超复数稀疏表示及其应用的研究
|
摘要
本文首先将稀疏表示的方法扩展到超复数域,提出超复数域正交匹配跟踪算法(QOMP),然后给出了超复数域的稀疏字典学习方法(QK-SVD)。QK-SVD算法学习得到的稀疏字典能够在捕获重要结构信息的同时也能获取重要的超复数各成分空间关联信息,并且用一个超复数字典取代三个色彩通道的稀疏字典。QK-SVD算法在彩色图像去噪的应用结果表明：超复数将彩色图像的R、G、B三个分量统一处理的手段,保证了色彩空间的完整性；通过和标量信号处理中K-SVD图像去噪算法的对比,彩色图像去噪在QK-SVD自适应稀疏字典下有更稀疏的表示形式；QK-SVD算法在处理彩色图像去噪时取得了更好的处理效果。
之后,针对在超复数稀疏表示的计算过程中,随着信号维度的上升,基于贪婪算法的计算复杂度大大增加的问题,本文提出了超复数平滑L0范数的稀疏表示求解算法(QSL0)。该算法在信号维度上升的同时仍能保持很好的计算复杂度。同时在稀疏成分分析这一问题上,QSL0能够很好的处理超复数矢量信号的各个维度,得到超复数域的稀疏成分分析结果。并且在处理有噪声情况下的超复数矢量时,QSL0可以保持很好的鲁棒性,分析近似出实际的稀疏信号源分量。
最后,在研究了现有结构相似性测度(SSIM)算法中存在的问题及其原因后,本文通过结合边缘结构信息,提出了边缘加权的结构相似性测度评价方法。该方法能够更好的与主观评价结果保持一致性和正确性。通过引入边缘信息,改进SSIM原有的结构评价部分,解决了原有SSIM算法中对模糊失真评价过高和强高斯噪声失真评价过低的问题,取得了更好的评价效果。另外,本文还利用超复数自适应稀疏表示字典对彩色图像进行了质量评估。该评估方法利用超复数稀疏表示字典获取彩色图像的重要结构和纹理信息来对失真图像进行评估。仿真实验表明,该方法可以很好地评估高斯模糊图像。
At first, we propose a hypercomplex adaptive sparse dictionary learning method (QK-SVD) after formulizing hypercomplex sparse representation problem. The QK-SVD algorithm can learn a hypercomplex adaptive sparse representation dictionary from training data by catching both the important structural atoms and component correlation atoms. We use QK-SVD in color image denoising problem. With the help of hypercomplex, we can process the three components of R, G, B channels at the same time, without losing the relationship between each other. This ensures the integrity of color space. In the experiments, we show that QK-SVD has better performance on color image denoising issue than using K-SVD separately on each color channel.
Considering the quick growth of computation complexity when signal's dimension rises, we propose a hypercomplex smooth Lo norm sparse representation (QSLo) algorithm. It is very suitable for hypercomplex sparse representation, due to its low computational complexity and little growth with higher signal's dimension. The QSLo can be effectively used in hypercomplex sparse component analysis (SCA). It gives good approximation of each dimensionality of hypercomplex sparse source. Also, in this paper, we extend our discussion to a noise setting and give a more robust smooth Lo algorithm (NSLo).
Finally, this paper introduces an edge-weighted structural similarity index (EWSSIM) in image quality assessment field. After analyzing issues in structural similarity index (SSIM), we show the reasons why SSIM gives poor evaluations on blurring images and high Guassian white noise distorted images. With the help of edge structural information, the proposed index outperforms SSIM in blurred and Gaussian white noise distorted images and also gives a better coherent evaluation for all kinds of distortions in LIVE database. This paper proposes a method to evaluate color image quality by using hypercomplex adaptive sparse dictionary. The adaptive dictionary extracts important structure and texture information to evaluate distorted images. This method shows better results on blurring images.
之后,针对在超复数稀疏表示的计算过程中,随着信号维度的上升,基于贪婪算法的计算复杂度大大增加的问题,本文提出了超复数平滑L0范数的稀疏表示求解算法(QSL0)。该算法在信号维度上升的同时仍能保持很好的计算复杂度。同时在稀疏成分分析这一问题上,QSL0能够很好的处理超复数矢量信号的各个维度,得到超复数域的稀疏成分分析结果。并且在处理有噪声情况下的超复数矢量时,QSL0可以保持很好的鲁棒性,分析近似出实际的稀疏信号源分量。
最后,在研究了现有结构相似性测度(SSIM)算法中存在的问题及其原因后,本文通过结合边缘结构信息,提出了边缘加权的结构相似性测度评价方法。该方法能够更好的与主观评价结果保持一致性和正确性。通过引入边缘信息,改进SSIM原有的结构评价部分,解决了原有SSIM算法中对模糊失真评价过高和强高斯噪声失真评价过低的问题,取得了更好的评价效果。另外,本文还利用超复数自适应稀疏表示字典对彩色图像进行了质量评估。该评估方法利用超复数稀疏表示字典获取彩色图像的重要结构和纹理信息来对失真图像进行评估。仿真实验表明,该方法可以很好地评估高斯模糊图像。
At first, we propose a hypercomplex adaptive sparse dictionary learning method (QK-SVD) after formulizing hypercomplex sparse representation problem. The QK-SVD algorithm can learn a hypercomplex adaptive sparse representation dictionary from training data by catching both the important structural atoms and component correlation atoms. We use QK-SVD in color image denoising problem. With the help of hypercomplex, we can process the three components of R, G, B channels at the same time, without losing the relationship between each other. This ensures the integrity of color space. In the experiments, we show that QK-SVD has better performance on color image denoising issue than using K-SVD separately on each color channel.
Considering the quick growth of computation complexity when signal's dimension rises, we propose a hypercomplex smooth Lo norm sparse representation (QSLo) algorithm. It is very suitable for hypercomplex sparse representation, due to its low computational complexity and little growth with higher signal's dimension. The QSLo can be effectively used in hypercomplex sparse component analysis (SCA). It gives good approximation of each dimensionality of hypercomplex sparse source. Also, in this paper, we extend our discussion to a noise setting and give a more robust smooth Lo algorithm (NSLo).
Finally, this paper introduces an edge-weighted structural similarity index (EWSSIM) in image quality assessment field. After analyzing issues in structural similarity index (SSIM), we show the reasons why SSIM gives poor evaluations on blurring images and high Guassian white noise distorted images. With the help of edge structural information, the proposed index outperforms SSIM in blurred and Gaussian white noise distorted images and also gives a better coherent evaluation for all kinds of distortions in LIVE database. This paper proposes a method to evaluate color image quality by using hypercomplex adaptive sparse dictionary. The adaptive dictionary extracts important structure and texture information to evaluate distorted images. This method shows better results on blurring images.
引文
[1].章毓晋.图像处理和分析[M].北京：清华大学出版社,1999.
[2]. Rafael C. Gonzalez, Richard E. Woods数字图像处理(第二版)[M].北京：电子工业出版社,2006.
[3].孙仲康,沈振康Vsual C++数字图像处理[M].北京：电子工业出版,1999.
[4]. Michael Elad, Ma'rio A. T. Figueiredo, Yi Ma. On the role of sparse and redundant representations in image processing[J]. Proceedings of the IEEE,2010, 98(6):972-982.
[5]. H. Andrews and B. Hunt. Digital Image Restoration[M]. Prentice-Hall,1977.
[6]. T. Chan, S. Esedoglu, F. Park, and A. Yip. Recent developments in total variation imagerestoration in Handbook of Mathematical Models in Computer Vision[M]. Springer-Verlag,2005.
[7]. A. Bruckstein, D. Donoho, and M. Elad. From sparse solutions of systems of equations to sparse modelling of signals and images[J], SIAM Rev., 2009,51:34-81.
[8]. Rafael C. Gonzalez, Richard E. Woods.数字图像处理(Matlab版)[M].北京：电子工业出版社,2006.
[9]. R. Coifman and D. L. Donoho. Translation invariant de-noising[A]. In Wavelets and Statistics[M]. Springer-Verlag,1995:125-150.
[10]. M. Figueiredo and R. Nowak. Wavelet-based image estimation:An empirical Bayes approach using Jeffreys'noninformative prior[J], IEEE Trans. Image Process.2001,10:1322-1331.
[11]. M. Elad and M. Aharon. Image denoising via sparse and redundant representations over learned dictionaries[J]. IEEE Trans. Image Process.2006, 15:3736-3745.
[12]. W.R.Hamilton. Elements of quaternions [M].London:Longmans, Green and Co.1866.
[13]. S. C. Pei, J. J. Ding, J. H. Chang. Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D FFT [J]. IEEE Trans. Signal Processing,2001,49(11):2783-2797.
[14]. C. J. Evans, S. J. Sangwine, T. A. Ell. Color-sensitive edge detection using Hypercomplex filters [C]. Processing EUSIPCO 2000, Tampere, Finland, Sep, 2000.
[15]. T.A.Ell, S.J.Sangwine. Decompositon of 2D hypercomplex fourier transforms into pairs of complex Fourier transforms[C]. European Signal Processing Conference (EUSIPCO).2000,151-154.
[16]. S.J.Sangwine and T.A.E11. The discrete Fourier transform of a colour image [A]. In J M Blackledge, M J Turner. Image Processing II Mathematical Methods, Algorithms and Applications [M]. Chichester, U.K.:Ellis Horwood, 2000:430-441.
[17]. S.J.Sangwine. Fourier transforms of colour images using quaternion, or hypercomplex, number[J], Electronics Letters,1996,32(1):1979-1980.
