM G S.Model-based image reconstruction from time-resolved diffusion data[J].Proc.SPIE,1997,3034:369-380.