Parametric Deslauriers-Dubuc Interpolating Wavelets:Construction and Performance Analysis for Image Coding
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摘要: 研究了采用提升构造具有任意偶数阶消失矩, 满足对称性, 且仅用一个自由参数表达的 Deslauriers-Dubuc (D-D)双正交插值小波. 首先,采用多相矩阵理论推导出了此类小波存在的条件; 然后,给出了对应小波滤波器和插值小波变换的构造算法. 采用算法具体构造了分别具有消失矩对(4, 2)、(4, 4)、(6, 2)以及(6, 4) 等4类一参数表达的D-D插值小波; 最后, 以自由参数为自变量, 根据编码增益准则, 优化设计了4种用于图像编码的插值小波, 其滤波器系数全为二进制分数, 可实现非乘法运算的离散小波变换(Discrete wavelet transform, DWT). 系统分析表明, 两种小波的压缩性能超过CDF-9/7小波, 对于纹理图像, PSNR增益达到0.44.dB, 并且计算复杂度可降低17%以上. 实验同时表明, 新小波的重构图像具有更好的主观可视质量.Abstract: This paper mainly focuses on how to construct new parametric Deslauriers-Dubuc (D-D) biorthogonal interpolating wavelets which have arbitrary vanishing moments, symmetry, and depend on one free parameter via lifting scheme. We first derive their existence conditions necessary for the wavelets with the polyphase matrix theory. Then, we demonstrate the detailed algorithm for constructing their associated wavelet filter bank and interpolating wavelet transforms. With the algorithm, four classes of parametric D-D wavelets with vanishing moment pairs of (4, 2), (4, 4), (6, 2) and (6, 4), respectively are constructed. Finally, according to the coding gain criterion, we design four new interpolating wavelets for image coding by adjusting the free parameter; they all have dyadic-fraction filter coefficients and can realize a multiplication-free DWT. Extensive simulations show that the two interpolating wavelets exhibit performances superior to the CDF-9/7 wavelet, especially with a gain of up to 0.44.dB in PSNR over the latter for rich-textured image and a lower computational cost by 17%. In addition, significant improvement in subjectively visual quality is also observed.
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[1] Dubuc S. Interpolation through an iterative scheme. Journal of Mathematical Analysis and Applications, 1986, 114(1): 185-204 [2] [2] Deslauriers G, Dubuc S. Symmetric iterative interpolation processes. Constructive Approximation, 1989, 5(1): 49-68 [3] [3] Saito N, Beylkin G. Multiresolution representations using the autocorrelation functions of compactly supported wavelets. IEEE Transactions on Signal Processing, 1993, 41(12): 3584-3590 [4] [4] Averbuch A Z, Zheludev V A. Construction of biorthogonal discrete wavelet transforms using interpolatory splines. Applied and Computational Harmonic Analysis, 2002, 12(1): 25-56 [5] [5] Olkkonen H, Olkkonen J T. Shift-invariant B-spline wavelet transform for multi-scale analysis of neuroelectric signals. IET Signal Processing, 2010, 4(6): 603-609 [6] [6] Shi Z E, Kouri D J, Wei G W, Hoffman D K. Generalized symmetric interpolating wavelets. Computer Physics Communications, 1999, 119(2-3): 194-218 [7] Hou Xia, Hu Shou-Song. A novel weighted wavelet with subdivision. Acta Automatica Sinica, 2004, 30(6): 1017-1020(侯霞, 胡寿松. 一种新的细分加权小波. 自动化学报, 2004, 30(6): 1017-1020) [8] Wang Yong-Li, Zhou Jing-Hua, Xu Hong-Bing, Dong Yi-Sheng, Liu Xue-Jun. An adaptive forecasting method for time-series data streams. Acta Automatica Sinica, 2007, 33(2): 197-201 (王永利, 周景华, 徐宏炳, 董逸生, 刘学军. 时间序列数据流的自适应预测. 自动化学报, 2007, 33(2): 197-201) [9] Wang Gang, Zhou Xiao-Hui. The study of the orthogonal balanced interpolation multi-wavelets with multiplicity r and dilation factor a. Acta Automatica Sinica, 2012, 38(12): 1996-2004(王刚, 周小辉. r重a尺度正交平衡插值多小波的设计. 