[18]. S.J.Sangwine. and T.A.Ell. Hypercomplex Fourier transforms of color images[A]. Proc. IEEE Int.Conf.Image Processing[C]. Thessaloniki,Greece, Oct. 7-10,2001,1:137-140.
[19]. T.A.Ell and S.J.Sangwine. Hypercomplex Fourier tranfroms of color images[J]. IEEE Transcations on Image Processing,2007,16(1):22-35.
[20]. C.E.Moxey, S.J.Sangwine, and T.A.Ell. Hypercomplex correlation techniques of vector images [J]. IEEE trans on Signal Processing,2003,51(7): 1941-1953.
[21]. C.E.Moxey, S.J.Sangwine, and T.A.Ell. Color-grayscale image registration using hypercomplex phase-corrleation[C]. Proc. IEEE Int. Conf. Image Process, Rochester,NY, Sept.22-25,2002,Ⅱ:385-388.
[22]. C. J. Evans, S. J. Sangwine, T. A. Ell. Color-sensitive edge detection using Hypercomplex filters [C]. Processing EUSIPCO 2000, Tampere, Finland, Sep, 2000.
[23]. A. M. Eskicioglu. Quality measurement for monochrome compressed images in the past 25 years[A]. In Proc. IEEE Int. Conf. Acoustics, Speech Signal Processing[C], Istanbul, Turkey, Jun.2000,4:1907-1910.
[24]. A. M. Eskicioglu and P. S. Fisher. A survey of image quality measures for gray scale image compression[A]. Proc. Space and Earth Science Data Compression Workshop[C], Snowbird, UT,1993:49-61.
[25]. Wang Zhou, Bovik Alan C, Sheikh Hamid R., and Simoncelli Eero P. Image quality assessment:from error visibility to structural similarity [J]. IEEE Transactions on Image Processing,2004,13(4):600-612.
[26]. R. A. DeVore. Nonlinear approximation [J]. Acta Numerica,1998,7: 51-150.
[27]. David Donoho. Scanning the technology[J]. Proceedings of the IEEE, 2011,98(6):910-912.
[28]. Richard G. Baranuik, Emmanuel Cande'S, Michael Elad, Yi Ma. Applications of sparse representation and compressive sensing[J]. Proceedings of the IEEE,2010,98(6):906-909.:
[29]. Joel A. Tropp, Stephen J. Wright. Computational methods for sparse solution of linear inverse problems[J]. Proceedings ofthe IEEE,2010,98(6):948-958.
[30]. D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies. Data compression and harmonic analysis[J]. IEEE Trans. Inf. Theory, Oct.1998,44(6): 2433-2452.
[31]. R. G. Baraniuk, V. Cevher, M. Duarte, and C. Hegde. Model-based compressive sensing[J],2008, submitted for publication.
[32]. S. Mallat and Z. Zhang. Matching pursuits with time-frequency dictionaries[J]. IEEE Trans. Signal Process. Dec.1993,41(12):3397-3415.
[33]. Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad. Orthogonal matching pursuit:Recursive function approximation with applications to wavelet decomposition[A], in Proc.27th Annu. Asilomar Conf. Signals[C].1993:40-44.
[34]. G. Davis, S. Mallat, and M. Avellaneda. Adaptive greedy approximation[J]. Constr.Approx.1997,13:57-98.
[35]. S. S. Chen, D. L. Donoho, and M. A. Saunders. Atomic decomposition by basis pursuit[J], SIAM Rev.2001,43(1):129-159.
[36]. D. Baron, S. Sarvotham, and R. G. Baraniuk. Bayesian compressive sensing via belief propagation[J], IEEE Trans. Signal Process. Jan.2010,58(1):269-280.
[37]. D. L. Donoho, A. Maliki, and A. Montanari. Message-passing algorithms for compressed sensing. Proc. Nat. Acad. Sci.2010:1-5.
[38]. C. E. Moxey, S. J. Sangwine, and T. A. Ell. Hypercomplex correlation techniques for vector images[J]. IEEE Trans. Signal Processing, July 2003, 51:1941-1953.
[39]. S. J. Sangwine. Colour image edge detector based on quaternion convolution[J]. Electron. Letter.1998,34(10):969-971.
[40]. Huijuan Yang, Jian Qiu Zhang, Bin Wang. Hypercomplex principle component weighted approach to multiplespectral and panchromatic images Fusions[A]. In Geoscience and Remote Sensing Symposium (2007 IEEE International IGARSS 2007) [C],2007:3096-3099.
[41]. Shu Hong JIANG, Jian Qiu ZHANG and Bo HU. An adaptive visible Watermarking Algorithm in Hypercomplex frequency domain[J]. Submitted to IEEE Trans. Image Processing. Jan.2008.
[42]. H. T. Anastassiu, P. E. Atlamazoglou, and D. I. Kaklamani. Application of bicomplex (quaternion) algebra to fundamental electromagnetics:a lower order alternative to the Helmholtz equation[J]. IEEE Transactions on Antennas and Propagation, Aug.2003,51(8):2130-2136.
