Abstract
Two dimensional (2D) nonseparable filter banks with linear phase (LP) are desired for image sub-band coding and compression. In this paper, we propose a method for designing 2D nonseparable filter banks with the LP and near perfect reconstruction (near-PR) properties. By combining the unimodular transformation and a separable |M|-channel LP filter bank, the design problem is simplified to that of two one-dimensional (1D) LP filter banks. For 1D case, a novel method by employing partial cosine modulation is used to design near-PR filter banks with LP analysis and synthesis filters. For 2D case, we cascade two 1D near-PR LP filter banks in the form of tree structure to design a separable LP filter bank. With the unimodular transformation, a nonseparable LP filter bank is obtained. In addition, the filter bank achieves the near-PR property without sophisticated nonlinear optimization procedures. Design example shows the efficiency and simplicity of the proposed method.
Work supported by National Natural Science Foundation of China (Grant No. 60372047) and Natural Science Foundation of Shaanxi (Grant No. 2005F18).
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References
Vetterli, M.: Multidimensional sub-band coding: Some theory and algorithms. Signal Processing 6, 97–112 (1984)
Woods, J.W., O’Neil, S.D.: Subband coding of images. IEEE Trans. ASSP 34(5), 1278–1288 (1986)
Karlsson, G., Vetterli, M.: Theory of two-dimensional multirate filter banks. IEEE Trans. ASSP 38(6), 925–937 (1990)
Viscito, E., Allebach, J.P.: The analysis and design of multidimensional FIR perfect reconstruction filter banks for arbitrary sampling lattices. IEEE Trans. CAS 38(1), 29–42 (1991)
Nguyen, T.T., Oraintara, S.: Multidimensional filter banks design by direct optimization. IEEE ISCAS 2, 1090–1093 (2005)
Lin, Y.P., Vaidyanathan, P.P.: Two-dimensional paraunitary cosine modulated perfect reconstruction filter banks. IEEE ISCAS 1, 752–755 (1995)
Ikehara, M.: Cosine-modulated 2 dimensional FIR filter banks satisfying perfect reconstruction. IEEE ICASSP 3, 137–140 (1994)
Lin, Y.P., Vaidyanathan, P.P.: Two-dimensional linear phase cosine modulated filter banks. IEEE ISCAS 2, 73–76 (1996)
Nagai, T., Ikehara, M.: Cosine modulated 2-dimensional perfect reconstruction FIR filter banks with linear phase. IEEE ICASSP 3, 1483–1486 (1996)
Vaidyanathan, P.P.: The role of Smith-form decomposition of integer-matrices, in multidimensional multirate systems. IEEE ICASSP 3, 1777–1780 (1991)
Vaidyanathan, P.P.: New results in multidimensional multirate systems. IEEE ISCAS 1, 468–471 (1991)
Lin, Y.P., Vaidyanathan, P.P.: On the study of four-parallelogram filter banks. IEEE Trans. SP 44(11), 2707–2717 (1996)
Lin, Y.P., Vaidyanathan, P.P.: Theory and design of two-dimensional filter banks: A review. Multidimensional Systems and Signal Processing 7, 236–330 (1996)
Vaidyanathan, P.P.: Multirate Systems and Filter Banks. Prentice Hall, Englewood Cliffs (1992)
Xie, X.M., Shi, G.M., Chen, X.Y.: Optimal prototype filters for near-perfect-reconstruction cosine-modulated filter banks. In: Hao, Y., Liu, J., Wang, Y.-P., Cheung, Y.-m., Yin, H., Jiao, L., Ma, J., Jiao, Y.-C. (eds.) CIS 2005. LNCS (LNAI), vol. 3802, pp. 851–856. Springer, Heidelberg (2005)
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Shi, G., Song, L., Xie, X., Liu, D. (2006). A Simple Method for Designing 2D |M|-Channel Near-PR Filter Banks with Linear Phase Property. In: Campilho, A., Kamel, M.S. (eds) Image Analysis and Recognition. ICIAR 2006. Lecture Notes in Computer Science, vol 4141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11867586_30
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DOI: https://doi.org/10.1007/11867586_30
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