单幅雾天及水下图像的复原方法研究
|
摘要
经过散射介质（如雾、霾，水体等）成像的图像会严重退化，导致细节丢失、对比度下降以及颜色偏移失真。雾天和水下图像的退化主要是由于介质的衰减和散射所造成的，散射又分为前向散射和后向散射，前向散射导致图像细节的轻微模糊，而后向散射导致图像严重雾化。散射退化图像的复原在许多应用领域都有十分重要的作用，因此受到国内外众多研究人员的关注。不少学者采用提高设备性能的方法解决雾天及水下图像成像距离短的问题，但成本较高，难以广泛应用；采用图像处理方法来提高雾天及水下图像质量更加简单和适用。
成像系统受散射介质的影响，图像退化原因复杂，对散射退化图像进行恢复时所需的先验知识必须完备。较早的复原方法通过多幅图像或人工交互获得更多的先验知识来进行去散射，也有不少基于测量的方法来获得散射介质的固有光学特性（IOP）参数并以此推导退化函数；这些方法不能有效解决现有退化图像实时性还原需求。
本文针对以上问题深入研究了基于单幅图像且无需对实际成像环境中的介质进行实际环境测量的复原方法，主要工作和创新点包括以下几个方面：
1）本文认为退化图像中的模糊程度和后向散射噪声本身包含了大量的与散射介质固有光学特性（IOP）相关的信息，结合微积分和物理极值条件的思想提出了散射介质分层分解模型来估计退化函数。假定每层厚度极小时后向散射噪声不相关，对分层模型进行无穷层数（即距离无穷远处）积分，然后利用纯后向散射背景（距离无穷远处如纯水体和天空区域）拟合得到以往需要实际测量的退化函数参数。
2）散射退化与景深和散射介质浓度有关，本文开展了实际水池环境实验，分析和验证模型在这两方面的相关性：首先对不同浑浊程度的水体后向散射噪声进行详细分析，比较不同水质的模型参数；其次对实验中相同水环境一系列不同距离的图像进行测距分析，验证了光学距离与实际距离成正比例关系，因此在距离已知的情况下，分层模型还可以辅助求解和介质IOP相关的参数值。
3）提出了一种迭代复原方法——“渐进反卷积”，完成图像去雾。通过模型推导出的退化函数和噪声信息可以结合多种反卷积方法对图像进行复原，本文提出了基于滤波器的线性渐进反卷积方法和基于全变分模型的非线性渐进反卷积方法;分别用这两种方法对实际雾天及水下图像进行复原，实验结果同目前广泛应用的两种单幅图像去雾方法进行了客观的比较和分析。
4）全变分复原在迭代时使用图像全变分最小作为正则项约束条件，而基于传统滤波器的线性迭代过程也需要正则项约束，本文研究和比较了几种不同的清晰度评价函数作为正则项的有效性，提出最大熵正则化方法,结果表明这种方法适合没有退化前清晰目标图像作为参考的雾天及水下退化图像迭代复原。
Images in a scattering medium (such as fog, water and smoke) are inevitably degraded,resulting in blurring details and color distortion as well as poor image contrast.Fog-degraded images and underwater images are both hazed due to the absorption andscattering of the scattering medium. The scattering can be divided into forwardscattering and backscattering, where the forward scattering leads to the light blur ofdetails and the backscattering causes the serious atomization. Image recovery in ascattering medium is highly desired for many applications and gains widely attentionsof the researchers: some researchers aim to solve the problem of increasing imagingrange by improving the equipment performance, which costs too much to be widelyused; some researches develop the image processing techniques to recover the hazeimage, which is considered to be more simple and powerful.
Degradation of imaging system in scattering medium is complex; it needs full-fledged prior knowledge on the scattering medium to recover the haze image. Theearlier recovery methods were based on two or more images to obtain more priorknowledge of scattering, others were based on measuring to derive the degradationfunction; these methods cannot effectively solve the existing degraded image forreal-time requirement.
In this paper, image recovery methods based on single image which are alsowithout measure of the scattering medium in the real environment are researched; themain work and innovations are listed as follows:
1) The blur degradation and the backscattering noise themselves contain a largenumber of information related to the inherent optical properties (IOP) of the scatteringmedium. This paper proposes a multi-layered decomposition of the scattering volumeand models blurring function of a single-layer scattering volume based on manners of the calculus and the physical extremum problem. Supposing the backscattering noiseof each tiny singe-layer is uncorrelated, when the model is integrated to infinite, it canfit the degradation parameters just by the pure backscattering region.
2) Since scattering degradation is associated with the depth of object andconcentration of the medium, this paper carried out an actual water environmentalexperiment to analyze the correctness of the multi-layered model on these two aspects.The experiment includes that: comparing the parameters of backscattering noise ofdifferent water; analyzing the depth correlation by images obtained at different rangesin the same water, and finding out the proportional relationship between the real depthand the parameter depth. What’s more, when the depth is known, this multi-layeredmodel can also help to solve the IOP related prior.
3）This paper proposes an effective method called propagating deconvolution torecover single image degraded in a scattering medium. Parameters of thedeconvolution algorithm are estimated just from in-situ measurement of the purescattered background from one single image. Two kinds of propagating deconvolutionare used which are linear filter propagating deconvolution and nonlinear totalvariation propagating deconvolution. The results are analyzed and compared with theother two widely used single image dehaze methods.