[43]. S. Miron, N. L. Bihan, and J. I. Mars. Quaternion-MUSIC for vector-sensor array processing[J]. IEEE Trans, signal processing, Apr,2006,54(4):1218-1229.
[44]. S. Miron, N. L. Bihan, and J.I. Mars. MUSIC algorithm for vector-sensor array processing using biquaternions[J]. IEEE Trans. signal processing, Sept, 2007,55(9):4523-4533.
[45]. N. Le Bihan and J. Mars. Quaternion subspace method for vector-sensor wave separation[A]. In Proc. XI Eur. Signal Process. Conf.[C]. Toulouse, France, 2002:637-640.
[46]. N. Le Bihan and J. Mars. Singular value decomposition of quaternion matrices:a new tool for vector-sensor signal processing[J]. Signal processing, 2004,84:1177-1199.
[47]. Jennifer Seberry, Ken Finlayson, Sarah Spence Adams, Tadeusz Antoni Wysocki, Tianbing Xia, and Beata Joanna Wysocki. The theory of quaternion orthogonal designs[J]. IEEE Trans. Signal Processing, Jan.2008,56(1):256-265.
[48]. 王友华.矢量水听器的超复数模型及DOA估计算法[D].上海：复旦大学,2008.
[49]. D. Wipf and B. Rao. Sparse Bayesian learning for basis selection[J]. IEEE Trans. Signal Process. Aug.2004,52(8):2153-2164.
[50]. R. Chartrand. Exact reconstruction of sparse signals via nonconvex minimization[J]. IEEE Signal Process. Lett. Oct.2007,14(10):707-710.
[51]. Donoho, D.L and Johnstone. Ideal spatial adaptation by wavelet shrinkage[J], Biometrika,1994,81(3):425-455.
[52]. Donoho, D.L. De-noising by soft thresholding[J], IEEE Transactions on Information Theory,1995,41(3):613-627.
[53]. Simoncelli, E.P. and Adelson, E.H. Noise removal via Bayesian wavelet coring[A].In Proceedings of the International Conference on Image Processing[C].Laussanne, Switzerland.1996.
[54]. Coifman, R. and Donoho, D.L. Translation invariant de-noising[A]. In Wavelets and Statistics, Lecture Notes in Statistics[M]. Springer Verlag. 1995:125-150.
[55]. Cand'es, E.J. and Donoho, D.L. New tight frames of curvelets and the problem of approximating piecewise C2 images with piecewise C2 edges[J], Comm. Pure Appl. Math.2004,57:219-266.
[56]. Do, M.N. and Vetterli, M. Contourlets, Beyond Wavelets[M], G. V. Welland ed., Academic Press,2003.
[57]. Donoho, D.L. Wedgelets:Nearly minimax estimation of edges[J]. Annals Of Statistics,1998,27(3):859-897.
[58]. Mallat, S. and LePennec, E. Sparse geometric image representation with bandelets[J]. IEEE Trans, on Image Processing,2005,14(4)423-438.
[59]. Freeman, W.T. and Adelson, E.H. The design and use of steerable fiIters[J], IEEE Pat. Anal. Mach. Intell.1991,13(9):891-906.
[60]. Starck, J.-L., Candes, E.J., and Donoho, D.L. The curvelet transform for image denoising[J]. IEEE Transactions On Image Processing,2002,11(6): 670-684.
[61]. Matalon, B., Elad, M. and Zibulevsky, M. Improved denoising of images using modeling of the redundant contourlet transform[A]. In Proceedings of the SPIE conference wavelets[C].2005.
[62]. Michael Elad, Michal Aharon. Image Denoising Via Learned Dictionaries and Sparse representation[J]. IEEE Trans. on Image Processing,2006, 15(12):3736-3745.
[63]. M. Protter and M. Elad. Image Sequence Denoising via Sparse and Redundant Representations[J]. IEEE Trans. on Image Processing,2009, 18(1):27-35.
[64]. J. Mairal, G. Sapiro, and M. Elad. Learning Multiscale Sparse Representations for Image and Video Restoration [J]. SIAM Multiscale Modeling and Simulation,2008,7(1):214-241.
[65]. A. M. Eskicioglu. Quality measurement for monochrome compressed images in the past 25 years[C]. In Proc. IEEE Int. Conf. Acoustics, Speech Signal Processing, Istanbul, Turkey, Jun.2000,4:1907-1910.
[66]. A. M. Eskicioglu and P. S. Fisher. A survey of image quality measures for gray scale image compression[A]. In Proc. Space and Earth Science Data Compression Workshop[C], Snowbird, UT, Apr.1993:49-61.
[67]. Wang Zhou, Bovik Alan C, Sheikh Hamid R., and Simoncelli Eero P. Image quality assessment:from error visibility to structural similarity [J]. IEEE Transactions on Image Processing,2004,13(4):600-612.
[68]. H. R. Sheikh, Z. Wang, A. C. Bovik, and L. K. Cormack. Image and Video Quality Assessment Research at LIVE[OL]. Available:http://live.ece. utexas.edu/research/quality/.
[69]. VQEG, Final report from the video quality experts group on the validation of objective models of video quality assessment [OL]. http://www.Vqeg.org/, Mar.2000.
[70]. W. K. Pratt. Digital Image Processing[M]. New York:Wiley,1978.
[71]. J. O. Limb. Distortion criteria of the human viewer[J]. IEEE Trans. Syst. Man. Cybern.,1979,9(6):778-793.
[72]. Scott Daly. The visible differences predictor:an algorithm for the assessment of image fidelity[A]. In Digital image and human vision[M], A.B. Watson. MIT Press, Cambridge, Massachusetts,1993:179-206.
[73]. Jian Wang. Visual discrimination model with H.264 [OB/OL]. http://www-ee.uta.edu/dip/Courses/EE5359/Project_Proposals_Spr2007/Jian_Wa ng.pdf.
[74]. P. C. Teo and D. J. Heeger. Perceptual image distortion[A]. In Proc. SPIE[C], 1994,2179:127-141.
[75]. Z. Wang, A. Bovik. A universal image quality index[J]. IEEE Signal Process, Lett. Mar,2002,9(3):81-84.
[76]. Rubinstein, R., Zibulevsky, M. and Elad, M. Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal Matching Pursuit[R], CS Technion, April 2008.
[77]. L. A. Wolf. Similarity of matrices in which elements are real quaternions[J]. Bull. Amer. Math. Soc,1936,42:737-743.
[78]. F. Zhang. Quaternions and matrices of quaternions[J]. Linear algebra and its applications,1997:21-57.
[79]. Nicolas Le Bihan, Jerome Mars. Singular value decomposition of quaternion matrices:a new tool for vector-sensor signal processing[J]. Signal Processing, 2004,84:1177-1199.
[80]. J. Mairal, M. Elad, and G. Sapiro. Sparse representation for color image restoration[J]. IEEE Trans. Image Process.2008,17:53-69.
[81]. H. Mohimani, M. Babaie-Zadeh, and C. Jutten. A fast approach for overcomplete sparse decomposition based on smoothed Lo norm[J]. IEEE Trans. on Signal Proc,2009,57(1):289-301.
[82]. Y. Li, A. Cichocki, and S. Amari. Sparse component analysis for blind source separation with less sensors than sources[A]. In Proc. Int. Conf. Independent Component Analysis (ICA)[C],2003:89-94.
[83]. Armin Eftekharil, Massoud Babaie-Zadeh2, Christian Jutten3, Hamid Abrishami Moghaddaml. Robust-SLo for Stable Sparse Representation In Noisy Settings[A], In Acoustics, Speech and Signal Processing, ICASSP. 2009:3433-3436.
[84]. A. Blake and A. Zisserman. Visual Reconstruction[M]. MIT Press,1987.
[85]. Guan-Hao Chen, Chun-Ling Yang, Lai-Man Po and Sheng-Li Xie. Structual Similarity For Image Quality Assessment[A]. In Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing[C], Toulouse, ICASSP,2006:933-936.
[86]. Pan Feng, Lin Xiao, and Susanto Rahardja. Fast mode decision algorithm for intraprediction in H.264/AVC video coding[J]. IEEE Trans.Circuits and Systems for Video Tech,2005:813-822.
[2]. Rafael C. Gonzalez, Richard E. Woods数字图像处理(第二版)[M].北京：电子工业出版社,2006.
[3].孙仲康,沈振康Vsual C++数字图像处理[M].北京：电子工业出版,1999.
[4]. Michael Elad, Ma'rio A. T. Figueiredo, Yi Ma. On the role of sparse and redundant representations in image processing[J]. Proceedings of the IEEE,2010, 98(6):972-982.
[5]. H. Andrews and B. Hunt. Digital Image Restoration[M]. Prentice-Hall,1977.
[6]. T. Chan, S. Esedoglu, F. Park, and A. Yip. Recent developments in total variation imagerestoration in Handbook of Mathematical Models in Computer Vision[M]. Springer-Verlag,2005.
[7]. A. Bruckstein, D. Donoho, and M. Elad. From sparse solutions of systems of equations to sparse modelling of signals and images[J], SIAM Rev., 2009,51:34-81.
[8]. Rafael C. Gonzalez, Richard E. Woods.数字图像处理(Matlab版)[M].北京：电子工业出版社,2006.
[9]. R. Coifman and D. L. Donoho. Translation invariant de-noising[A]. In Wavelets and Statistics[M]. Springer-Verlag,1995:125-150.
[10]. M. Figueiredo and R. Nowak. Wavelet-based image estimation:An empirical Bayes approach using Jeffreys'noninformative prior[J], IEEE Trans. Image Process.2001,10:1322-1331.