自动化学报, 2012, 38(12): 1996-2004) [10] Ansari R, Guillemot C, Kaiser J F. Wavelet construction using Lagrange halfband filters. IEEE Transactions on Circuits and Systems, 1991, 38(9): 1116-1118 [11] Cohen A, Daubechies I, Feauveau J C. Biorthogonal bases of compactly supported wavelets. Communications on Pure Applied Mathematics, 1992, 45(5): 485-560 [12] Sweldens W. The lifting scheme: a custom-design construction of biorthogonal wavelets. Applied Computational and Harmonic Analysis, 1996, 3(2): 186-200 [13] Wei D, Tian J, Wells R O Jr, Burrus C S. A new class of biorthogonal wavelet systems for image transform coding. IEEE Transactions on Image Processing, 1998, 7(7): 1000-1013 [14] Shui P L, Bao Z. Construction of nearly orthogonal interpolating wavelets. Signal Processing, 1999, 79(3): 289-300 [15] Shui P L, Bao Z. Recursive biorthogonal interpolating wavelets and signal-adapted interpolating filter banks. IEEE Transactions on Signal Processing, 2000, 48(9): 2585-2593 [16] Liu Z D, Zheng N N. Parametrization construction of integer wavelet transforms for embedded image coding. International Journal of Computer Mathematics, 2007, 84(9): 1339-1352 [17] Liu Zai-De, Chang Jin-Yi, Shen Jun-Yi. Parameterization construction of a class of biorthogonal interpolating wavelets and their application to image coding. Journal of Image and Graphics, 2010, 15(4): 557-564(刘在德, 常晋义, 沈钧毅. 一类双正交插值小波的参数化构造及图像编码应用. 中国图象图形学报, 2010, 15(4): 557-564) [18] Daubechies I, Sweldens W. Factoring wavelet transforms into lifting steps. Journal of Fourier Analysis and Applications, 1998, 4(3): 247-269 [19] Information Technology-JPEG 2000 Image Coding System: Core Coding System (2nd Edition). ISO/IEC 15444-1, 2004 [20] Liu Z D, Zheng N N. Parametrization construction of biorthogonal wavelet filter banks for image coding. Signal, Image and Video Processing, 2007, 1(1): 63-76 [21] Liu Z D, Gao C X. Construction of parametric biorthogonal wavelet filter banks with two parameters for image coding. Signal, Image and Video Processing, 2008, 2(3): 195-206 [22] Katto J, Yasuda Y. Performance evaluation of subband coding and optimization. In: Proceeding of SPIE Symposium on Visual Communications and Image Processing. Boston, USA: SPIE, 1991, 1605: 95-106 [23] Information Technology-JPEG 2000 Image Coding System: Extensions. ISO/IEC 15444-2, 2004 [24] Said A, Pearlman W A. A new, fast, and efficient image codec based on set partitioning in hierarchical trees. IEEE Transactions on Circuits and Systems for Video Technology, 1996, 6(3): 243-250 [25] Ding W P, Wu F, Wu X L, Li S P, Li H Q. Adaptive directional lifting-based wavelet transform for image coding. IEEE Transactions on Image Processing, 2007, 16(2): 416-427 [26] Zhang Nan, Lv Yan, Wu Feng, Yin Bao-Cai. Multiple description image coding based on directional lifting wavelet transform. Acta Automatica Sinica, 2007, 33(6): 567-576(张楠, 吕岩, 吴枫, 尹宝才. 基于方向提升小波变换的多描述图像编码. 自动化学报, 2007, 33(6): 567-576) [27] Velisavljević V, Beferull-Lozano B, Vetterli M, Dragotti P L. Directionlets: anisotropic multidirectional representation with separable filtering. IEEE Transactions on Image Processing, 2006, 15(7): 1916-1933 [28] Bai Jing, Wu Jia-Ji, Lu Shan, Jiao Li-Cheng. Zeroblock embedded image coding algorithm based on lifting directionlet transform. Acta Automatica Sinica, 2011, 37(3): 283-289(白静, 吴家骥, 卢山, 焦李成. 基于提升Directionlet 变换的零块嵌入图像编码算法. 自动化学报, 2011, 37(3): 283-289) [29] Yang Bo, Jing Zhong-Liang. Image fusion algorithm based on the quincunx-sampled discrete wavelet frame. Acta Automatica Sinica, 2010, 36(1): 12-22 (杨波, 敬忠良. 梅花形采样离散小波框架图像融合算法. 自动化学报, 2010, 36(1): 12-22) [30] Lan X G, Zheng N N, Ma W, Yuan Y. Arbitrary ROI-based wavelet video coding. Neurocomputing, 2011, 74(12-13): 2114-2122 [31] Lan X G, Yang M, Yuan Y, Zhao S L, Zheng Nan-Ning. Adaptively post-encoding multiple description video coding. Neurocomputing, 2013, 101(4): 149-160
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