4）Total variation (TV) restoration uses the image TV minimization as theconvergence regularization in the iterations; While traditional linear filter also needs aconvergence criterion in the iterations of propagating deconvolution. This paperresearches several different criteria and come to a conclusion that image entropymaximization is suitable for the fog-degraded images and underwater images whosereference images are not available.
成像系统受散射介质的影响，图像退化原因复杂，对散射退化图像进行恢复时所需的先验知识必须完备。较早的复原方法通过多幅图像或人工交互获得更多的先验知识来进行去散射，也有不少基于测量的方法来获得散射介质的固有光学特性（IOP）参数并以此推导退化函数；这些方法不能有效解决现有退化图像实时性还原需求。
本文针对以上问题深入研究了基于单幅图像且无需对实际成像环境中的介质进行实际环境测量的复原方法，主要工作和创新点包括以下几个方面：
1）本文认为退化图像中的模糊程度和后向散射噪声本身包含了大量的与散射介质固有光学特性（IOP）相关的信息，结合微积分和物理极值条件的思想提出了散射介质分层分解模型来估计退化函数。假定每层厚度极小时后向散射噪声不相关，对分层模型进行无穷层数（即距离无穷远处）积分，然后利用纯后向散射背景（距离无穷远处如纯水体和天空区域）拟合得到以往需要实际测量的退化函数参数。
2）散射退化与景深和散射介质浓度有关，本文开展了实际水池环境实验，分析和验证模型在这两方面的相关性：首先对不同浑浊程度的水体后向散射噪声进行详细分析，比较不同水质的模型参数；其次对实验中相同水环境一系列不同距离的图像进行测距分析，验证了光学距离与实际距离成正比例关系，因此在距离已知的情况下，分层模型还可以辅助求解和介质IOP相关的参数值。
3）提出了一种迭代复原方法——“渐进反卷积”，完成图像去雾。通过模型推导出的退化函数和噪声信息可以结合多种反卷积方法对图像进行复原，本文提出了基于滤波器的线性渐进反卷积方法和基于全变分模型的非线性渐进反卷积方法;分别用这两种方法对实际雾天及水下图像进行复原，实验结果同目前广泛应用的两种单幅图像去雾方法进行了客观的比较和分析。
4）全变分复原在迭代时使用图像全变分最小作为正则项约束条件，而基于传统滤波器的线性迭代过程也需要正则项约束，本文研究和比较了几种不同的清晰度评价函数作为正则项的有效性，提出最大熵正则化方法,结果表明这种方法适合没有退化前清晰目标图像作为参考的雾天及水下退化图像迭代复原。
Images in a scattering medium (such as fog, water and smoke) are inevitably degraded,resulting in blurring details and color distortion as well as poor image contrast.Fog-degraded images and underwater images are both hazed due to the absorption andscattering of the scattering medium. The scattering can be divided into forwardscattering and backscattering, where the forward scattering leads to the light blur ofdetails and the backscattering causes the serious atomization. Image recovery in ascattering medium is highly desired for many applications and gains widely attentionsof the researchers: some researchers aim to solve the problem of increasing imagingrange by improving the equipment performance, which costs too much to be widelyused; some researches develop the image processing techniques to recover the hazeimage, which is considered to be more simple and powerful.
Degradation of imaging system in scattering medium is complex; it needs full-fledged prior knowledge on the scattering medium to recover the haze image. Theearlier recovery methods were based on two or more images to obtain more priorknowledge of scattering, others were based on measuring to derive the degradationfunction; these methods cannot effectively solve the existing degraded image forreal-time requirement.
In this paper, image recovery methods based on single image which are alsowithout measure of the scattering medium in the real environment are researched; themain work and innovations are listed as follows:
1) The blur degradation and the backscattering noise themselves contain a largenumber of information related to the inherent optical properties (IOP) of the scatteringmedium. This paper proposes a multi-layered decomposition of the scattering volumeand models blurring function of a single-layer scattering volume based on manners of the calculus and the physical extremum problem. Supposing the backscattering noiseof each tiny singe-layer is uncorrelated, when the model is integrated to infinite, it canfit the degradation parameters just by the pure backscattering region.
2) Since scattering degradation is associated with the depth of object andconcentration of the medium, this paper carried out an actual water environmentalexperiment to analyze the correctness of the multi-layered model on these two aspects.The experiment includes that: comparing the parameters of backscattering noise ofdifferent water; analyzing the depth correlation by images obtained at different rangesin the same water, and finding out the proportional relationship between the real depthand the parameter depth. What’s more, when the depth is known, this multi-layeredmodel can also help to solve the IOP related prior.
3）This paper proposes an effective method called propagating deconvolution torecover single image degraded in a scattering medium. Parameters of thedeconvolution algorithm are estimated just from in-situ measurement of the purescattered background from one single image. Two kinds of propagating deconvolutionare used which are linear filter propagating deconvolution and nonlinear totalvariation propagating deconvolution. The results are analyzed and compared with theother two widely used single image dehaze methods.
4）Total variation (TV) restoration uses the image TV minimization as theconvergence regularization in the iterations; While traditional linear filter also needs aconvergence criterion in the iterations of propagating deconvolution. This paperresearches several different criteria and come to a conclusion that image entropymaximization is suitable for the fog-degraded images and underwater images whosereference images are not available.