[11]. M. Elad and M. Aharon. Image denoising via sparse and redundant representations over learned dictionaries[J]. IEEE Trans. Image Process.2006, 15:3736-3745.
[12]. W.R.Hamilton. Elements of quaternions [M].London:Longmans, Green and Co.1866.
[13]. S. C. Pei, J. J. Ding, J. H. Chang. Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D FFT [J]. IEEE Trans. Signal Processing,2001,49(11):2783-2797.
[14]. C. J. Evans, S. J. Sangwine, T. A. Ell. Color-sensitive edge detection using Hypercomplex filters [C]. Processing EUSIPCO 2000, Tampere, Finland, Sep, 2000.
[15]. T.A.Ell, S.J.Sangwine. Decompositon of 2D hypercomplex fourier transforms into pairs of complex Fourier transforms[C]. European Signal Processing Conference (EUSIPCO).2000,151-154.
[16]. S.J.Sangwine and T.A.E11. The discrete Fourier transform of a colour image [A]. In J M Blackledge, M J Turner. Image Processing II Mathematical Methods, Algorithms and Applications [M]. Chichester, U.K.:Ellis Horwood, 2000:430-441.
[17]. S.J.Sangwine. Fourier transforms of colour images using quaternion, or hypercomplex, number[J], Electronics Letters,1996,32(1):1979-1980.
[18]. S.J.Sangwine. and T.A.Ell. Hypercomplex Fourier transforms of color images[A]. Proc. IEEE Int.Conf.Image Processing[C]. Thessaloniki,Greece, Oct. 7-10,2001,1:137-140.
[19]. T.A.Ell and S.J.Sangwine. Hypercomplex Fourier tranfroms of color images[J]. IEEE Transcations on Image Processing,2007,16(1):22-35.
[20]. C.E.Moxey, S.J.Sangwine, and T.A.Ell. Hypercomplex correlation techniques of vector images [J]. IEEE trans on Signal Processing,2003,51(7): 1941-1953.
[21]. C.E.Moxey, S.J.Sangwine, and T.A.Ell. Color-grayscale image registration using hypercomplex phase-corrleation[C]. Proc. IEEE Int. Conf. Image Process, Rochester,NY, Sept.22-25,2002,Ⅱ:385-388.
[22]. C. J. Evans, S. J. Sangwine, T. A. Ell. Color-sensitive edge detection using Hypercomplex filters [C]. Processing EUSIPCO 2000, Tampere, Finland, Sep, 2000.
[23]. A. M. Eskicioglu. Quality measurement for monochrome compressed images in the past 25 years[A]. In Proc. IEEE Int. Conf. Acoustics, Speech Signal Processing[C], Istanbul, Turkey, Jun.2000,4:1907-1910.
[24]. A. M. Eskicioglu and P. S. Fisher. A survey of image quality measures for gray scale image compression[A]. Proc. Space and Earth Science Data Compression Workshop[C], Snowbird, UT,1993:49-61.
[25]. Wang Zhou, Bovik Alan C, Sheikh Hamid R., and Simoncelli Eero P. Image quality assessment:from error visibility to structural similarity [J]. IEEE Transactions on Image Processing,2004,13(4):600-612.
[26]. R. A. DeVore. Nonlinear approximation [J]. Acta Numerica,1998,7: 51-150.
[27]. David Donoho. Scanning the technology[J]. Proceedings of the IEEE, 2011,98(6):910-912.
[28]. Richard G. Baranuik, Emmanuel Cande'S, Michael Elad, Yi Ma. Applications of sparse representation and compressive sensing[J]. Proceedings of the IEEE,2010,98(6):906-909.:
[29]. Joel A. Tropp, Stephen J. Wright. Computational methods for sparse solution of linear inverse problems[J]. Proceedings ofthe IEEE,2010,98(6):948-958.
[30]. D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies. Data compression and harmonic analysis[J]. IEEE Trans. Inf. Theory, Oct.1998,44(6): 2433-2452.
[31]. R. G. Baraniuk, V. Cevher, M. Duarte, and C. Hegde. Model-based compressive sensing[J],2008, submitted for publication.
[32]. S. Mallat and Z. Zhang. Matching pursuits with time-frequency dictionaries[J]. IEEE Trans. Signal Process. Dec.1993,41(12):3397-3415.
[33]. Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad. Orthogonal matching pursuit:Recursive function approximation with applications to wavelet decomposition[A], in Proc.27th Annu. Asilomar Conf. Signals[C].1993:40-44.
[34]. G. Davis, S. Mallat, and M. Avellaneda. Adaptive greedy approximation[J]. Constr.Approx.1997,13:57-98.
[35]. S. S. Chen, D. L. Donoho, and M. A. Saunders. Atomic decomposition by basis pursuit[J], SIAM Rev.2001,43(1):129-159.
