Wavelet-based decompositions for nonlinear signal processing

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 2825, Issue , 1996, Pages 260-271

  Nowak, Robert D ^a   Baraniuk, Richard G ^a  

^a Rice University   (United States)

Author keywords

nonlinear signal processing; tensor spaces; wavelets

Indexed keywords

NON-LINEAR SIGNAL PROCESSING; NON-LINEARITY; NONLINEAR SIGNALS; OPTIMAL BASIS; REAL-WORLD; SIGNAL DECOMPOSITION; SIGNAL PROCESSING PROBLEMS; TENSOR NORM; TENSOR SPACES; WAVELETS;

IMAGE PROCESSING; IMAGING SYSTEMS; NONLINEAR ANALYSIS; SIGNAL DISTORTION; TENSORS;

SIGNAL PROCESSING;

EID: 78751637405     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.255237     Document Type: Conference Paper

References (20)

1. T. André, R. Nowak, and B. Van Veen, "Low Rank Estimation of Higher Order Statistics," IEEE International Conference on Acoustics, Speech, and Signal Processing, Atlanta, GA, May 1996.
2. W. Beckner, "Inequalities in Fourier Analysis," Annals of Math., 102, pp. 159-182, 1975.
3. J. W. Brewer, "Kronecker products and matrix calculus in system theory," IEEE Trans. Cir. and Sys., Vol. 25, pp. 772-781, 1978.
4. H.-H. Chiang, C. L. Nikias, and A. N. Venetsanopoulos, "Efficient implementations of quadratic filters," IEEE Trans. on Acoustics , Speech, and Signal Proc., vol. 34, pp. 1511-1528, 1986.
5. K. C. Chou and L. P. Heck, "A multiscale stochastic modelling approach to the monitoring of mechanical systems," 1994 IEEE-SP International Symposium on Time-frequency and Time-scale Analysis.
6. I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, no. 61, SIAM, 1992.
7. A. Defant and K. Floret, Tensor Norms and Operator Ideals, North-Holland Mathematics Studies 176, Elsevier Science Publishers, 1993.
8. J. Diestel, H. Jarchow, and A. Tonge, Absolutely Summing Operators, Cambridge Studies in Advanced Mathematics: 43, Cambridge University Press, 1995.
9. D. L. Donoho, "Unconditional bases are optimal bases for data compression and for statistical estimation," Applied and Computational Harmonic Analysis, pp. 100-115, vol. 1, no. 1, December, 1993.
10. B. R. Gelbaum and J. Gil de Lamadrid, "Bases of tensor products of Banach spaces," Pacific Journal of Mathematics, 11, pp. 1281-1286, 1961.
11. V. J. Mathews, "Adaptive polynomial filters," IEEE SP Magazine, vol. 8, no. 3, pp. 10-26, 1991.
12. Y. Meyer, Wavelets and Operators, Cambridge Studies in Advanced Mathematics: 37, Cambridge University Press, 1992.
13. C. L. Nikias and A. P. Petropulu, Higher-Order Spectra Analysis. A Nonlinear Signal Processing Framework, Prentice Hall Signal Processing Series, 1993.
14. R. D. Nowak and R. G. Baraniuk, "Optimal weighted highpass filters using multiscale analysis," Proceedings of the IEEE Southwest Symposium on Image Analysis and Interpretation, pp. 224-229, San Antonio, 1996.
15. R. D. Nowak and R. G. Baraniuk, "Wavelet and filter bank decompositions for nonlinear signal processing," Rice University Technical Report, ECE-TR-9605, Rice University, Houston, TX, July 1996.
16. A. Oravesky, personal communications, 1996.
17. T. M. Panicker and V.J. Mathews, "Parallel-cascade realizations and approximations of truncated Volterra systems," Proceedings of the 1996 IEEE Intl. Conf. on Acoustics, Speech, and Signal Proc., pp. 1589-1592, Atlanta, 1996.
18. G. Pisier, Factorization of Linear Operators and Geometry of Banach Spaces, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, no. 60, AMS, Providence. Rhode Island, 1986.
19. G. L. Sicuranza, "Quadratic filters for signal processing," Proc. of the IEEE, vol. 90, p p. 1263-1285, August 1992.
20. T. Yokonuma, Tensor Spaces and Exterior Algebra, Translations of Mathematical Monographs, Vol. 108, AMS, Providence, Rhode Island, 1991.