引文
[1] Amin Sarafraz, Shahriar Negahdaripour and Yoav Y. Schechner,“Enhancing images inscattering media utilizing stereovision and polarization,” Proc. IEEE WACV (2009).
[2]滕云枫，基于水下激光视觉技术分析的低功率半导体水下成像系统，中国海洋大学（学位论文），2006.
[3] Larochelle V, Mathieu P, Simard J R. Two generations of Canadian active imagingsystems:ALBEDOS and ELVISS[C]. SPIE Conference on Infrared Technology andApplications,1999,229-243.
[4]徐启阳,杨坤涛,王新兵等.蓝绿激光雷达海洋探测[M].北京:国防工业出版社,2002
[5] Acharekar M. Underwater laser imaging system [J]. SP IE,1998,3079:750～761
[6] Mcleane A, Burris H R, Strand M P. Short-pulse range-gated optical imaging inturbid water [J]. Applied Optics,1995,34(21):4343～4351
[7] INTEVAC. LIVAR Model4000Preliminary Specifications[Z]. SantaClaraCA,INTEVAC,2006.
[8] OBZERV. Active Range-Gated Camera ARGC-2400Datasheet[Z]. Quebec QcCanada,OBZERV,2006.
[9] Robert R. Alfano, S G D.Imaging of objects based upon the polarization or depolarization oflight, US Patent,5847394[P],1996
[10] Giakos G. Multispectral, multifusion,laser-polarimetric optical imaging system, US Patent2006164643[P],2006.
[11] Giakos G. Multi-spectral mixed radation, plarmetric systems: WO Patent,2007130001[P],2007
[12]王琪.透雾镜头助力森林远程监控[J].中国公共安全(综合版).2011(05)
[13]胡际先,胡锋.透雾连续变焦镜头的小型化设计[J].应用光学.2009(04)
[14] S.G. Narasimhan and S.K. Nayar,“Vision and the Atmosphere,” International Journal ofComputer Vision, vol.48,233-254(2002).
[15] S.G. Narasimhan and S.K. Nayar,“Chromatic Framework for Vision in BadWeather,” in Proceedings of IEEE Conference on Computer Vision and PatternRecognition (IEEE,2000), pp.598-605.
[16] S.K. Nayar and S.G. Narasimhan,“Vision in Bad Weather,” in Proceedingsof Seventh IEEE International Conference on Computer Vision(IEEE,1999), vol.2, pp.820-827,
[17] Y. Schechner, S.G. Narasimhan, and S.K. Nayar,“Instant Dehazing of Images UsingPolarization,” in Proceedings of IEEE Conference on Computer Vision and PatternRecognition (IEEE,2001), vol.1, pp.325-332.
[18] Yoav Y. Schechner and Nir Karpel,“Recovery of underwater visibility and structure bypolarization analysis,” IEEE Journal of Oceanic Engineering, Vol.30, No.3, pp.570-587(2005).
[19] Tali Treibitz and Yoav Y. Schechner,“Active polarization descattering,” IEEE Trans. PatternAnalysis&Machine Intelligence, Vol.31, No.3, pp.385-399(2009).
[20]陈功,王唐,周荷琴.基于物理模型的雾天图像复原新方法[J].中国图象图形学报,2008,13(5):888-893.
[21] R. Tan,“Visibility in bad weather from a single image” in Proceedings of IEEE Conferenceon CVPR (IEEE2008),1-8.
[22] R. Fattal,“Single Image Dehazing,” J. ACM Siggraph08,1-9(2008).
[23] Kaiming He, Jian Sun, and Xiaoou Tang,“Single image haze removal using dark channelprior,” in Proceedings of IEEE Conference on Computer Vision and PatternRecognition (IEEE,2009), pp.1956-1963
[24] Yoav Y. Schechner and Nir Karpel,“Clear underwater vision,” in Proceedings of IEEEConference on Computer Vision and Pattern Recognition(IEEE,2004), Vol.1, pp.536-543
[25] Iqbal, K., Abdul Salam, R., Osman, A., Zawawi Talib, A.: Underwater image enhancementusing an integrated color model. J. Computer Science34,2–12(2007
[26] L. E. Mertens, J. F. S. Replogle,“Use of point spread and beam spread functions for analysisof imaging systems in water,” J. Opt. Soc. Am., A67,1105-1117(1977).
[27] K. J. Voss,“Simple empirical model of the oceanic point spread function,” App. Opt.30,2647-2651(1991).
[28] Phillip N. Reinersman and Kendall L. Carder “Monte Carlo simulation of the atmosphericpoint-spread function with an application to correction for the adjacency effect” AppliedOptics, Vol.34, Issue21, pp.4453-4471(1995)
[29]蓝信钜.激光技术[M].北京:科学出版社,2000:303-307.
[30] Houghton, J.T. The Physics of Atmospheres2nd ed. Chapter2
[31]默斯顿L E.水中摄影学[M].北京：科学出版社，1980
[32]孙传东，陈良益，高立民，张建生，卢笛.水的光学特性及其对水下成像的影响[J].2000，21(4):39－46.
[33]郑冰,孙骄禾,粟京.一种水下激光成像的新方法.中国海洋大学学报,2006,36(1):119～122
[34] J. S. Jaffe, Computer modeling and design of optimal underwater imaging systems, IEEEJournal of Oceanic Engineering,1990,15(2):101-111.
[35] J. Jaffe, K. Moore, J. McLean, M. Strand, Underwater optical imaging: status and prospects,Oceanography,2001, vol.14:66-76.