[36]. D. Baron, S. Sarvotham, and R. G. Baraniuk. Bayesian compressive sensing via belief propagation[J], IEEE Trans. Signal Process. Jan.2010,58(1):269-280.
[37]. D. L. Donoho, A. Maliki, and A. Montanari. Message-passing algorithms for compressed sensing. Proc. Nat. Acad. Sci.2010:1-5.
[38]. C. E. Moxey, S. J. Sangwine, and T. A. Ell. Hypercomplex correlation techniques for vector images[J]. IEEE Trans. Signal Processing, July 2003, 51:1941-1953.
[39]. S. J. Sangwine. Colour image edge detector based on quaternion convolution[J]. Electron. Letter.1998,34(10):969-971.
[40]. Huijuan Yang, Jian Qiu Zhang, Bin Wang. Hypercomplex principle component weighted approach to multiplespectral and panchromatic images Fusions[A]. In Geoscience and Remote Sensing Symposium (2007 IEEE International IGARSS 2007) [C],2007:3096-3099.
[41]. Shu Hong JIANG, Jian Qiu ZHANG and Bo HU. An adaptive visible Watermarking Algorithm in Hypercomplex frequency domain[J]. Submitted to IEEE Trans. Image Processing. Jan.2008.
[42]. H. T. Anastassiu, P. E. Atlamazoglou, and D. I. Kaklamani. Application of bicomplex (quaternion) algebra to fundamental electromagnetics:a lower order alternative to the Helmholtz equation[J]. IEEE Transactions on Antennas and Propagation, Aug.2003,51(8):2130-2136.
[43]. S. Miron, N. L. Bihan, and J. I. Mars. Quaternion-MUSIC for vector-sensor array processing[J]. IEEE Trans, signal processing, Apr,2006,54(4):1218-1229.
[44]. S. Miron, N. L. Bihan, and J.I. Mars. MUSIC algorithm for vector-sensor array processing using biquaternions[J]. IEEE Trans. signal processing, Sept, 2007,55(9):4523-4533.
[45]. N. Le Bihan and J. Mars. Quaternion subspace method for vector-sensor wave separation[A]. In Proc. XI Eur. Signal Process. Conf.[C]. Toulouse, France, 2002:637-640.
[46]. N. Le Bihan and J. Mars. Singular value decomposition of quaternion matrices:a new tool for vector-sensor signal processing[J]. Signal processing, 2004,84:1177-1199.
[47]. Jennifer Seberry, Ken Finlayson, Sarah Spence Adams, Tadeusz Antoni Wysocki, Tianbing Xia, and Beata Joanna Wysocki. The theory of quaternion orthogonal designs[J]. IEEE Trans. Signal Processing, Jan.2008,56(1):256-265.
[48]. 王友华.矢量水听器的超复数模型及DOA估计算法[D].上海：复旦大学,2008.
[49]. D. Wipf and B. Rao. Sparse Bayesian learning for basis selection[J]. IEEE Trans. Signal Process. Aug.2004,52(8):2153-2164.
[50]. R. Chartrand. Exact reconstruction of sparse signals via nonconvex minimization[J]. IEEE Signal Process. Lett. Oct.2007,14(10):707-710.
[51]. Donoho, D.L and Johnstone. Ideal spatial adaptation by wavelet shrinkage[J], Biometrika,1994,81(3):425-455.
[52]. Donoho, D.L. De-noising by soft thresholding[J], IEEE Transactions on Information Theory,1995,41(3):613-627.
[53]. Simoncelli, E.P. and Adelson, E.H. Noise removal via Bayesian wavelet coring[A].In Proceedings of the International Conference on Image Processing[C].Laussanne, Switzerland.1996.
[54]. Coifman, R. and Donoho, D.L. Translation invariant de-noising[A]. In Wavelets and Statistics, Lecture Notes in Statistics[M]. Springer Verlag. 1995:125-150.
[55]. Cand'es, E.J. and Donoho, D.L. New tight frames of curvelets and the problem of approximating piecewise C2 images with piecewise C2 edges[J], Comm. Pure Appl. Math.2004,57:219-266.
[56]. Do, M.N. and Vetterli, M. Contourlets, Beyond Wavelets[M], G. V. Welland ed., Academic Press,2003.
[57]. Donoho, D.L. Wedgelets:Nearly minimax estimation of edges[J]. Annals Of Statistics,1998,27(3):859-897.
[58]. Mallat, S. and LePennec, E. Sparse geometric image representation with bandelets[J]. IEEE Trans, on Image Processing,2005,14(4)423-438.
[59]. Freeman, W.T. and Adelson, E.H. The design and use of steerable fiIters[J], IEEE Pat. Anal. Mach. Intell.1991,13(9):891-906.
[60]. Starck, J.-L., Candes, E.J., and Donoho, D.L. The curvelet transform for image denoising[J]. IEEE Transactions On Image Processing,2002,11(6): 670-684.
