COSM中基于三维高斯点扩展函数的解卷积算法的研究
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摘要
在三维显微成像里，可以将显微镜聚焦在生物样本的不同深度来获取二维图像序列，再通过序列图像获得样本的三维信息。但是，每个聚焦层面的图像，不仅包含本层面的信息，还包含其它层面的离焦模糊信息，导致图像质量下降。通常使用两种方法来复原图像：一种是激光扫描共焦显微术(LSCM)，它可以通过光路去模糊而得到物体的三维图像；另一种是计算光学切片显微术(COSM)，它通过计算的方法来分离图像序列中焦平面上和焦平面外的光信息，从而得到样本正确的三维形态。同LSCM相比，COSM具有信噪比高，对样本不产生漂白现象和价格便宜等优势，但由于其数据量大，有运算速度慢的缺点。
本文提出了基于三维高斯点扩展函数模型的参数盲解卷积算法(PBD)。由于PBD算法需要在估计样本函数的同时估计点扩展函数(PSF)的参数，而通常采用的PSF模型较为复杂，计算量大，收敛慢，而采用三维高斯模型的PBD算法只需要估计两个参数，因此在保证复原效果的前提下，计算量大大降低了。
本文又提出了基于变化PSF模型的Hopfield神经网络图像复原算法。因为在利用Hopfield神经网络进行图像复原的算法中，都是基于PSF不变的模型，而在实际显微系统中由于样本的折射率和透镜折射率不匹配，致使不同深度的PSF是不一样的。同时为了实现三维图像序列的复原，还首次将Hopfield神经网络用于三维图像序列的复原中，并提出了基于三维高斯PSF的复原算法，取得了较好的复原效果。
In the 3D microscopical imaging, 2D serial images could be recorded when the microscope is focused on different planes of the biological specimen. So the 3D information of the specimen could be recorded through these serial images. But each in-focus plane does not only have information from its own plane, but also from out-of-focus planes, which leads to the image degrading. Usually, there are two ways to restore the image. One is the Laser Scanning Confocal Microscopy (LSCM). It can get the 3D image of the object through the light route by debluring. The other one is the Computational Optical Sectioning Microscopy (COSM). It can get the correct 3D configuration of the object by separating the light information of the in-focus plane from the out-of-focus planes. Compared with the LSCM, the COSM has the advantages of high SNR, no bleaching and low price. But because of a large amount of data, it also has the disadvantage of low computation rate.
In this paper, we present a Parametric Blind Deconvolution algorithm (PBD) based on 3D Gauss Point Spread Function (PSF). The PBD algorithm needs to estimate the specimen function and the parameters of the PSF simultaneously. The practical medel of the PSF is so complex that it requires a large computation and it converges slowly. But based on the simplified 3D Gauss model, the PBD algorithm only needs to estimate two parameters. While retaining the restoring effect, the
本文提出了基于三维高斯点扩展函数模型的参数盲解卷积算法(PBD)。由于PBD算法需要在估计样本函数的同时估计点扩展函数(PSF)的参数，而通常采用的PSF模型较为复杂，计算量大，收敛慢，而采用三维高斯模型的PBD算法只需要估计两个参数，因此在保证复原效果的前提下，计算量大大降低了。
本文又提出了基于变化PSF模型的Hopfield神经网络图像复原算法。因为在利用Hopfield神经网络进行图像复原的算法中，都是基于PSF不变的模型，而在实际显微系统中由于样本的折射率和透镜折射率不匹配，致使不同深度的PSF是不一样的。同时为了实现三维图像序列的复原，还首次将Hopfield神经网络用于三维图像序列的复原中，并提出了基于三维高斯PSF的复原算法，取得了较好的复原效果。
In the 3D microscopical imaging, 2D serial images could be recorded when the microscope is focused on different planes of the biological specimen. So the 3D information of the specimen could be recorded through these serial images. But each in-focus plane does not only have information from its own plane, but also from out-of-focus planes, which leads to the image degrading. Usually, there are two ways to restore the image. One is the Laser Scanning Confocal Microscopy (LSCM). It can get the 3D image of the object through the light route by debluring. The other one is the Computational Optical Sectioning Microscopy (COSM). It can get the correct 3D configuration of the object by separating the light information of the in-focus plane from the out-of-focus planes. Compared with the LSCM, the COSM has the advantages of high SNR, no bleaching and low price. But because of a large amount of data, it also has the disadvantage of low computation rate.
In this paper, we present a Parametric Blind Deconvolution algorithm (PBD) based on 3D Gauss Point Spread Function (PSF). The PBD algorithm needs to estimate the specimen function and the parameters of the PSF simultaneously. The practical medel of the PSF is so complex that it requires a large computation and it converges slowly. But based on the simplified 3D Gauss model, the PBD algorithm only needs to estimate two parameters. While retaining the restoring effect, the
引文
[1]J. P. Pawley. Handbook of biological confocal microscopy 2e[M]. New York: Plenum Press, 1995.
[2]T. Wilson. Confocal Microscopy[M]. San Diego: Academic Press, 1990.
[3]J. A. Conchello. Fluorescence photobleaching correction for expectation maximization algorithm[C]. San Jose, CA : Proceeding of the 1995 IS&T/SPIE Symposium on Electroinic Imaging Science and Techonology, 1995. SPIE Code Number 2412-21.
[4]J. A. Conchello, J. J. Kim, E. W. Hansen. Enhanced 3-D Reconstruction From Confocal Scanning Microscope Images. 2: Depth Discrimination vs. Signal-to-Noise Ration in Partially Confocal Images[J]. Applied Optics, 1995, 33(17): 3740-3750.
[5]C. Preza, M. I. Miller, L. J. Thomas. Regularized method for reconstruction of three-dimensional microscopic objects from optical sections [J]. J. Opt. Soc. Am. A, 1992, 9(2): 219-228.
[6]S. Joshi, M. I. Miller. Maximum a posteriori Estimation with Good' s Roughness for Optical Sectioning Microscopy [J]. Journal of the Optical Society of America A, Feature Issue on Signal Recovery and Synthesis, 1993, 10(5): 1078-1085.
[7]A. Erhardt, G. Zinser, D. Komitowski. Reconstructing 3-D Light-Microscopic Images by Digital Image Processing[J] Appl. Opt, 1985, 24: 194-200.
[8]B. R. Frieden. Image Enhancement and restoration[J]. Picture Processing and image filtering, Topics in Applied Physics, 1975, 6: 227-229.
[9]D. A. Agard. Optical Sectioning Microscopy [J]. Ann. Rev. Biophys. Bioeng, 1984, 13: 191-219.
[10]T. J. Holmes. Blind deconvolution of quantum-limited incoherent imagery[J].J. Opt. Soc. Am. A, 1992, 9(7): 1052-1061.
[11]G. B. Avinash. Simultaneous blur and image restoration in 3D optical microscopy[J]. Zoological Studies, 1995, 34: 184-185.
[12] Y. Yang, N. P. Galastanos, H. Stark. Projection-based blind deconvolution[J]. J. Opt. Soc. Am. A, 1994, 11(9): 2401-2409.
[13] M. Born, E. Wolf. Principles of optics[M]. Oxford: Peramon Press, 1980.
[14] A. Ghatak. Optics[M]. New Delhi: Tara McGraw Hill Inc, 1977.
[15] T. J. Holmes. Expectation-maximization restoration of band limited, truncated point-process intensities with application in microscopy[J]. J. Opt. Soc. Am. A, 1989, 6(7): 1006-1014.
[16] F. S. Gibson, F. Lanni. Experiment test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light mivroscopy[J]. J. Opt. Soc. Am. A, 1991, 8: 1601-1613.
[17] T. J. Holmes, S. Cooper, J. A. Hanzel. Light Microscopic Images Reconstructed by Maximum Likelihood Deconvolution[M]. , New York: Prenum Press, 1995, 24: 389-402.
[18] V. Krishnamurthi, J. N. Turner, Y. Liu. Blind Deconvolution for Fluorescent Microscopy by Maximum Likelihood Estimation[J]. Applied Optics, 1995, 34: 6633-6647.
[19] 陶青川．计算光学切片显微三维成像技术研究[C]．成都：四川大学，2005．
[20] M. R. Banham, K. Katsaggelos. Digital Image Restoration[J]. IEEE Signal Processing Magazine, 1997, 14(2): 24-42.
[21] D. S. Biggs. Accelerated Iterative Blind Deconvolution[C]. Ph.D. New Zealand: University of Auckland, 1998.
[22] T. J. Holmes, Y. H. Liu. Image Restoration for 2-D and 3-D Fluorescence Microscopy[J]. Visualization in Biomedical Microscopies: Three-Dimension Imaging and Computer Application, 1992, 283-327.