[36]钟森城,李泽仁,王荣波,前向散射对激光水下成像的影响,[J]强激光与粒子束，2012年1月
[37]李建，水下图像后向散射噪声的去噪问题研究，中国海洋大学（学位论文），2009.
[38] G.R.Fournier. Range-gated underwater laser imaging system. Opt.Eng,1993,32(9):2185～2190
[39] L.R.Marshall. Blue-green laser plumb the mysteries of the deep. Laser FocusWorld,1993,(4):185～197
[40] S Q Duntley. The Reduction of Apparent Contrast by the Atmosphere. Journal of the OpticalSociety of America,1948，38(2):179-191
[41]冈萨雷斯，数字图像处理（第二版），电子工业出版社，2003.
[42] Sos S. Agaian, Karen P. Lentz, Artyom M. Grigoryan, A new measure of imageenhancement,[C]. IASTED Int.Conf. Signal Processing&Communication,Marbella,Spain,2000.
[43]祝培，朱虹，钱学明，一种有雾天气图像景物摄影的清晰化方法[J]，中国图象图形学报，2004，9(1):124-128.
[44]祝培，恶劣天气环境下图像的清晰化，西安理工大学（学位论文），2004.
[45] CHENG H D, XU HUI JUAN. A novel fuzzy logic approach to mammogram contrastenhancement [J]. Information Sciences2002,148:167-184
[46]翟艺书，柳晓鸣，涂雅瑗，基于模糊逻辑的雾天降质图像对比度增强算法，计算机应用，2008，28（3）：662-664
[47]王彬,水下图像增强算法的研究[D].中国海洋大学,2008.
[48]蓝国宁；李建；籍芳；基于小波的水下图像后向散射噪声去除，[J].海洋技术，2010，vol29(2):43-47
[49] M. Chambah, D. Semani, A. Renouf, P. Courtellemont, A. Rizzi, Underwater color constancy:enhancement of automatic live fish recognition, Color Imaging IX: Processing, Hardcopy,and Applications, January2004, vol.5293, pp.157–168
[50] L. A. Torres Mendez, G. Dudek, Color correction of underwater images for aquatic robotinspection, Proceedings of the5th International Workshop on Energy Minimization Methodsin Computer Vision and Pattern Recognition, Eds., vol.3757of Lecture Notes in ComputerScience, pp.60–73, Springer, St. Augustine, Fla, USA, November2005.
[51] S. Bazeille, I. Quidu, L. Jaulin, J. P. Malkasse, Automatic underwater image pre-processing,in Proceedings of the Caracterisation du Milieu Marin (CMM’06),2006.
[52] S. Bazeille, Vision sous-marine monoculaire pour la reconnaissance d’objets, Ph.D. thesis,University of Bretagne Occidentale,2008
[53] YITZHAKY Y,KOPEIKA N S.Identification of blur parameters from motion blurredimages[J]. CVGIP: Graphical Models and Image Processing,1997,59(5)
[54] W. Hou, Deric J. Gray, Alan D. Weidemann, and Robert A. Arnone, Comparison andvalidation of point spread models for imaging in natural waters, OPTICS EXPRESS, Vol.16,No.13, pp.9958-9965,2008.
[55] W. Hou, D. J. Gray, A. D. Weidemann, G. R. Fournier, J. L. Forand, Automated underwaterimage restoration and retrieval of related optical properties, in Proceedings of the IEEEInternational Geoscience and Remote Sensing Symposium (IGARSS’07), pp.1889–1892,2007
[56] W. Hou, A. D. Weidemann, D. J. Gray, G. R. Fournier, Imagery-derived modulation transferfunction and its applications for underwater imaging, in Applications of Digital ImageProcessing, vol.6696of Proceedings of SPIE,SanDiego, Calif, USA, August2007.
[57]张赫，徐玉如，万磊，唐旭东，蔡昊鹏，水下退化图像处理方法，天津大学学报，2010，43(9):827-833.
[58]钟仡龙,单幅图像去雾处理算法研究及软件实现,西南交通大学(学位论文)，2012
[59]杨福生，[M]独立分量分析的原理与应用,清华大学出版社,2006.
[60]黄百钢;李俊山,应用ICA滤波器技术提取图像纹理特征,[J]光电工程，2008.06.
[61]刘爱平，付琨，尤红建，刘忠，基于MAR-MRF的SAR图像分割方法
[62] Anat Levin, Dani Lischinski, Yair Weiss, A Closed Form Solution to Natural Image Matting
[63] Kaiming He, Jian Sun, and Xiaoou Tang, Guided Image Filtering, in TPAMI2013.
[64] Ziyang Ma, Kaiming He, Yichen Wei, Jian Sun, and Enhua Wu, Constant Time WeightedMedian Filtering for Stereo Matching and Beyond, in ICCV2013.
[65] J. Zhang, Q. Zhang, G. He,“Blind deconvolution of a noisy degraded image,” Applied Optics,48(12),2350-2355(2009).
[66] A. Levin, Y.Weiss, F. Durand, W. Freeman,“Understanding and evaluating blinddeconvolution algorithms,” in Proceedings of IEEE Conference on Computer Vision andPattern Recognition (IEEE2009), pp.1964-1971.
[67] J. L. Horner,” Optical Restoration of Images Blurred by Atmospheric TurbulenceUsing Optimum Filter Theory”, Applied Optics, Vol.9, Issue1, pp.167-171(1970)
[68] G. Wang, B. Zheng, F. F. Sun,“Estimation-based approach for underwater image restoration,”Optics Letters,36(13),2384-2386(2011).
[69]孙飞飞，水下图像增强和算法研究，中国海洋大学（学位论文），2010.
[70]蓝国宁，基于变分偏微分方程的细胞神经网络水下图像噪声抑制，中国海洋大学（学位论文），2010.
[71]王鸿南,钟文,汪静,夏德深;图像清晰度评价方法研究,[J],中国图象图形学报,2004.07.
[72]杨琬;吴乐华;范晔;数字图像客观质量评价方法研究;[J]通信技术,2008年7月.
[73] Huynh-Thu, Q.; Ghanbari, M.. Scope of validity of PSNR in image/video qualityassessment.[J] Electronics Letters,2008,44(13):800
[74]曹茂永，孙农亮,郁道银，基于灰度梯度的数字图像评价函数，[J]光电工程，vol30,no.4,2003, pp69-72
[75] Cao Maoyong, Sun Nongliang, Yu Daoyin, Digital image evaluation function based on graygradient,[J] Opto-Electronic Engineering, vol30,no.4,2003, pp69-72
[76] Feynman, R, Leighton, R, and Sands, M. Chapter12: Electrostatic Analogs//The FeynmanLectures on Physics.1970. Volume2. Addison-Wesley-Longman.
[77] Jarvis R A. Focus optimization criteria for computer Image Processing [J].Microscope,1976,24(2):163-180.
[78] B. R. Frieden,“Restoring with maximum likelihood and maximum entropy,” J. Opt. Soc.Am.,62,511-518(1972).
[79] M. Willis, B.D. Jeffs, D.G. Long,“Maximum entropy image restoration revisited,” inProceedings of IEEE International Conference on Image Processing (IEEE2000), pp.89-92.
[80] M. Pinchas, B.Z. Bobrovsky,“A Maximum Entropy approach for blind deconvolution,”Signal Processing,86(10),2913-2931(2006).
[81] QidwaiU,ChenC-H.Blind Image Restor-ation for Ultrasonic C-Scan Using Constrained2D-HOS [A]. IEEEInternationalConference onAcousticsSpeech andSignalProcessing.2001
[82][JordiSolé, AnisseTaleb, ChristianJutten. ParametricApproach to Blind Deconvolution ofNonlinear Channels. ESANN’’2000-EuropeanSymposium on Artificial Neural Networks.2000
[83]余昕,杨绿溪,邹采荣.基于确定性约束和局部空间自适应正则化的图像盲复原算法[J].数据采集与处理.2002(02)
[84]薛梅,邹采荣,杨娟,杨绿溪.一种空间自适应正则化图象盲复原算法[J].中国图象图形学报.2002(04)
[85]刘琚,何振亚.利用SVD对带噪声的模糊图像进行盲复原[J].数据采集与处理.2002(01)
[86]吴亚东.图像复原算法研究[D].电子科技大学(学位论文)2006
[87]仵冀颖.偏微分方程在图像处理中应用的研究[D].北京交通大学(学位论文)2009
[88] Tony F.Chan、 Jianhong（Jackie）Shen,[M]图像处理与分析:变分、PDE、小波及随机方法,科学出版社,2013
[89]孙玉宝;肖亮;韦志辉;吴慧中,基于偏微分方程的户外图像去雾方法,[J]系统仿真学报2007/16
[90] Krim H, Schick U C. Minimax description length for signal denoising and optimizedrepresentation. IEEE transactions on Information Theory,1999,45(3):898-908.
[91] Leonid I. Rudin L, Stanley Osher and Emad Fatemi Nonlinear total variation based noiseremoval algorithms1992Physica D: Nonlinear Phenomena,60,259-268.
[92] Rudin L, Osher S, Total variation based image restoration with free local constraints [c]Austin, Proc lst IEEE Int’l Conf o n Image Processing,1994,10:231:241.
[93] Osher S, Rudin L. Feature-oriented image enhancement using shock filters. SIAM JNumerAnal,1990,27:919-940
[94] Perona P,Malik J. Scale-space and edge detection using anisotropic diffusion. IEEETransactions on Pattern Analysis and Machine Intelligence，1990，12(7):629-639.
[95] Tikhonov A.N,On Solving Incorrectly Posed Problems Method of Regularization.Dokl.Acad. Nauk USSR,151(3),1963.
[96] Tony F.Chan, Jianhong(Jaekie)Shen，and Luminita Vese，“Variational PDE Models in ImageProfessing，Noteices of The AMS，2002，vol.50:14-26
[97]周密．整体变分法的数字图像修复技术研究[D]．西北大学硕士论文，2008
[98] Vogel C.R, Oman M.E, Iterative methods for total variation denoising[J] SIAM Scicomput,1996,17:227-238.
[99] Dobson D.C, Vogel C.R Convergence of an Iterative Method for Total Variation Denoising,[J] SIAM J Numerical Analysis,1997,34(5):1779-1791.
[100] Chan T F,Golub G,Mulet P.A nonlinear primal-dual method for total variation-basedimage restoration. SIAM J.Sci.Comp.1999,20:1964-1977.
[101] Chan TF Osher S Shen J.The digital TV filter and nonlinear denoising, ImageProcessing,IEEE Transactions on,2001,10(2):231-241.
