Approximation and compression of piecewise smooth functions

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 357, Issue 1760, 1999, Pages 2573-2591

  Prandoni, Paolo ^a   Vetterli, Martin ^a,b  

^a EPFL   (Switzerland)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Data compression; Data modelling; Dynamic allocation; Joint segmentation quantization; Rate distortion optimality; Wavelet approximation

Indexed keywords

EID: 0347507433     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.1999.0449     Document Type: Article

References (19)

1. Bellman, R. 1957 Dynamic programming. Princeton University Press.
2. Berger, T. 1971 Rate distortion theory. Englewood Cliffs, NJ: Prentice Hall.
3. Cohen, A., Daubechies, I. & Vial, P. 1993 Wavelet bases on the interval and fast algorithms. J. Appl. Comput. Harmonic Analysis 1, 54-81.
4. Cohen, A., Daubechies, I., Guleryuz, O. & Orchard, M. 1999 On the importance of combining wavelet-based non-linear approximation in coding strategies. (In preparation.)
5. Coifman, R. R. & Wickerhauser, M. V. 1992 Entropy-based algorithms for best basis selection. IEEE Trans. Information Theory 38, 713-718.
6. Donoho, D. L., Vetterli, M., DeVore, R. A. & Daubechies, I.1998 Data compression and harmonic analysis. IEEE Trans. Information Theory 44, 2435-2476.
7. Gersho, A. & Gray, R. M. 1992 Vector quantization and signal compression. Dordrecht: Kluwer.
8. Mallat, S. 1997 A wavelet tour of signal processing. San Diego, CA: Academic.
9. Mallat, S. & Falzon, F. 1998 Analysis of low bit rate image transform coding. IEEE Trans. Signal Processing 46, 1027-1042.
10. Ortega, A. & Ramchandran, K. 1998 Rate-distortion methods for image and video compression. IEEE Signal Processing Magazine November, pp. 23-50.
11. Prandoni, P. 1999 Optimal segmentation techniques for piecewise stationary signals. PhD thesis, École Polytechnique Fédérale de Lausanne, Switzerland.
12. Prandoni, P., Goodwin, M. & Vetterli, M. 1997 Optimal time segmentation for signal modeling and compression. In Proc. ICASSP, vol. 3, pp. 2029-2032.
13. Ramchandran, K. & Vetterli, M. 1993 Best wavelet packet bases in a rate-distortion sense. IEEE Trans. Image Processing 2, 160-175.
14. Shannon, C. E. 1948 A mathematical theory of communication. Bell Syst. Tech. Jl 27, 623-656.
15. Shannon, C. E. 1959 Coding theorems for a discrete source with a fidelity criterion. IRE Nat. Conv. Rec. 142-163.
16. Shapiro, J. M. 1993 Embedded image coding using zerotrees of wavelet coefficients. IEEE Trans. Signal Processing, 41, 3445-3462.
17. Shoham, Y. & Gersho, A. 1988 Efficient bit allocation for an arbitrary set of quantizers. IEEE Trans. Acoust. Speech Signal Processing 36, 1445-1453.
18. Vetterli, M. & Kovačević, J. 1995 Wavelets and subband coding. Englewood Cliffs, NJ: Prentice Hall.
19. Xiong, Z., Ramchandran, K., Herley, C. & Orchard, M. T. 1994 Flexible time segmentations for time-varying wavelet packets. IEEE Proc. Int. Symp. on Time-Frequency and Time-Scale Analysis, pp. 9-12. New York: IEEE.