[61]. Matalon, B., Elad, M. and Zibulevsky, M. Improved denoising of images using modeling of the redundant contourlet transform[A]. In Proceedings of the SPIE conference wavelets[C].2005.
[62]. Michael Elad, Michal Aharon. Image Denoising Via Learned Dictionaries and Sparse representation[J]. IEEE Trans. on Image Processing,2006, 15(12):3736-3745.
[63]. M. Protter and M. Elad. Image Sequence Denoising via Sparse and Redundant Representations[J]. IEEE Trans. on Image Processing,2009, 18(1):27-35.
[64]. J. Mairal, G. Sapiro, and M. Elad. Learning Multiscale Sparse Representations for Image and Video Restoration [J]. SIAM Multiscale Modeling and Simulation,2008,7(1):214-241.
[65]. A. M. Eskicioglu. Quality measurement for monochrome compressed images in the past 25 years[C]. In Proc. IEEE Int. Conf. Acoustics, Speech Signal Processing, Istanbul, Turkey, Jun.2000,4:1907-1910.
[66]. A. M. Eskicioglu and P. S. Fisher. A survey of image quality measures for gray scale image compression[A]. In Proc. Space and Earth Science Data Compression Workshop[C], Snowbird, UT, Apr.1993:49-61.
[67]. Wang Zhou, Bovik Alan C, Sheikh Hamid R., and Simoncelli Eero P. Image quality assessment:from error visibility to structural similarity [J]. IEEE Transactions on Image Processing,2004,13(4):600-612.
[68]. H. R. Sheikh, Z. Wang, A. C. Bovik, and L. K. Cormack. Image and Video Quality Assessment Research at LIVE[OL]. Available:http://live.ece. utexas.edu/research/quality/.
[69]. VQEG, Final report from the video quality experts group on the validation of objective models of video quality assessment [OL]. http://www.Vqeg.org/, Mar.2000.
[70]. W. K. Pratt. Digital Image Processing[M]. New York:Wiley,1978.
[71]. J. O. Limb. Distortion criteria of the human viewer[J]. IEEE Trans. Syst. Man. Cybern.,1979,9(6):778-793.
[72]. Scott Daly. The visible differences predictor:an algorithm for the assessment of image fidelity[A]. In Digital image and human vision[M], A.B. Watson. MIT Press, Cambridge, Massachusetts,1993:179-206.
[73]. Jian Wang. Visual discrimination model with H.264 [OB/OL]. http://www-ee.uta.edu/dip/Courses/EE5359/Project_Proposals_Spr2007/Jian_Wa ng.pdf.
[74]. P. C. Teo and D. J. Heeger. Perceptual image distortion[A]. In Proc. SPIE[C], 1994,2179:127-141.
[75]. Z. Wang, A. Bovik. A universal image quality index[J]. IEEE Signal Process, Lett. Mar,2002,9(3):81-84.
[76]. Rubinstein, R., Zibulevsky, M. and Elad, M. Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal Matching Pursuit[R], CS Technion, April 2008.
[77]. L. A. Wolf. Similarity of matrices in which elements are real quaternions[J]. Bull. Amer. Math. Soc,1936,42:737-743.
[78]. F. Zhang. Quaternions and matrices of quaternions[J]. Linear algebra and its applications,1997:21-57.
[79]. Nicolas Le Bihan, Jerome Mars. Singular value decomposition of quaternion matrices:a new tool for vector-sensor signal processing[J]. Signal Processing, 2004,84:1177-1199.
[80]. J. Mairal, M. Elad, and G. Sapiro. Sparse representation for color image restoration[J]. IEEE Trans. Image Process.2008,17:53-69.
[81]. H. Mohimani, M. Babaie-Zadeh, and C. Jutten. A fast approach for overcomplete sparse decomposition based on smoothed Lo norm[J]. IEEE Trans. on Signal Proc,2009,57(1):289-301.
[82]. Y. Li, A. Cichocki, and S. Amari. Sparse component analysis for blind source separation with less sensors than sources[A]. In Proc. Int. Conf. Independent Component Analysis (ICA)[C],2003:89-94.
[83]. Armin Eftekharil, Massoud Babaie-Zadeh2, Christian Jutten3, Hamid Abrishami Moghaddaml. Robust-SLo for Stable Sparse Representation In Noisy Settings[A], In Acoustics, Speech and Signal Processing, ICASSP. 2009:3433-3436.
[84]. A. Blake and A. Zisserman. Visual Reconstruction[M]. MIT Press,1987.
[85]. Guan-Hao Chen, Chun-Ling Yang, Lai-Man Po and Sheng-Li Xie. Structual Similarity For Image Quality Assessment[A]. In Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing[C], Toulouse, ICASSP,2006:933-936.
[86]. Pan Feng, Lin Xiao, and Susanto Rahardja. Fast mode decision algorithm for intraprediction in H.264/AVC video coding[J]. IEEE Trans.Circuits and Systems for Video Tech,2005:813-822.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |