面向IICCD相机不完全随机采样遥感图像的重建算法
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摘要
由于图像增强型CCD (ⅡCCD)相机具有高信噪比、高增益、能在微光条件下稳定的工作等优点,在遥感和军事中具有广阔的应用前景。但是,由于ⅡCCD相机成像不可避免存在光学模糊、噪声干扰等质量退化过程,以及高分辨率图像数据传输,因此人们希望研究不完全采样下的遥感图像复原重建问题。目前,结合稀疏表示和正则化方法的图像复原理论和算法研究是国际研究热点。
本文在综述当前压缩感知和图像复原技术的国内外研究现状的基础上,以变分正则化图像复原技术为主线,从完全采样和不完全采样两种情况来探讨图像复原重建的模型及算法。
本文的主要创新性工作包括：
第一,提出一个基于全变差(TV)正则化和稀疏性约束的耦合图像复原(TV-一)模型。模型通过全变差图像模型、图像Curvelet变换下l1稀疏性和数据保真模型的联合优化,达到图像边缘结构和纹理特征保持的图像复原。本文针对最优化模型的求解问题,基于算子分裂法原理,设计了一种多步迭代的数值算法。实验证明本文算法复原图像的视觉质量优于快速TV复原算法(FTVdG)的复原结果。
第二,针对不完全随机采样遥感图像复原(去模糊)问题,设计和实现了基于Curvelet收缩和泊松奇异积分的图像复原重建算法(Curvelet-PSI);提出一个基于Curvelet迭代阈值收缩和傅立叶收缩(FoRD)的图像复原重建算法(Curvelet-FoRD)。本文新算法Curvelet-FoRD与Curvelet-PSI算法相比,在复原重建性能相当的情况下具有：参数少、参数调节简单、便于快速实现的优点。
第三,钭对IICCD相机系统,综合分析了IICCD相机的成像机制,通过光学传递函数和噪声特性建立了IICCD图像退化的模型；提出了完全采样下TV-l1的IICCD图像复原算法；设计并给出了Curvelet-FoRD下的不完全随机采样下的图像复原重建算法。实验证明了本文算法的有效性。
Because the Image Intensified CCD (IICCD) camera works in dim light conditions, with high gain, high SNR, a lower illumination level in the work, it is widely used in remote sensing and military. However, it is inevitable that IICCD camera arises the degradation of image quality because of optical blur, noise and other disturbances and high-resolution image data transmission pressure increases, so people come to pay close attention to the highly incomplete measurements technique in remote sensing image restoration and reconstruction. Currently, the sparse representation and regularization method is an international research focus for image restoration theory and algorithm.
In this paper, the summary of the current compressed sensing and image restoration technique is given. Moreover variation regularization image restoration is the main core and the reconstruction model and algorithm of image restoration in complete sampling and incomplete sampling is discussed.
The primary contributions of this dissertation contain the following points:
Firstly, total variation (TV) regularization image restoration coupled model based on sparsity constraint is proposed. This model is composed of TV regularization restoration model, curvelet transform sparsity of the image and data fidelity model. It is good at restoring the edge and texture of the image. Combined with operator splitting method, a numerical algorithm of the optimization model is given, which is a multi-step iterative algorithm. Experiments show that the algorithm is superior to the fast TV (FTVdG) algorithm in visual quality of the restored image.
Secondly, for remote sensing image restoration (deblurring) in incompletely random sampling, an image restoration and reconstruction algorithm based on Poisson singular integral and Curvelet threshold shrinkage (Curvelet-PSI) is designed and implemented. Anew image restoration and reconstruction algorithm based Fourier shrinkage and Curvelet Iteration threshold shrinkage (FoRD) is proposed. The restoration and reconstruction capacity of the new algorithm Curvelet-FoRD is equivalent in Curvelet-PSI. However, it requires less parameter, and the parameter adjustment is easy and simple. Moreover, it is fast implemented.
Thirdly, for IICCD camera system, the comprehensive analysis of the IICCD camera imaging mechanism is done, and the IICCD image degradation model is established according to the optical transfer function and noise characteristics. The IICCD image restoration algorithm based on TV-l1is proposed in completely sampling.Moreover, the Curvelet-FoRD IICCD image restoration and reconstruction algorithm in incompletely random sampling is designed and given. Then experimental results show these algorithms are effective.
