基于方向滤波器和小波变换的图像编码
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摘要
多媒体技术给人们的生活带来无穷乐趣,然而,面对庞大的图像数据信息,如何更高效地表示、存储和传输?图像压缩就是要解决这个问题。
小波变换以其良好的空间-频率局部特性和与人眼视觉特性相符的变换机制,在图像编码领域得到了广泛应用和深入研究。图像的小波变换就是把图像分解为低频部分和高频部分,分别表示图像概貌和图像细节,而图像能量主要集中在低频分量上。然后,对变换后的小波系数进行量化、编码,便达到了图像压缩的目的。相比于小波变换,方向滤波器能够更好地提取图像的方向及边缘信息。在图像压缩中,小波变换和方向滤波器都是作为图像变换的方法。
本文主要研究基于小波变换和方向滤波器的图像压缩,而在多种类型的方向滤波器中,我们选用梅花型方向滤波器。所做工作主要有两方面:一是矢量量化编码中的格型矢量量化,另一个是梅花型方向滤波器的提升实现。
在图像压缩中,格型矢量量化因其规则的结构降低了编码时间和计算复杂度。在格型矢量量化中很重要的一点是参数尺度因子的调节问题,会影响到基本量化单元的大小,进而影响图像编码的比特率和失真。本文我们提出了一种新的调节此参数的方法,将其与码书半径的累积概率密度函数联系起来。然后,将这种调节尺度因子的方法应用到基于矢量死区的格型矢量量化,即死区格型矢量量化,并得出一种改进的比特率失真模型。实验结果表明该模型优于带有死区的塔式格型矢量量化中的比特率失真模型。
本文为梅花型方向滤波器提升实现中的预测和更新算子提出了一种简明且系数对称的方法,并将其应用到基于嵌入式零树小波的图像编码中。另外,通过结合“2的幂”和“整数的平方”两种取量化阈值的策略,我们得到一种新的量化方法。在图像编码中,“2的幂”作为量化阈值用于高比特率编码,而“整数的平方”则用于低比特率编码。实验结果表明,本文提出的方法可以提高重构图像的质量。
The technique of multi-media makes people's lives much creative, however, in the face of huge information of images, how to represent, store and transmit it more effectively? Image compression is very to solve this problem.
Wavelet transforms have been applied and studied in the image coding field extensively because of its good feature of space-frequency and human visual system. Wavelet transforms of an image is to decompose the image into low frequency components and high frequency components, the former ones represent approximation of the image and the latter ones indicate details, and the energy of the image mainly lies in the low frequency components. Then, by making quantization and entropy coding on these wavelet coefficients, the work of compressing the image is finished. Contrast to wavelet transforms, Directional Filter Banks(DFB) can extract directional and edge information of images better. In image compression, wavelet transforms and DFB are both regarded as methods of image transformation.
This thesis investigates image coding based on wavelet transform and directional filter banks, among various of directional filter banks, we adopt quincunx directional filter banks. The work can be mainly divided into two aspects: lattice vector quantization in vector quantization coding for images and the lifting realization of the quincunx directional filter banks.
In image compression, lattice vector quantization (LVQ) reduces coding and computational complexity because of its regular structure in image compression. An important issue of LVQ is the tuning of its key parameter, the scaling factor, having the effect of altering the size of the basic quantization cell and influencing bit-rates and distortion while encoding. In this thesis, we propose a new method for tuning this key parameter, which is related to the cumulative probability density function of the radius of the codebook shell. This scheme is then applied to a LVQ scheme based on the use of a vector dead zone (DZLVQ) and results in an improved rate-distortion model. Experimental results illustrate this model is superior to the rate-distortion model in pyramidal dead zone lattice vector quantization.
This thesis proposes a simple scheme with symmetric coefficients for the prediction and update operators in quincunx lifting, which is then applied into image coding based on Embedded Zerotree Wavelet (EZW) algorithm. In addition, we present a new quantization method for taking quantization threshold by combining the power of 2 with the square of integer. The former is used for image coding at higher bit rates and the latter at lower bit rates. The experimental results demonstrate that the proposed method can improve the quality of the reconstructed image.
小波变换以其良好的空间-频率局部特性和与人眼视觉特性相符的变换机制,在图像编码领域得到了广泛应用和深入研究。图像的小波变换就是把图像分解为低频部分和高频部分,分别表示图像概貌和图像细节,而图像能量主要集中在低频分量上。然后,对变换后的小波系数进行量化、编码,便达到了图像压缩的目的。相比于小波变换,方向滤波器能够更好地提取图像的方向及边缘信息。在图像压缩中,小波变换和方向滤波器都是作为图像变换的方法。
本文主要研究基于小波变换和方向滤波器的图像压缩,而在多种类型的方向滤波器中,我们选用梅花型方向滤波器。所做工作主要有两方面:一是矢量量化编码中的格型矢量量化,另一个是梅花型方向滤波器的提升实现。
在图像压缩中,格型矢量量化因其规则的结构降低了编码时间和计算复杂度。在格型矢量量化中很重要的一点是参数尺度因子的调节问题,会影响到基本量化单元的大小,进而影响图像编码的比特率和失真。本文我们提出了一种新的调节此参数的方法,将其与码书半径的累积概率密度函数联系起来。然后,将这种调节尺度因子的方法应用到基于矢量死区的格型矢量量化,即死区格型矢量量化,并得出一种改进的比特率失真模型。实验结果表明该模型优于带有死区的塔式格型矢量量化中的比特率失真模型。
本文为梅花型方向滤波器提升实现中的预测和更新算子提出了一种简明且系数对称的方法,并将其应用到基于嵌入式零树小波的图像编码中。另外,通过结合“2的幂”和“整数的平方”两种取量化阈值的策略,我们得到一种新的量化方法。在图像编码中,“2的幂”作为量化阈值用于高比特率编码,而“整数的平方”则用于低比特率编码。实验结果表明,本文提出的方法可以提高重构图像的质量。
The technique of multi-media makes people's lives much creative, however, in the face of huge information of images, how to represent, store and transmit it more effectively? Image compression is very to solve this problem.
Wavelet transforms have been applied and studied in the image coding field extensively because of its good feature of space-frequency and human visual system. Wavelet transforms of an image is to decompose the image into low frequency components and high frequency components, the former ones represent approximation of the image and the latter ones indicate details, and the energy of the image mainly lies in the low frequency components. Then, by making quantization and entropy coding on these wavelet coefficients, the work of compressing the image is finished. Contrast to wavelet transforms, Directional Filter Banks(DFB) can extract directional and edge information of images better. In image compression, wavelet transforms and DFB are both regarded as methods of image transformation.
This thesis investigates image coding based on wavelet transform and directional filter banks, among various of directional filter banks, we adopt quincunx directional filter banks. The work can be mainly divided into two aspects: lattice vector quantization in vector quantization coding for images and the lifting realization of the quincunx directional filter banks.
In image compression, lattice vector quantization (LVQ) reduces coding and computational complexity because of its regular structure in image compression. An important issue of LVQ is the tuning of its key parameter, the scaling factor, having the effect of altering the size of the basic quantization cell and influencing bit-rates and distortion while encoding. In this thesis, we propose a new method for tuning this key parameter, which is related to the cumulative probability density function of the radius of the codebook shell. This scheme is then applied to a LVQ scheme based on the use of a vector dead zone (DZLVQ) and results in an improved rate-distortion model. Experimental results illustrate this model is superior to the rate-distortion model in pyramidal dead zone lattice vector quantization.
This thesis proposes a simple scheme with symmetric coefficients for the prediction and update operators in quincunx lifting, which is then applied into image coding based on Embedded Zerotree Wavelet (EZW) algorithm. In addition, we present a new quantization method for taking quantization threshold by combining the power of 2 with the square of integer. The former is used for image coding at higher bit rates and the latter at lower bit rates. The experimental results demonstrate that the proposed method can improve the quality of the reconstructed image.
引文
[1]向辉.基于小波理论的图像压缩算法研究[D].Master's thesis,华东师范大学,2005
[2]杜会斌.基于小波变换的静止图像编码技术研究[D].Master's thesis,山东大学,2006
[3]Roberto H.Bamberger,Mark J.T.Smith.A Filter Bank for the Directional Decomposition of Images:Theory and Design[J].IEEE Transactions on Signal Processing.April 1992,40(4):882-893
[4]白友利.静态图像压缩标准—JPEG2000分析与应用[D].Master's thesis,大连理工大学
[5]丁媛媛.基于小波变换的图像压缩编码算法的研究与VLSI设计[D].Master's thesis,吉林大学,2006
[6]沈兰荪.图像编码与异步传输[M].北京:人民邮电出版社,2001
[7]王雪梅.小波分析在图像压缩中的应用[D].Master's thesis,华中科技大学,2005
[8]刘学锋.基于小波零树的嵌入式图像编码技术的研究与改进[D].Master's thesis,西安科技大学,2006
[9]S.G.Mallat.Multifrequency Channel Decompositions of Images and Wavelet Models[J].IEEE Transations on Acoustics Speech and Signal Processing.1989,37(12):2091-2110
[10]杨凤禄.小波变换在数字视频图像压缩编码中的应用[D].Master's thesis,燕山大学,2005
[11]T.Wiegand,G.J.Sullivan,G.Bjontegaard.Overview of the H.264/AVC Video Coding Standard[J].IEEE Transations on Circuits and Systems for Video Technology.2003,13(7):560-576
[12]Ingrid Daubechies.小波十讲[M].北京:国防工业出版社,2005
[13]胡广书.现代信号处理教程[M].北京:清华大学出版社,2005
[14]詹翠丽.嵌入式小波图像编码算法研究[D].Master's thesis,华中师范大学,2007
[15]孙延奎.小波分析及其应用[M].北京:机械工业出版社,2005
[16]T.T.Nguyen,S.Oraintara.Multiresolution Directional Filter Banks:Theory,Design and Applications[J].IEEE Transations on Signal Processing.2005,53(10):3895-3905
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[20]Guohua Lu,Yinwei Zhan.Embedded Zerotree Wavelet based Image Coding via Quincunx Lifting[C].2008 International Congress on Image and Signal Processing.Sanya,China,May 2008
[21]J.A.Nalon,J.B.T.Yabu-Uti.Compression of Quincunx Subbands[C].Proceedings of the XV Brazilian Symposium on Computer Graphics and Image Processing.Brazil,October 2002,335-341
[22]S.M.Phoong,C.W.Kim,P.P.Vaidyanathan,R.Ansari.A New Class of Two-Channel Biorthogonal Filter Banks and Wavelet Bases[J].IEEE Transactions on Signal Processing.1995,43(3):649-665
[23]R.Eslami,H.Radha.New Image Transforms Using Hybrid Wavelets and Directional Filter Banks:Analysis and Design[C].IEEE International Conference on Image Processing.September 2005,vol.1,733-736
[24]R.Eslami,H.Radha.Regular Hybrid Wavelets and Directional Filter Banks-Extensions and Applications[C].IEEE International Conference on Image Processing.October 2006,1609-1612
[25]R.Eslami,H.Radha.A New Family of Nonredundant Transforms Using Hybrid Wavelets and Directional Filter Banks[J].IEEE Transations on Image Processing.2007,16(4):1152-1167
[26]程正兴.小波分析算法与应用[M].西安:西安交通大学出版社,1998
[27]木春梅.图像压缩中矢量量化技术研究[D].Master's thesis,合肥工业大学,2005
[28]唐建.矢量量化码书设计与矢量量化应用研究[D].Ph.D.thesis,中国科学技术大学,2006
[29]胡骏.基于矢量量化的医学图像压缩编码算法的研究[D].Master's thesis,中南民族大学,2007
[30]Y.Linde,A.Buzo,M.Gray.An Algorithm for Vector Quantizer Design[J].IEEE Transations on Communications.1980,28(1):84-95
[31]邹爱民.基于区域特征的分块三维DCT域矢量量化图像编码[D].Master's thesis,吉林大学,2007
[32]P.Raffy,M.Antonini,M.Barlaud.Distortion-rate models for entropy-coded lattice vector quantization[J].IEEE Transations on Image Processing.2000,9(12):2006-2017
[33]李静.基于格型矢量量化的分布式信源编码研究[D].Master's thesis,北京交通大学,2006
[34]M.Barlaud,P.Sole,T.Goidon,M.Antonini,P.Mathieu.Pyramidal Lattice Vector Quantization for Multiscale Image Coding[J].IEEE Transations on Image Processing.1994,3(4):367-381
[35]D.G.Jeong,J.D.Gibson.Lattice Vector Quantization for Image Coding[C].IEEE International Conference on Acoustic Speech and Signal Processing.May 1989,1743-1746
[36]T.Voinson,L Guillemot,J.M.Moureaux.Image Compression Using Lattice Vector Quantization with Code Book Shape Adapted Thresholding[C].IEEE International Conference on Image Processing.Rochester,New York,September 2002,vol.2,641-644
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[38]L.Guillemot,Y.Gaudeau,J.M.Moureaux.A New Fast Bit Allocation Procedure for Image Coding based on Wavelet Transform and Dead Zone Lattice Vector Quantization[C].IEEE International Conference on Image Processing.Genoa,Italy,September 2005
[39]L.Guillemot,Y.Gaudeau,S.Moussaoui,J.M.Moureaux.An Analytical Gamma Mixture based Rate-Distortion Model for Lattice Vector Quantization[C].European Signal Processing Conference.Italy,September 2006
[40]Guohua Lu,Yinwei Zhan,Min Li.An Improved Rate-Distortion Model for Dead Zone Lattice Vector Quantization[C].The 11th World Multi-Conference on Systemics,Cybernetics and Informatics.Orlando,Florida,USA,July 2007,vol.Ⅴ,238-241
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[2]杜会斌.基于小波变换的静止图像编码技术研究[D].Master's thesis,山东大学,2006
[3]Roberto H.Bamberger,Mark J.T.Smith.A Filter Bank for the Directional Decomposition of Images:Theory and Design[J].IEEE Transactions on Signal Processing.April 1992,40(4):882-893
[4]白友利.静态图像压缩标准—JPEG2000分析与应用[D].Master's thesis,大连理工大学
[5]丁媛媛.基于小波变换的图像压缩编码算法的研究与VLSI设计[D].Master's thesis,吉林大学,2006
[6]沈兰荪.图像编码与异步传输[M].北京:人民邮电出版社,2001
[7]王雪梅.小波分析在图像压缩中的应用[D].Master's thesis,华中科技大学,2005
[8]刘学锋.基于小波零树的嵌入式图像编码技术的研究与改进[D].Master's thesis,西安科技大学,2006
[9]S.G.Mallat.Multifrequency Channel Decompositions of Images and Wavelet Models[J].IEEE Transations on Acoustics Speech and Signal Processing.1989,37(12):2091-2110
[10]杨凤禄.小波变换在数字视频图像压缩编码中的应用[D].Master's thesis,燕山大学,2005
[11]T.Wiegand,G.J.Sullivan,G.Bjontegaard.Overview of the H.264/AVC Video Coding Standard[J].IEEE Transations on Circuits and Systems for Video Technology.2003,13(7):560-576
[12]Ingrid Daubechies.小波十讲[M].北京:国防工业出版社,2005
[13]胡广书.现代信号处理教程[M].北京:清华大学出版社,2005
[14]詹翠丽.嵌入式小波图像编码算法研究[D].Master's thesis,华中师范大学,2007
[15]孙延奎.小波分析及其应用[M].北京:机械工业出版社,2005
[16]T.T.Nguyen,S.Oraintara.Multiresolution Directional Filter Banks:Theory,Design and Applications[J].IEEE Transations on Signal Processing.2005,53(10):3895-3905
[17]T.T.Nguyen,S.Oraintara.A Class of Multiresolution Directional Filter Banks[J].IEEE Transations on Signal Processing.2007,55(3):949-961
[18]R.Andrews,D.Nguyen.Separable and Quincunx Wavelet Image Coding[C].6th IEEE International Workshop on Signal Processing and Communication Systems.Melbourne,Australia,November 1998
[19]M.Feilner,D.V.D.Ville,M.Unser.An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order[J].IEEE Transations on Image Processing.2005,14(4):499-510
[20]Guohua Lu,Yinwei Zhan.Embedded Zerotree Wavelet based Image Coding via Quincunx Lifting[C].2008 International Congress on Image and Signal Processing.Sanya,China,May 2008
[21]J.A.Nalon,J.B.T.Yabu-Uti.Compression of Quincunx Subbands[C].Proceedings of the XV Brazilian Symposium on Computer Graphics and Image Processing.Brazil,October 2002,335-341
[22]S.M.Phoong,C.W.Kim,P.P.Vaidyanathan,R.Ansari.A New Class of Two-Channel Biorthogonal Filter Banks and Wavelet Bases[J].IEEE Transactions on Signal Processing.1995,43(3):649-665
[23]R.Eslami,H.Radha.New Image Transforms Using Hybrid Wavelets and Directional Filter Banks:Analysis and Design[C].IEEE International Conference on Image Processing.September 2005,vol.1,733-736
[24]R.Eslami,H.Radha.Regular Hybrid Wavelets and Directional Filter Banks-Extensions and Applications[C].IEEE International Conference on Image Processing.October 2006,1609-1612
[25]R.Eslami,H.Radha.A New Family of Nonredundant Transforms Using Hybrid Wavelets and Directional Filter Banks[J].IEEE Transations on Image Processing.2007,16(4):1152-1167
[26]程正兴.小波分析算法与应用[M].西安:西安交通大学出版社,1998
[27]木春梅.图像压缩中矢量量化技术研究[D].Master's thesis,合肥工业大学,2005
[28]唐建.矢量量化码书设计与矢量量化应用研究[D].Ph.D.thesis,中国科学技术大学,2006
[29]胡骏.基于矢量量化的医学图像压缩编码算法的研究[D].Master's thesis,中南民族大学,2007
[30]Y.Linde,A.Buzo,M.Gray.An Algorithm for Vector Quantizer Design[J].IEEE Transations on Communications.1980,28(1):84-95
[31]邹爱民.基于区域特征的分块三维DCT域矢量量化图像编码[D].Master's thesis,吉林大学,2007
[32]P.Raffy,M.Antonini,M.Barlaud.Distortion-rate models for entropy-coded lattice vector quantization[J].IEEE Transations on Image Processing.2000,9(12):2006-2017
[33]李静.基于格型矢量量化的分布式信源编码研究[D].Master's thesis,北京交通大学,2006
[34]M.Barlaud,P.Sole,T.Goidon,M.Antonini,P.Mathieu.Pyramidal Lattice Vector Quantization for Multiscale Image Coding[J].IEEE Transations on Image Processing.1994,3(4):367-381
[35]D.G.Jeong,J.D.Gibson.Lattice Vector Quantization for Image Coding[C].IEEE International Conference on Acoustic Speech and Signal Processing.May 1989,1743-1746
[36]T.Voinson,L Guillemot,J.M.Moureaux.Image Compression Using Lattice Vector Quantization with Code Book Shape Adapted Thresholding[C].IEEE International Conference on Image Processing.Rochester,New York,September 2002,vol.2,641-644
[37]J.H.Conway,N.J.A.Sloane.Sphere Packing Lattices and Group[M].Springer Verlag,1988
[38]L.Guillemot,Y.Gaudeau,J.M.Moureaux.A New Fast Bit Allocation Procedure for Image Coding based on Wavelet Transform and Dead Zone Lattice Vector Quantization[C].IEEE International Conference on Image Processing.Genoa,Italy,September 2005
[39]L.Guillemot,Y.Gaudeau,S.Moussaoui,J.M.Moureaux.An Analytical Gamma Mixture based Rate-Distortion Model for Lattice Vector Quantization[C].European Signal Processing Conference.Italy,September 2006
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