基于改进R矩阵方法的光谱反射率重建研究
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摘要
为了解决传统R矩阵方法重建光谱反射率过程中的病态问题,提出了一种正则化R矩阵改进方法。研究了如何使用Tikhonov正则化来限制R矩阵方法求解Moore-Penrose伪逆矩阵中所产生的病态问题,同时使用L曲线方法从训练样本数据中得到有效限制病态情况的最优正则化参数。实验结果表明:与R矩阵方法相比,改进的正则化R矩阵方法重建的光谱精度的平均均方根误差值降低了0.004 25,平均适应度系数值提高了1.325%,色度精度的平均色差值降低了0.141 9,并且在实际的应用中具有较好的表现。该方法能够满足精度较高的文物艺术品颜色再现的需要。
In order to solve the ill-posed problem in the process of reconstructing the spectral reflec-tance using the traditional matrix R method,an improved matrix R method was proposed in this paper.The Tikhonov regularization method was researched to restrict the ill-posed problem to solve the Moore-Penrose pseudo inverse matrix.The L-curve method was used to obtain the optimal regularization parameter by training samples data in order to effectively restrict the ill-posed situation.The experimental results verified that compared with traditional matrix R method,the proposed regularization matrix R method had higher spectral and chromatic accuracy of reconstructed spectrum whose mean root mean square error value reduced 0.00425,mean goodness of fit coefficient value improved 1.325%,and mean color difference value reduced 0.1419.At the same time,the proposed regularization matrix R method achieved good performance in practical application.It can meet the high accuracy of cultural relics color reproduction needs.
In order to solve the ill-posed problem in the process of reconstructing the spectral reflec-tance using the traditional matrix R method,an improved matrix R method was proposed in this paper.The Tikhonov regularization method was researched to restrict the ill-posed problem to solve the Moore-Penrose pseudo inverse matrix.The L-curve method was used to obtain the optimal regularization parameter by training samples data in order to effectively restrict the ill-posed situation.The experimental results verified that compared with traditional matrix R method,the proposed regularization matrix R method had higher spectral and chromatic accuracy of reconstructed spectrum whose mean root mean square error value reduced 0.00425,mean goodness of fit coefficient value improved 1.325%,and mean color difference value reduced 0.1419.At the same time,the proposed regularization matrix R method achieved good performance in practical application.It can meet the high accuracy of cultural relics color reproduction needs.
引文
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[11]穆治亚,艾华,樊孝贺,等.采用整体最小二乘法的条纹图配准方法[J].中国光学,2016,9(6):625-632.MU Z Y,AI H,FAN X H,et al.Inference fringe image registration using total least square method[J].Chinese Optics,2016,9(6):625-632.(in Chinese).
[12]BELL J B.Solutions of ill-posed problems by A.N.Tikhonov,V.Y.Arsenin[J].Mathematics of Computation,1978,32(144):1320-1322.
[13]BONESKY T.Morozov's discrepancy principle and Tikhonov-type functionals[J].Inverse Problems,2009,25(1):015015.
[14]REZGHI M,HOSSEINI S M.A new variant of L-curve for Tikhonov regularization[J].Journal of Computational and Applied Mathematics,2009,231(2):914-924.
[15]刘怡轩,颜昌翔.在线式分光测色仪发展现状[J].中国光学,2014,7(5):712-722.LIU Y X,YAN C X.Development and status of on-line spectrophotometer[J].Chinese Optics,2014,7(5):712-722.(in Chinese)
[2]何颂华,刘真,陈桥.基于矩阵R~理论的光谱降维方法研究[J].光学学报,2014,34(2):0233001.HE S H,LIU Z,CHEN Q.Research of spectral dimension reduction method based on matrix R~theory[J].Acta Optica Sinica,2014,34(2):0233001.(in Chinese).
[3]梅风华,李超,张玉鑫.光谱成像技术在海域目标探测中的应用[J].中国光学,2017,10(6):708-718.MEI F H,LI C,ZHANG Y X.Application of spectral imaging technology in maritime target detection[J].Chinese Optics,2017,10(6):708-718.(in Chinese)
[4]于海琦,刘真,田全慧.一种基于GA-BP神经网络结合PCA的LCD显示器光谱特征化模型[J].液晶与显示,2016,31(2):201-207.YU H Q,LIU Z,TIAN Q H.Spectral characterization model of liquid crystal display based on GA-BP neural network and PCA[J].Chinese Journal of Liquid Crystals and Displays,2016,31(2):201-207.(in Chinese)
[5]URBAN P,ROSEN M R,BERNS R S.Spectral image reconstruction using an edge preserving spatio-spectral wiener estimation[J].Journal of the Optical Society of America A,2009,26(8):1865-1875.
[6]WYSZECKI G.Evaluation of metameric colors[J].Journal of the Optical Society of America,1958,48(7):451-454.
[7]COHEN J B,KAPPAUF W E.Metameric color stimuli,fundamental metamers,and Wyszecki's metameric black[J].The American Journal of Psychology,1982,95(4):537-564.
[8]NEUMAIER A.Solving ill-conditioned and singular linear systems:A tutorial on regularization[J].SIAM Review,1998,40(3):636-666.
[9]SHIMANO N,TERAI K,HIRONAGA M.Recovery of spectral reflectances of objects being imaged by multispectral cameras[J].Journal of the Optical Society of America A,2007,24(10):3211-3219.
[10]ZHAO Y H,BERNS R S.Image-based spectral reflectance reconstruction using the matrix R method[J].Color Research and Application,2007,32(5):343-351.
[11]穆治亚,艾华,樊孝贺,等.采用整体最小二乘法的条纹图配准方法[J].中国光学,2016,9(6):625-632.MU Z Y,AI H,FAN X H,et al.Inference fringe image registration using total least square method[J].Chinese Optics,2016,9(6):625-632.(in Chinese).
[12]BELL J B.Solutions of ill-posed problems by A.N.Tikhonov,V.Y.Arsenin[J].Mathematics of Computation,1978,32(144):1320-1322.
[13]BONESKY T.Morozov's discrepancy principle and Tikhonov-type functionals[J].Inverse Problems,2009,25(1):015015.
[14]REZGHI M,HOSSEINI S M.A new variant of L-curve for Tikhonov regularization[J].Journal of Computational and Applied Mathematics,2009,231(2):914-924.
[15]刘怡轩,颜昌翔.在线式分光测色仪发展现状[J].中国光学,2014,7(5):712-722.LIU Y X,YAN C X.Development and status of on-line spectrophotometer[J].Chinese Optics,2014,7(5):712-722.(in Chinese)