本文在综述当前压缩感知和图像复原技术的国内外研究现状的基础上,以变分正则化图像复原技术为主线,从完全采样和不完全采样两种情况来探讨图像复原重建的模型及算法。
本文的主要创新性工作包括：
第一,提出一个基于全变差(TV)正则化和稀疏性约束的耦合图像复原(TV-一)模型。模型通过全变差图像模型、图像Curvelet变换下l1稀疏性和数据保真模型的联合优化,达到图像边缘结构和纹理特征保持的图像复原。本文针对最优化模型的求解问题,基于算子分裂法原理,设计了一种多步迭代的数值算法。实验证明本文算法复原图像的视觉质量优于快速TV复原算法(FTVdG)的复原结果。
第二,针对不完全随机采样遥感图像复原(去模糊)问题,设计和实现了基于Curvelet收缩和泊松奇异积分的图像复原重建算法(Curvelet-PSI);提出一个基于Curvelet迭代阈值收缩和傅立叶收缩(FoRD)的图像复原重建算法(Curvelet-FoRD)。本文新算法Curvelet-FoRD与Curvelet-PSI算法相比,在复原重建性能相当的情况下具有：参数少、参数调节简单、便于快速实现的优点。
第三,钭对IICCD相机系统,综合分析了IICCD相机的成像机制,通过光学传递函数和噪声特性建立了IICCD图像退化的模型；提出了完全采样下TV-l1的IICCD图像复原算法；设计并给出了Curvelet-FoRD下的不完全随机采样下的图像复原重建算法。实验证明了本文算法的有效性。
Because the Image Intensified CCD (IICCD) camera works in dim light conditions, with high gain, high SNR, a lower illumination level in the work, it is widely used in remote sensing and military. However, it is inevitable that IICCD camera arises the degradation of image quality because of optical blur, noise and other disturbances and high-resolution image data transmission pressure increases, so people come to pay close attention to the highly incomplete measurements technique in remote sensing image restoration and reconstruction. Currently, the sparse representation and regularization method is an international research focus for image restoration theory and algorithm.
In this paper, the summary of the current compressed sensing and image restoration technique is given. Moreover variation regularization image restoration is the main core and the reconstruction model and algorithm of image restoration in complete sampling and incomplete sampling is discussed.
The primary contributions of this dissertation contain the following points:
Firstly, total variation (TV) regularization image restoration coupled model based on sparsity constraint is proposed. This model is composed of TV regularization restoration model, curvelet transform sparsity of the image and data fidelity model. It is good at restoring the edge and texture of the image. Combined with operator splitting method, a numerical algorithm of the optimization model is given, which is a multi-step iterative algorithm. Experiments show that the algorithm is superior to the fast TV (FTVdG) algorithm in visual quality of the restored image.
Secondly, for remote sensing image restoration (deblurring) in incompletely random sampling, an image restoration and reconstruction algorithm based on Poisson singular integral and Curvelet threshold shrinkage (Curvelet-PSI) is designed and implemented. Anew image restoration and reconstruction algorithm based Fourier shrinkage and Curvelet Iteration threshold shrinkage (FoRD) is proposed. The restoration and reconstruction capacity of the new algorithm Curvelet-FoRD is equivalent in Curvelet-PSI. However, it requires less parameter, and the parameter adjustment is easy and simple. Moreover, it is fast implemented.
Thirdly, for IICCD camera system, the comprehensive analysis of the IICCD camera imaging mechanism is done, and the IICCD image degradation model is established according to the optical transfer function and noise characteristics. The IICCD image restoration algorithm based on TV-l1is proposed in completely sampling.Moreover, the Curvelet-FoRD IICCD image restoration and reconstruction algorithm in incompletely random sampling is designed and given. Then experimental results show these algorithms are effective.
引文
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[2]Moran W W, Ulich B L, Elkins W P, et al. Intensified CCD (ICCD) dynamic range and noise performance [A]. Proc SPIE[C].1997,3173.430-457.
[3]E Candes and M Wakin. An introduction to compressive sampling [J]. IEEE Signal Processing Magazine, March 2008,21-30.
[4]金君.遥感成像观察技术综述[J].东北测绘.2000,23(4)：7-8.
[5]刘杨,姚娅媚,李兵.ICCD相机成像模拟模型[A].2002年全国光电技术学术交流会论文集(上)[C].天津：红外与激光工程编辑部,2002,100-102.
[6]E Candes, J Romberg. Sparsity and incoherence in compressive sampling [J]. Inverse Problems,2007,23(3):969-985.
[7]D Donoho, Y Tsaig. Extensions of compressed sensing [J]. Signal Processing,2006, 86(3):533-548.
[8]E Candes, J Romberg, T Tao. Robust uncertainty principles:Exact signal reconstruction from highly incomplete frequency information [J]. IEEE Trans, on Information Theory, 2006,52(2):489-509.
[9]M Duarte, M Davenport, D Takhar, J Laska, T Sun, K Kelly, R Baraniuk. Single-pixel imaging via compressive sampling [J]. IEEE Signal Process. Mag.2008,25(2):83-91.
[10]Jianwei Ma and Francois-Xavier Le Dimet. Deblurring from highly incomplete measurements for remote sensing [J]. IEEE Trans. Geoscience and Remote Sensing.2009, 47(3):792-802.
[11]L Rudin, S Osher, E Fatemi. Nonliner total variation noise removal algorithms [J]. Phys.D 1992,60:259-268.
[12]肖亮,吴慧中,韦志辉.基于总体变差模型的数字滤波器设计及其性能研究[J].信号处理.2003,19(3)：247-251.
[13]A Carasso. Singular integerals, image Smoothness, and the recovery of texture in image deblurring [J]. SIAM J.Appl.Math.2004,64:1749-1774.
[14]秦前清.实用小波分析[M].西安：西安电子科技大学出版社,1994.
[15]E Candes. Ridgelets:theory and applications [A]. [Ph.D.dissertation]. USA:Department of Statistics, Stanford University,1998.
[16]D L Donoho, M R Duncan. Digital curvelet transform:Strategy, implementation and experiments [J]. In:Proc. SPIE. San Jose, CA:SPIE Press,2000,12-30.
[17]Ozkan M K, Erdem A T, Sezan M I, et al. Efficient multiframe Wiener restoration of blurred and noisy image sequences [J]. IEEE Tansactions on Image Processing,1992, 1(4):453-476.
[18]C G Rafael. E W Richard. Digital Image Processing [M]. Second Edition. Beijing: Publishing House of Electronics Industry,2002:231-234.
[19]Yan L, Wang L. Image restoration using chaotic simulated annealing [C]. In Proceedings of the International Joint Conference on Neural Networks,2003,4:3060-3064.
[20]Wong H, Guan L. A neural learning approach for adaptive image restoration using fuzzy model-based network architecture [J]. IEEE Trans. Neural Networks,2001,12(3): 516-531.
[21]Aubert G, Kornprobst P. Mathematical Problems in Image Processing [M]. New York: Springer-Verlag.2002.
[22]Chan T F, Shen J. A good image model eases restoration [EB/OL]. Technical Report, UCLA,2002. Availabe at http://www.ima.umn.edu/preprints/feb02/1829.pdf.
[23]Roe P L. Approximate riemann solvers, parameter vectors, and difference schemes [J]. J.Comput. Phys,1981,43:357-372.
[24]Leveque R J. Numerical methods for conservation laws [M]. Zurich:Birkhauser Verlag, 1990.
[25]Jamylle Laurie Carter. Dual methods for TV-based image restoration [D]. UCLA CAM. 2002,2-13.
[26]J F Aujol and G Gilboa. Implementation and parameter selection for BV-Hilbert space regularizations [R]. UCLA CAM Report.2004,4-66.
[27]Huang Y M, Micheal K N, Wen Y W. A fast total variation minimization method for image restoration [J]. Mutiscale Modeling and Simulation,2008,7(2):774-795.
[28]Y Wang, J Yang, W Yin, and Y Zhang. A new alternating minimization algorithm for total variation image reconstruction [J]. SIAM J. Imaging Sci.2008,1:248-272.
[29]A Carasso. Singular integerals, image Smoothness, and the recovery of texture in image deblurring [J]. SIAM J.Appl.Math.2004,64:1749-1774).
[30]M H Taibleson. Lipschitz classes of functions and distributions on En [J]. Bull, Amer, Math, Soc.1963,69:487-493.
[31]R Neelamani, H Choi and R Baraniuk. ForWaRD:Fourier-Wavelet regularized deconvolution for ill-conditioned systems [J]. IEEE Trans, on Signal Processing.2004, 52(2):418-433.
[32]D S Taubman, M W Marcellin. JPEG 2000:Image Compression Fundamentals, Standards and Practice [M]. Kluwer International Series in Engineering and Computer Science.2002,11:20-63
[33]H Rauhut, K Schass, P Vandergheynst. Compressed sensing and redundant dictionaries [J]. IEEE Trans on Information Theory.2008,54(5):2210-2219
[34]E J Candes. Monoscale Ridgelet for the representation of images with edges[R]. Dept.Statist, Stanford Univ, Stanford, CA, Tech. Rep,1999.
[35]E J Candes, D Donoho. New tight frames of curvelets and optimal representation of objects with piecewise C2 singularities[R]. California institute of Technology,2002:1-68.
[36]E J Candes, L Demanet, D Donoho, et al. Fast discrete curvelet transforms [R]. Pasadena, California:California institute of Technology,2005:1-43.
[37]I Daubechies, M Defrise, and C DeMol. An iterative thresholding algorithm for linear inverse problems [J]. Comm, Pure Appl, Math.57 (2004), no.11,1413-1457.
[38]I Daubechies, G Teschke, and L Vese. On some iterative concepts for image restoration [A]. In P.W.Hawkes, editor, Advances in Imaging and Electron Physics [M].2008, volume 150, pages 2-51.
[39]M Figueiredo, J Bioucas-Dias, and R Nowak. Majorization-minimization algorithms for wavelet-based image restoration [J]. IEEE Trans, Image Process.2007, 16(12):2980-2991.
[40]A Beck and M Teboulle. A fast iterative shrinkage-thresholding algorithm for linear inverse problems [J]. SIAM J, Imag, Sci.2009,2(1):183-202.
[41]J M Bioucas-Dias and M A T Figueiredo. A new TwIST:Two-step iterative shrinkage/thresholding algorithms for image restoration [J]. IEEE Trans, Image Process. 2007,16(12):2992-3004.
[42]D L Donoho and I M Johnstone. Ideal spatial adaptation via wavelet shrinkage [J]. Biometrika, April 1994,81(3):425-55.
[43]E P Simoncell, E H Adelson. Noise removal via Bayesian wavelet coring[C]. Proc, Of IEEE Inter, Conf, Image Proc. [S.I.]:IEEE,1996:379-382.
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