[23] P. A. Jansson, R. H. Hunt, E. K. Plyler. Resolution Enhancement of Spectra[J]. Journal of the Optical Society of America, 1970, 60: 596-599.
[24] D. A. Agard. Optical Sectioning Microscopy[J]. Cellular architecture in three dimensions, Annu. Rev. Biophys. Bioeng, 1984, 13: 191-219.
[25] A. N. Tikhonov, V. Y. Arsenin. Solution of Ill-Posed Problems[M]. New York :Wiley, 1977.
[26]W. Carrington. Image Restoration in 3D Microscopy with Limited Data[J]. Proceedings of the SPIE, Bioimaging and Two-Dimensional Spectroscopy, 1990, 1205: 72-83.
[27]W. Carrington, R. M. Lynch, E. D. Moore. Supperresolution Three-Dimensional Images of Fluorescence in Cells with Minimal Light Exposure[J]. Science, 1995, 268: 1483-1486.
[28]N. P. Galatsanos, A. K. Katsaggelos. Methods for Choosing the Regularization Parameter And Estimating the Noise Variance in Image Restoration And Their Relation[J]. IEEE Transaction on Image Processing, 1992, 1: 322-336.
[29]S. J. Reeves, R. M. Mersereay. Blur Identification by the Method of Generalized Cross~validation[J]. IEEE Transaction on Image Processing, 1992, 1: 301-311.
[30]Van Kempen, van Vliet, L. J. The Influence of Regularization Parameter And the First Estimation on the Performance of Tikhonov Regularized Non-Linear Image Restoration Algorithm[J]. Journal of Microscopy, 2000, 198: 63-75.
[31]P. J. Verveer, T. M. Jovin. Efficient Superresolution Restoration Algorithms Using Maximum a Posteriori Estimation with Application to Fluorescence Microscopy[J]. Journal of the Optical Society of America, A (14), 1997, 1696-1706.
[32]M. Bertero, P. Boccacci. Regularization Methods in Image Restoration: An Application to HST Image[J]. Int. J. Imaging Syst. Technol, 1995, 6: 376-386.
[33]T. J. Schulz. Multiframe blind deconvolution of astronomical images [J]. J. Opt. Soc. Am-A, 1993, 10(5): 1064-1073.
[34] R. G. Lane. Blind deconvolution of speckle images [J]. J. Opt. Soc. Am-A, 1992, 9(9): 1508-1514.
[35]R. G. Paxman, T. J. Schulz, J. R. Fienup. Joint Estimation of Object and Aberrations by Using Phase Diversity[J]. J. Opt. Soc. Am-A, 1992, 9(7): 1072-1085.
[36]A. P. Katsaggelos, K. T. Lay. Maximum Likelihood from Incomplete Data via the EM Algorithm[J]. Journal of the Royal Statistical Society B, 1977, 39(1): 1-38.
[37] J. A. Conchello, J. G. McNally. Fast regularization technique for expectation maximization algorithm for computational optical sectioning microscopy[C]. San Jose, CA: Proceeding of the 1996 IS&T/SPIE symposium on electronic imaging: Science and technology, 1996, SPIE code No 2655-24.
[38] V. Krishnamuthi, Y. H. Liu, S. Bhattacharyya. Blind deconvolution of fluorescence micrographs by maximum-likelihood estimation[J]. Applied Optics, 1995, 34(9): 6633-6647.
[39] A. K. Katsaggelos, K. T. Lay. Maximum likelihood blur identification and image restoration using EM Algorithm[J]. IEEE Trans. Sig. Proc, 1991, 39(3): 729-733.
[40] J. A. Conchello, Q. R. Yu. Parametric blind deconvolution of fluorescence microscopy images: preliminary results[C]. San Jose, CA: Proceeding of the 1996 IS&T/SPIE symposium on electronic imaging: Science and technology, SPIE code No 2655-24, 1996.
[41] 刘莹，何小海，陶青川．基于三维高斯模型的参数盲解卷积算法[J]．光电子．激光，2006，17(4)：493-497．
[42] Castleman, K. R. Digital Imaging Processing[M]. NJ: Prentice Hall, 1979.
[43] J. A. Conchello, E. W. Hansen. Enhanced 3-D reconstruction from confocal scanning microscope images, 1: Deterministic and maximum likelihood reconstructions[J]. Applied Optics, 1990, 29(26): 3795-3804.
[44] D. Snyder, M. I. Miller. Random point processed in time and space[M]. New York: Springer-Verlag, 1991.
[45] R. Fletcher, C. M. Reeves. Function minimization by conjugate gradients[J]. Comput. J, 1964, 7: 149-154.
[46] E. Polak. Computationam methods in optimization: A unified approach[M]. New York : Academic Press, 1971.
[47] Y. T. Zhou, R. Chellappa, B. K. Jenkins. Image restoration using a neural network[J]. IEEE Trans. Acoust., Speech, Signal Processing, 1988, ASSP-36: 1141-1151.
[48] J. J. Hopfield, D. W. Tank. Neural computation of decisions in optimization problems, [J]. Biol. Cybern, 1985, 52: 141-152.
[49] J. J. Hopfield. Neural networks and physical systems with emergent collective computational abilities[J]. Proc. Nat. Acad. Sci, 1982, 79: 2554-2558.
[50] J. K. Paik, A. K. Katsaggelos. Image restoration using a modified Hopfield network[J]. IEEE Trans. Image Processing, 1992, 1(1): 49-63.
[51] T. Poggio, V. Torre, C. Koch. Computational vision and regularization theory[J]. Nature, 1985, 317: 314-319.
[52] E. Goles-Chacc, F. Fogelman-Soulie, D. Pellegrin. Decreasing energy functions as a toll for studying threshold networks[J]. Disc. Appl. Math, 1985, 12: 261-277.
[53] S. J. Yeh, H. Stark, M. L. Sezan. Hopfield-type neural networks[J]. In Digital Image restoration, 1991, 23:ch. 3.
[54] J. K. Paik. Image restoration and edge detection using neural networks[C]. USA: Northwestern Univ, 1990.
[55] 张亮，罗鹏飞．基于连续函数的自反馈Hopfield神经网络图像复原算法[J]．计算机与现代化，2004，7：62-64．
[56] C. Preza, J. A. Conchello. Depth-variant maximum-likelihood restoration for three-dimensional fluorescence microscopy[J]. Optical Society of America, 2003.
[57] C. Preza, J. A. Conchello. Image estimation accounting for point-spread function depth variation in three-dimensional fluorescence microscopy[C]. 3D and Multidimensional Microscopy: Image Acquistion and Processing X, Proc. SPIE, 2003, vol. 4964:27.
[58] S. W. Perry. Perception Based Neural Network Modals and Algorithm[C]. Sydney Univ. 2006.
[2]T. Wilson. Confocal Microscopy[M]. San Diego: Academic Press, 1990.
[3]J. A. Conchello. Fluorescence photobleaching correction for expectation maximization algorithm[C]. San Jose, CA : Proceeding of the 1995 IS&T/SPIE Symposium on Electroinic Imaging Science and Techonology, 1995. SPIE Code Number 2412-21.
[4]J. A. Conchello, J. J. Kim, E. W. Hansen. Enhanced 3-D Reconstruction From Confocal Scanning Microscope Images. 2: Depth Discrimination vs. Signal-to-Noise Ration in Partially Confocal Images[J]. Applied Optics, 1995, 33(17): 3740-3750.
[5]C. Preza, M. I. Miller, L. J. Thomas. Regularized method for reconstruction of three-dimensional microscopic objects from optical sections [J]. J. Opt. Soc. Am. A, 1992, 9(2): 219-228.
[6]S. Joshi, M. I. Miller. Maximum a posteriori Estimation with Good' s Roughness for Optical Sectioning Microscopy [J]. Journal of the Optical Society of America A, Feature Issue on Signal Recovery and Synthesis, 1993, 10(5): 1078-1085.
[7]A. Erhardt, G. Zinser, D. Komitowski. Reconstructing 3-D Light-Microscopic Images by Digital Image Processing[J] Appl. Opt, 1985, 24: 194-200.
[8]B. R. Frieden. Image Enhancement and restoration[J]. Picture Processing and image filtering, Topics in Applied Physics, 1975, 6: 227-229.
[9]D. A. Agard. Optical Sectioning Microscopy [J]. Ann. Rev. Biophys. Bioeng, 1984, 13: 191-219.
[10]T. J. Holmes. Blind deconvolution of quantum-limited incoherent imagery[J].J. Opt. Soc. Am. A, 1992, 9(7): 1052-1061.
[11]G. B. Avinash. Simultaneous blur and image restoration in 3D optical microscopy[J]. Zoological Studies, 1995, 34: 184-185.
[12] Y. Yang, N. P. Galastanos, H. Stark. Projection-based blind deconvolution[J]. J. Opt. Soc. Am. A, 1994, 11(9): 2401-2409.
[13] M. Born, E. Wolf. Principles of optics[M]. Oxford: Peramon Press, 1980.
[14] A. Ghatak. Optics[M]. New Delhi: Tara McGraw Hill Inc, 1977.
[15] T. J. Holmes. Expectation-maximization restoration of band limited, truncated point-process intensities with application in microscopy[J]. J. Opt. Soc. Am. A, 1989, 6(7): 1006-1014.
[16] F. S. Gibson, F. Lanni. Experiment test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light mivroscopy[J]. J. Opt. Soc. Am. A, 1991, 8: 1601-1613.
[17] T. J. Holmes, S. Cooper, J. A. Hanzel. Light Microscopic Images Reconstructed by Maximum Likelihood Deconvolution[M]. , New York: Prenum Press, 1995, 24: 389-402.
[18] V. Krishnamurthi, J. N. Turner, Y. Liu. Blind Deconvolution for Fluorescent Microscopy by Maximum Likelihood Estimation[J]. Applied Optics, 1995, 34: 6633-6647.
[19] 陶青川．计算光学切片显微三维成像技术研究[C]．成都：四川大学，2005．
[20] M. R. Banham, K. Katsaggelos. Digital Image Restoration[J]. IEEE Signal Processing Magazine, 1997, 14(2): 24-42.
[21] D. S. Biggs. Accelerated Iterative Blind Deconvolution[C]. Ph.D. New Zealand: University of Auckland, 1998.
[22] T. J. Holmes, Y. H. Liu. Image Restoration for 2-D and 3-D Fluorescence Microscopy[J]. Visualization in Biomedical Microscopies: Three-Dimension Imaging and Computer Application, 1992, 283-327.
[23] P. A. Jansson, R. H. Hunt, E. K. Plyler. Resolution Enhancement of Spectra[J]. Journal of the Optical Society of America, 1970, 60: 596-599.
[24] D. A. Agard. Optical Sectioning Microscopy[J]. Cellular architecture in three dimensions, Annu. Rev. Biophys. Bioeng, 1984, 13: 191-219.
[25] A. N. Tikhonov, V. Y. Arsenin. Solution of Ill-Posed Problems[M]. New York :Wiley, 1977.
[26]W. Carrington. Image Restoration in 3D Microscopy with Limited Data[J]. Proceedings of the SPIE, Bioimaging and Two-Dimensional Spectroscopy, 1990, 1205: 72-83.
[27]W. Carrington, R. M. Lynch, E. D. Moore. Supperresolution Three-Dimensional Images of Fluorescence in Cells with Minimal Light Exposure[J]. Science, 1995, 268: 1483-1486.
[28]N. P. Galatsanos, A. K. Katsaggelos. Methods for Choosing the Regularization Parameter And Estimating the Noise Variance in Image Restoration And Their Relation[J]. IEEE Transaction on Image Processing, 1992, 1: 322-336.
[29]S. J. Reeves, R. M. Mersereay. Blur Identification by the Method of Generalized Cross~validation[J]. IEEE Transaction on Image Processing, 1992, 1: 301-311.
[30]Van Kempen, van Vliet, L. J. The Influence of Regularization Parameter And the First Estimation on the Performance of Tikhonov Regularized Non-Linear Image Restoration Algorithm[J]. Journal of Microscopy, 2000, 198: 63-75.
[31]P. J. Verveer, T. M. Jovin. Efficient Superresolution Restoration Algorithms Using Maximum a Posteriori Estimation with Application to Fluorescence Microscopy[J]. Journal of the Optical Society of America, A (14), 1997, 1696-1706.
[32]M. Bertero, P. Boccacci. Regularization Methods in Image Restoration: An Application to HST Image[J]. Int. J. Imaging Syst. Technol, 1995, 6: 376-386.
[33]T. J. Schulz. Multiframe blind deconvolution of astronomical images [J]. J. Opt. Soc. Am-A, 1993, 10(5): 1064-1073.
[34] R. G. Lane. Blind deconvolution of speckle images [J]. J. Opt. Soc. Am-A, 1992, 9(9): 1508-1514.
[35]R. G. Paxman, T. J. Schulz, J. R. Fienup. Joint Estimation of Object and Aberrations by Using Phase Diversity[J]. J. Opt. Soc. Am-A, 1992, 9(7): 1072-1085.
[36]A. P. Katsaggelos, K. T. Lay. Maximum Likelihood from Incomplete Data via the EM Algorithm[J]. Journal of the Royal Statistical Society B, 1977, 39(1): 1-38.
[37] J. A. Conchello, J. G. McNally. Fast regularization technique for expectation maximization algorithm for computational optical sectioning microscopy[C]. San Jose, CA: Proceeding of the 1996 IS&T/SPIE symposium on electronic imaging: Science and technology, 1996, SPIE code No 2655-24.
[38] V. Krishnamuthi, Y. H. Liu, S. Bhattacharyya. Blind deconvolution of fluorescence micrographs by maximum-likelihood estimation[J]. Applied Optics, 1995, 34(9): 6633-6647.
[39] A. K. Katsaggelos, K. T. Lay. Maximum likelihood blur identification and image restoration using EM Algorithm[J]. IEEE Trans. Sig. Proc, 1991, 39(3): 729-733.
[40] J. A. Conchello, Q. R. Yu. Parametric blind deconvolution of fluorescence microscopy images: preliminary results[C]. San Jose, CA: Proceeding of the 1996 IS&T/SPIE symposium on electronic imaging: Science and technology, SPIE code No 2655-24, 1996.
[41] 刘莹，何小海，陶青川．基于三维高斯模型的参数盲解卷积算法[J]．光电子．激光，2006，17(4)：493-497．
[42] Castleman, K. R. Digital Imaging Processing[M]. NJ: Prentice Hall, 1979.
[43] J. A. Conchello, E. W. Hansen. Enhanced 3-D reconstruction from confocal scanning microscope images, 1: Deterministic and maximum likelihood reconstructions[J]. Applied Optics, 1990, 29(26): 3795-3804.
[44] D. Snyder, M. I. Miller. Random point processed in time and space[M]. New York: Springer-Verlag, 1991.
[45] R. Fletcher, C. M. Reeves. Function minimization by conjugate gradients[J]. Comput. J, 1964, 7: 149-154.
[46] E. Polak. Computationam methods in optimization: A unified approach[M]. New York : Academic Press, 1971.
[47] Y. T. Zhou, R. Chellappa, B. K. Jenkins. Image restoration using a neural network[J]. IEEE Trans. Acoust., Speech, Signal Processing, 1988, ASSP-36: 1141-1151.
[48] J. J. Hopfield, D. W. Tank. Neural computation of decisions in optimization problems, [J]. Biol. Cybern, 1985, 52: 141-152.
[49] J. J. Hopfield. Neural networks and physical systems with emergent collective computational abilities[J]. Proc. Nat. Acad. Sci, 1982, 79: 2554-2558.
[50] J. K. Paik, A. K. Katsaggelos. Image restoration using a modified Hopfield network[J]. IEEE Trans. Image Processing, 1992, 1(1): 49-63.
[51] T. Poggio, V. Torre, C. Koch. Computational vision and regularization theory[J]. Nature, 1985, 317: 314-319.
[52] E. Goles-Chacc, F. Fogelman-Soulie, D. Pellegrin. Decreasing energy functions as a toll for studying threshold networks[J]. Disc. Appl. Math, 1985, 12: 261-277.
[53] S. J. Yeh, H. Stark, M. L. Sezan. Hopfield-type neural networks[J]. In Digital Image restoration, 1991, 23:ch. 3.
[54] J. K. Paik. Image restoration and edge detection using neural networks[C]. USA: Northwestern Univ, 1990.
[55] 张亮，罗鹏飞．基于连续函数的自反馈Hopfield神经网络图像复原算法[J]．计算机与现代化，2004，7：62-64．
[56] C. Preza, J. A. Conchello. Depth-variant maximum-likelihood restoration for three-dimensional fluorescence microscopy[J]. Optical Society of America, 2003.
[57] C. Preza, J. A. Conchello. Image estimation accounting for point-spread function depth variation in three-dimensional fluorescence microscopy[C]. 3D and Multidimensional Microscopy: Image Acquistion and Processing X, Proc. SPIE, 2003, vol. 4964:27.
[58] S. W. Perry. Perception Based Neural Network Modals and Algorithm[C]. Sydney Univ. 2006.