[2]滕云枫，基于水下激光视觉技术分析的低功率半导体水下成像系统，中国海洋大学（学位论文），2006.
[3] Larochelle V, Mathieu P, Simard J R. Two generations of Canadian active imagingsystems:ALBEDOS and ELVISS[C]. SPIE Conference on Infrared Technology andApplications,1999,229-243.
[4]徐启阳,杨坤涛,王新兵等.蓝绿激光雷达海洋探测[M].北京:国防工业出版社,2002
[5] Acharekar M. Underwater laser imaging system [J]. SP IE,1998,3079:750～761
[6] Mcleane A, Burris H R, Strand M P. Short-pulse range-gated optical imaging inturbid water [J]. Applied Optics,1995,34(21):4343～4351
[7] INTEVAC. LIVAR Model4000Preliminary Specifications[Z]. SantaClaraCA,INTEVAC,2006.
[8] OBZERV. Active Range-Gated Camera ARGC-2400Datasheet[Z]. Quebec QcCanada,OBZERV,2006.
[9] Robert R. Alfano, S G D.Imaging of objects based upon the polarization or depolarization oflight, US Patent,5847394[P],1996
[10] Giakos G. Multispectral, multifusion,laser-polarimetric optical imaging system, US Patent2006164643[P],2006.
[11] Giakos G. Multi-spectral mixed radation, plarmetric systems: WO Patent,2007130001[P],2007
[12]王琪.透雾镜头助力森林远程监控[J].中国公共安全(综合版).2011(05)
[13]胡际先,胡锋.透雾连续变焦镜头的小型化设计[J].应用光学.2009(04)
[14] S.G. Narasimhan and S.K. Nayar,“Vision and the Atmosphere,” International Journal ofComputer Vision, vol.48,233-254(2002).
[15] S.G. Narasimhan and S.K. Nayar,“Chromatic Framework for Vision in BadWeather,” in Proceedings of IEEE Conference on Computer Vision and PatternRecognition (IEEE,2000), pp.598-605.
[16] S.K. Nayar and S.G. Narasimhan,“Vision in Bad Weather,” in Proceedingsof Seventh IEEE International Conference on Computer Vision(IEEE,1999), vol.2, pp.820-827,
[17] Y. Schechner, S.G. Narasimhan, and S.K. Nayar,“Instant Dehazing of Images UsingPolarization,” in Proceedings of IEEE Conference on Computer Vision and PatternRecognition (IEEE,2001), vol.1, pp.325-332.
[18] Yoav Y. Schechner and Nir Karpel,“Recovery of underwater visibility and structure bypolarization analysis,” IEEE Journal of Oceanic Engineering, Vol.30, No.3, pp.570-587(2005).
[19] Tali Treibitz and Yoav Y. Schechner,“Active polarization descattering,” IEEE Trans. PatternAnalysis&Machine Intelligence, Vol.31, No.3, pp.385-399(2009).
[20]陈功,王唐,周荷琴.基于物理模型的雾天图像复原新方法[J].中国图象图形学报,2008,13(5):888-893.
[21] R. Tan,“Visibility in bad weather from a single image” in Proceedings of IEEE Conferenceon CVPR (IEEE2008),1-8.
[22] R. Fattal,“Single Image Dehazing,” J. ACM Siggraph08,1-9(2008).
[23] Kaiming He, Jian Sun, and Xiaoou Tang,“Single image haze removal using dark channelprior,” in Proceedings of IEEE Conference on Computer Vision and PatternRecognition (IEEE,2009), pp.1956-1963
[24] Yoav Y. Schechner and Nir Karpel,“Clear underwater vision,” in Proceedings of IEEEConference on Computer Vision and Pattern Recognition(IEEE,2004), Vol.1, pp.536-543
[25] Iqbal, K., Abdul Salam, R., Osman, A., Zawawi Talib, A.: Underwater image enhancementusing an integrated color model. J. Computer Science34,2–12(2007
[26] L. E. Mertens, J. F. S. Replogle,“Use of point spread and beam spread functions for analysisof imaging systems in water,” J. Opt. Soc. Am., A67,1105-1117(1977).
[27] K. J. Voss,“Simple empirical model of the oceanic point spread function,” App. Opt.30,2647-2651(1991).
[28] Phillip N. Reinersman and Kendall L. Carder “Monte Carlo simulation of the atmosphericpoint-spread function with an application to correction for the adjacency effect” AppliedOptics, Vol.34, Issue21, pp.4453-4471(1995)
[29]蓝信钜.激光技术[M].北京:科学出版社,2000:303-307.
[30] Houghton, J.T. The Physics of Atmospheres2nd ed. Chapter2
[31]默斯顿L E.水中摄影学[M].北京：科学出版社，1980
[32]孙传东，陈良益，高立民，张建生，卢笛.水的光学特性及其对水下成像的影响[J].2000，21(4):39－46.
[33]郑冰,孙骄禾,粟京.一种水下激光成像的新方法.中国海洋大学学报,2006,36(1):119～122
[34] J. S. Jaffe, Computer modeling and design of optimal underwater imaging systems, IEEEJournal of Oceanic Engineering,1990,15(2):101-111.
[35] J. Jaffe, K. Moore, J. McLean, M. Strand, Underwater optical imaging: status and prospects,Oceanography,2001, vol.14:66-76.
[36]钟森城,李泽仁,王荣波,前向散射对激光水下成像的影响,[J]强激光与粒子束，2012年1月
[37]李建，水下图像后向散射噪声的去噪问题研究，中国海洋大学（学位论文），2009.
[38] G.R.Fournier. Range-gated underwater laser imaging system. Opt.Eng,1993,32(9):2185～2190
[39] L.R.Marshall. Blue-green laser plumb the mysteries of the deep. Laser FocusWorld,1993,(4):185～197
[40] S Q Duntley. The Reduction of Apparent Contrast by the Atmosphere. Journal of the OpticalSociety of America,1948，38(2):179-191
[41]冈萨雷斯，数字图像处理（第二版），电子工业出版社，2003.
[42] Sos S. Agaian, Karen P. Lentz, Artyom M. Grigoryan, A new measure of imageenhancement,[C]. IASTED Int.Conf. Signal Processing&Communication,Marbella,Spain,2000.
[43]祝培，朱虹，钱学明，一种有雾天气图像景物摄影的清晰化方法[J]，中国图象图形学报，2004，9(1):124-128.
[44]祝培，恶劣天气环境下图像的清晰化，西安理工大学（学位论文），2004.
[45] CHENG H D, XU HUI JUAN. A novel fuzzy logic approach to mammogram contrastenhancement [J]. Information Sciences2002,148:167-184
[46]翟艺书，柳晓鸣，涂雅瑗，基于模糊逻辑的雾天降质图像对比度增强算法，计算机应用，2008，28（3）：662-664
[47]王彬,水下图像增强算法的研究[D].中国海洋大学,2008.
[48]蓝国宁；李建；籍芳；基于小波的水下图像后向散射噪声去除，[J].海洋技术，2010，vol29(2):43-47
[49] M. Chambah, D. Semani, A. Renouf, P. Courtellemont, A. Rizzi, Underwater color constancy:enhancement of automatic live fish recognition, Color Imaging IX: Processing, Hardcopy,and Applications, January2004, vol.5293, pp.157–168
[50] L. A. Torres Mendez, G. Dudek, Color correction of underwater images for aquatic robotinspection, Proceedings of the5th International Workshop on Energy Minimization Methodsin Computer Vision and Pattern Recognition, Eds., vol.3757of Lecture Notes in ComputerScience, pp.60–73, Springer, St. Augustine, Fla, USA, November2005.
[51] S. Bazeille, I. Quidu, L. Jaulin, J. P. Malkasse, Automatic underwater image pre-processing,in Proceedings of the Caracterisation du Milieu Marin (CMM’06),2006.
[52] S. Bazeille, Vision sous-marine monoculaire pour la reconnaissance d’objets, Ph.D. thesis,University of Bretagne Occidentale,2008
[53] YITZHAKY Y,KOPEIKA N S.Identification of blur parameters from motion blurredimages[J]. CVGIP: Graphical Models and Image Processing,1997,59(5)
[54] W. Hou, Deric J. Gray, Alan D. Weidemann, and Robert A. Arnone, Comparison andvalidation of point spread models for imaging in natural waters, OPTICS EXPRESS, Vol.16,No.13, pp.9958-9965,2008.
[55] W. Hou, D. J. Gray, A. D. Weidemann, G. R. Fournier, J. L. Forand, Automated underwaterimage restoration and retrieval of related optical properties, in Proceedings of the IEEEInternational Geoscience and Remote Sensing Symposium (IGARSS’07), pp.1889–1892,2007
[56] W. Hou, A. D. Weidemann, D. J. Gray, G. R. Fournier, Imagery-derived modulation transferfunction and its applications for underwater imaging, in Applications of Digital ImageProcessing, vol.6696of Proceedings of SPIE,SanDiego, Calif, USA, August2007.
[57]张赫，徐玉如，万磊，唐旭东，蔡昊鹏，水下退化图像处理方法，天津大学学报，2010，43(9):827-833.
[58]钟仡龙,单幅图像去雾处理算法研究及软件实现,西南交通大学(学位论文)，2012
[59]杨福生，[M]独立分量分析的原理与应用,清华大学出版社,2006.
[60]黄百钢;李俊山,应用ICA滤波器技术提取图像纹理特征,[J]光电工程，2008.06.
[61]刘爱平，付琨，尤红建，刘忠，基于MAR-MRF的SAR图像分割方法
[62] Anat Levin, Dani Lischinski, Yair Weiss, A Closed Form Solution to Natural Image Matting
[63] Kaiming He, Jian Sun, and Xiaoou Tang, Guided Image Filtering, in TPAMI2013.
[64] Ziyang Ma, Kaiming He, Yichen Wei, Jian Sun, and Enhua Wu, Constant Time WeightedMedian Filtering for Stereo Matching and Beyond, in ICCV2013.
[65] J. Zhang, Q. Zhang, G. He,“Blind deconvolution of a noisy degraded image,” Applied Optics,48(12),2350-2355(2009).
[66] A. Levin, Y.Weiss, F. Durand, W. Freeman,“Understanding and evaluating blinddeconvolution algorithms,” in Proceedings of IEEE Conference on Computer Vision andPattern Recognition (IEEE2009), pp.1964-1971.
[67] J. L. Horner,” Optical Restoration of Images Blurred by Atmospheric TurbulenceUsing Optimum Filter Theory”, Applied Optics, Vol.9, Issue1, pp.167-171(1970)
[68] G. Wang, B. Zheng, F. F. Sun,“Estimation-based approach for underwater image restoration,”Optics Letters,36(13),2384-2386(2011).
[69]孙飞飞，水下图像增强和算法研究，中国海洋大学（学位论文），2010.
[70]蓝国宁，基于变分偏微分方程的细胞神经网络水下图像噪声抑制，中国海洋大学（学位论文），2010.
[71]王鸿南,钟文,汪静,夏德深;图像清晰度评价方法研究,[J],中国图象图形学报,2004.07.
[72]杨琬;吴乐华;范晔;数字图像客观质量评价方法研究;[J]通信技术,2008年7月.
[73] Huynh-Thu, Q.; Ghanbari, M.. Scope of validity of PSNR in image/video qualityassessment.[J] Electronics Letters,2008,44(13):800
[74]曹茂永，孙农亮,郁道银，基于灰度梯度的数字图像评价函数，[J]光电工程，vol30,no.4,2003, pp69-72
[75] Cao Maoyong, Sun Nongliang, Yu Daoyin, Digital image evaluation function based on graygradient,[J] Opto-Electronic Engineering, vol30,no.4,2003, pp69-72
[76] Feynman, R, Leighton, R, and Sands, M. Chapter12: Electrostatic Analogs//The FeynmanLectures on Physics.1970. Volume2. Addison-Wesley-Longman.
[77] Jarvis R A. Focus optimization criteria for computer Image Processing [J].Microscope,1976,24(2):163-180.
[78] B. R. Frieden,“Restoring with maximum likelihood and maximum entropy,” J. Opt. Soc.Am.,62,511-518(1972).
[79] M. Willis, B.D. Jeffs, D.G. Long,“Maximum entropy image restoration revisited,” inProceedings of IEEE International Conference on Image Processing (IEEE2000), pp.89-92.
[80] M. Pinchas, B.Z. Bobrovsky,“A Maximum Entropy approach for blind deconvolution,”Signal Processing,86(10),2913-2931(2006).
[81] QidwaiU,ChenC-H.Blind Image Restor-ation for Ultrasonic C-Scan Using Constrained2D-HOS [A]. IEEEInternationalConference onAcousticsSpeech andSignalProcessing.2001
[82][JordiSolé, AnisseTaleb, ChristianJutten. ParametricApproach to Blind Deconvolution ofNonlinear Channels. ESANN’’2000-EuropeanSymposium on Artificial Neural Networks.2000
[83]余昕,杨绿溪,邹采荣.基于确定性约束和局部空间自适应正则化的图像盲复原算法[J].数据采集与处理.2002(02)
[84]薛梅,邹采荣,杨娟,杨绿溪.一种空间自适应正则化图象盲复原算法[J].中国图象图形学报.2002(04)
[85]刘琚,何振亚.利用SVD对带噪声的模糊图像进行盲复原[J].数据采集与处理.2002(01)
[86]吴亚东.图像复原算法研究[D].电子科技大学(学位论文)2006
[87]仵冀颖.偏微分方程在图像处理中应用的研究[D].北京交通大学(学位论文)2009
[88] Tony F.Chan、 Jianhong（Jackie）Shen,[M]图像处理与分析:变分、PDE、小波及随机方法,科学出版社,2013
[89]孙玉宝;肖亮;韦志辉;吴慧中,基于偏微分方程的户外图像去雾方法,[J]系统仿真学报2007/16
[90] Krim H, Schick U C. Minimax description length for signal denoising and optimizedrepresentation. IEEE transactions on Information Theory,1999,45(3):898-908.
[91] Leonid I. Rudin L, Stanley Osher and Emad Fatemi Nonlinear total variation based noiseremoval algorithms1992Physica D: Nonlinear Phenomena,60,259-268.
[92] Rudin L, Osher S, Total variation based image restoration with free local constraints [c]Austin, Proc lst IEEE Int’l Conf o n Image Processing,1994,10:231:241.
[93] Osher S, Rudin L. Feature-oriented image enhancement using shock filters. SIAM JNumerAnal,1990,27:919-940
[94] Perona P,Malik J. Scale-space and edge detection using anisotropic diffusion. IEEETransactions on Pattern Analysis and Machine Intelligence，1990，12(7):629-639.
[95] Tikhonov A.N,On Solving Incorrectly Posed Problems Method of Regularization.Dokl.Acad. Nauk USSR,151(3),1963.
[96] Tony F.Chan, Jianhong(Jaekie)Shen，and Luminita Vese，“Variational PDE Models in ImageProfessing，Noteices of The AMS，2002，vol.50:14-26
[97]周密．整体变分法的数字图像修复技术研究[D]．西北大学硕士论文，2008
[98] Vogel C.R, Oman M.E, Iterative methods for total variation denoising[J] SIAM Scicomput,1996,17:227-238.
[99] Dobson D.C, Vogel C.R Convergence of an Iterative Method for Total Variation Denoising,[J] SIAM J Numerical Analysis,1997,34(5):1779-1791.
[100] Chan T F,Golub G,Mulet P.A nonlinear primal-dual method for total variation-basedimage restoration. SIAM J.Sci.Comp.1999,20:1964-1977.
[101] Chan TF Osher S Shen J.The digital TV filter and nonlinear denoising, ImageProcessing,IEEE Transactions on,2001,10(2):231-241.