Liu Zai-de, Zheng Nan-ning, Liu Yue-hu, Yang Guo-an, Tian Li-hua. Optimization Design of 17/11 Biorthogonal Wavelet and Its Performance Analysis for Image Compression[J]. Journal of Electronics & Information Technology, 2007, 29(6): 1403-1407. doi: 10.3724/SP.J.1146.2005.01358
Citation:
Liu Zai-de, Zheng Nan-ning, Liu Yue-hu, Yang Guo-an, Tian Li-hua. Optimization Design of 17/11 Biorthogonal Wavelet and Its Performance Analysis for Image Compression[J]. Journal of Electronics & Information Technology, 2007, 29(6): 1403-1407. doi: 10.3724/SP.J.1146.2005.01358
Liu Zai-de, Zheng Nan-ning, Liu Yue-hu, Yang Guo-an, Tian Li-hua. Optimization Design of 17/11 Biorthogonal Wavelet and Its Performance Analysis for Image Compression[J]. Journal of Electronics & Information Technology, 2007, 29(6): 1403-1407. doi: 10.3724/SP.J.1146.2005.01358
Citation:
Liu Zai-de, Zheng Nan-ning, Liu Yue-hu, Yang Guo-an, Tian Li-hua. Optimization Design of 17/11 Biorthogonal Wavelet and Its Performance Analysis for Image Compression[J]. Journal of Electronics & Information Technology, 2007, 29(6): 1403-1407. doi: 10.3724/SP.J.1146.2005.01358
Many wavelet filter banks suitable for image coding, e.g. CDF-9/7, Winger-17/11 (W-17/11), Villasenor-6/10 and 10/18 (V-6/10 and V-10/18), have irrational coefficients, and thus require infinite computational precision to implement the corresponding Discrete Wavelet Transforms (DWT). Here a simple technique for parametrization construction of 17/11 biorthogonal wavelet family is presented: first, the associated synthesis filter is formulated as one trigonometric polynomial represented by two free parameters; then the perfect reconstruction condition of the filter bank is reduced to one system of linear equations; finally the analysis filter is obtained by solving this system of linear equations. Thus, the exact free parameter expressions for the 17/11 biorthogonal wavelet filter banks are derived. By adjusting the free parameters, one can easily construct any linear phase 17/11 filters (a pair) with desired features. As a case study, a previously unpublished 17/11 biorthogonal wavelet filter bank with rational coefficients is constructed, which has optimum coding gain. Extensive simulations show that the new filter bank has the compression performance comparable to that of W-17/11 and V-10/18 for image transform coding, while surpasses the CDF-9/7 and V-6/10 far away.
Cohen A, Daubechies I, and Feauveau J C. Biorthogonal bases of compactly supported wavelets[J].Commun. Pure Appl. Math.1992, 45(5):485-560[2]Sweldens W. The lifting scheme: A custom-design of biorthogonal wavelets[J].Applied Computational and Harmonic Analysis.1996, 3(2):186-200[3]Winger L L and Venetsanopoulos A N. Biorthogonal nearly coifet wavelets for image compression[J].Signal Processing: Image Communication.2001, 16(9):859-869[4]Villasenor J D, Belzer B, and Liao J. Wavelet filter evaluation for image compression[J].IEEE Trans. on Image Processing.1995, 4(8):1053-1060[5]Tsai M J, Villasenor J D, and Chen F. Stack-run image coding[J].IEEE Trans. on Circuits and Systems Video Tech.1996, 6(5):519-521[6]ISO/IEC 15444-1 (2nd Edition), Information technology― JPEG 2000 image coding system: core coding system. 2004.[7]Daubechies I and Sweldens W. Factoring wavelet transforms into lifting steps[J].J. Fourier Analysis and Applications.1998, 4(3):247-269[8]刘在德，郑南宁，宋永红等. 高性能、有理系数9/7双正交小波滤波器组的设计. 西安交大学报(自然版), 2005, 39(8): 848-851.[9]Katto J and Yasuda Y. Performance evaluation of subband coding and optimization. Proc. SPIE Symposium on Visual Comm. and Image Proc., Boston, U.S.A, 1991, vol. 1605: 95-106.[10]Woods J W and Naveen T. A filter based bit allocation scheme for subband compression of HDTV[J].IEEE Trans. on Image Processing.1992, 1(3):436-440[11]Said A and Pearlman W A. A new, fast, efficient image codec based on set partitioning in hierarchical tree[J].IEEE Trans. on Circuits and Systems Video Tech.1996, 6(3):243-250
DownLoad: