Abstract
Biorthogonal and orthogonal filter pairs derived from the family of binomial product filters are considered for wavelet transform implementation with the goal of high performance lossy image compression. Using experimental rate-distortion performance as the final measure of comparison, a number of new and existing filters are presented with excellent image coding capabilities. In addition, numerous filter attributes such as orthonormality, transition band sharpness, coding gain, low-band reconstruction error, regularity, and vanishing moments are assessed to determine their importance with regards to the fidelity of the decoded images. While image data compression is specifically addressed, many of the proposed techniques are applicable to other coding applications.
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References
P. P. Vaidyanathan, Multirate Systems and Filter Banks, Englewood Cliffs, NJ: Prentice Hall, 1993.
M. Vetterli and C. Herley, “Wavelets and filter banks: theory and design,” IEEE Trans. on Signal Processing, vol. 40, 1992, pp. 2207–2232.
J. D. Johnston, “A filter family designed for use in quadrature mirror filter banks,” in Proc. of the Int. Conf. on Acoust. Speech and Sig. Proc., 1980, pp. 291–294.
F. Grenez, “Chebyshev design of filters for subband coders,” IEEE Trans. Acoust., Speech, and Signal Processing, vol. 36, 1988, pp. 182–185.
M. J. T. Smith and T. P. Barnwell, “Exact reconstruction techniques for tree-structured subband coders,” IEEE Trans. Acoust., Speech, and Signal Processing, vol. 34, 1986, pp. 434–441.
J. W. Woods and S. D. O'Neil, “Subband coding of images,” IEEE Trans. Acoust., Speech, and Signal Processing, vol. 34, 1986, pp. 1278–1288.
I. Daubechies, Ten Lectures on Wavelets, Philadelphia, PA: SIAM, 1992.
A. Gersho and R. M. Gray, Vector Quantization and Signal Compression, Boston: Kluwer Academic Publishers, 1992.
J. Katto and Y. Yasuda, “Performance evaluation of subband coding and optimization of its filter coefficients,” in Proc. of the SPIE Symposium on Visual Comm. and Image Proc., vol. 1605, 1991, pp. 95–106.
M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies, “Image coding using the wavelet transform,” IEEE Trans. on Image Processing, vol. 1, 1992, pp. 205–220.
I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Communications on Pure and Applied Mathematics, vol. XLI, 1988, pp. 909–996.
D. L. Gall and A. Tabatabai, “Subband coding of digital images using symmetric short kernal filters and arithmetic coding techniques,” in Proc. of the Int. Conf. on Acoust. Speech and Sig. Proc., 1988, pp. 761–764.
R. Ansari and D. L. Gall, “Advanced television coding using exact reconstruction filter banks,” in J.W. Woods (ed.), Subband Image Coding, Boston, MA: Kluwer Academic Publishers, 1991, pp. 273–318.
E. Majani and M. Lightstone, “Wavelet compression of seismic data,” Int. Conf. on Wavelets, Theory, Algorithms, and Applications, Taorimina, Italy, 1993, pp. 14–20.
M. Lightstone and E. Majani, “Low bit-rate design considerations for wavelet-based image coding,” in Proc. of the SPIE Symposium on Visual Comm. and Image Proc., vol. 2308, Chicago, IL, 1994, pp. 501–512.
E. Majani and M. Lightstone, “Biorthogonal wavelets for data compression,” in Proceedings of the Data Compression Conference, Snowbird, UT, 1994, p. 462.
J. N. Bradley, C. M. Brislawn, and T. Hopper, “The FBI wavelet/scalar quantization for gray-scale fingerprint image compression,” Los Alamos Technical Report, vol. LA-UR-93-1659.
A. V. Oppenheim and R.W. Schafer, Discrete-time signal processing, Englewood Cliffs, NJ: Prentice-Hall, 1989.
A. K. Soman and P. P. Vaidyanathan, “Coding gain in paraunitary analysis/synthesis systems,” IEEE Trans. on Signal Processing, vol. 41, 1993, pp. 1824–1835.
I. Djokovic and P. P. Vaidyanathan, “Statistical wavelet and filter bank optimization,” in Conference Record of The Twenty-Seventh Asilomar Conference on Signals, Systems and Computers, vol. 2, 1993, pp. 911–915.
N. S. Jayant and P. Noll, Digital coding of waveforms, Englewood Cliff, New Jersey: Prentice-Hall, 1984.
J. D. Villasenor, B. Belzer, and J. Liao, “Filter evaluation and selection in wavelet image compression,” in Proceedings of the Data Compression Conference, Snowbird, UT, 1994, pp. 351–360.
O. Rioul, “Simple regularity criteria for subdivision schemes,” SIAM J. Math. Anal., vol. 23, 1992, pp. 1544–1576.
E. Majani, “Biorthogonal wavelets for image compression,” in Proc. of the SPIE Symposium on Visual Comm. and Image Proc., vol. 2308, Part 1, Chicago, IL, 1994, pp. 478–488.
R. M. de Queiroz and H. S. Malvar, “On the asymptotic performance of hierarchical transforms,” IEEE Trans. on Signal Processing, vol. 40, 1992, pp. 2620–2622.
J. M. Shapiro, “An embedded wavelet hierarchical image coder,” in Proc. of the Int. Conf. on Acoust. Speech and Sig. Proc., 1992, p. 1992.
J. M. Shapiro, “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. on Signal Processing, vol. 41, 1993, pp. 3445–3462.
C. Herley and M. Vetterli, “Orthogonal time-varying filter banks and wavelet packets,” IEEE Trans. on Signal Processing, vol. 42, 1994, pp. 2650–2663.
M. J. T. Smith and S. L. Eddins, “Analysis/synthesis techniques for subband image coding,” IEEE Trans. Acoust., Speech, and Signal Processing, vol. 38, 1990, pp. 1446–1456.
G. Karlsson and M. Vetterli, “Extension of finite length signals for subband image coding,” Signal Processing, vol. 17, 1989, pp. 161–168.
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Lightstone, M., Majani, E. & Mitra, S.K. Low Bit-Rate Design Considerations for Wavelet-Based Image Coding. Multidimensional Systems and Signal Processing 8, 111–128 (1997). https://doi.org/10.1023/A:1008221023577
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DOI: https://doi.org/10.1023/A:1008221023577