J. E. Odegard, R. A. Gopinath, and C. S. Burrus. Op- timal Wavelets for Signal Decomposition and the Existence of Scale-Limited Signals. In Proceedings of the ICASSP '92, San Francisco. IEEE, March 1992. Home/Search Document Details and Download
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Galerkin-wavelet modeling of wave propagation: Optimal.. - Robertsson Blanch Symes (1993) (1 citation) Self-citation (Burrus) (Correct)
....in equation (2.1) must satisfy the equation X k h k = 2; 2.6) as well as the N 2 equations X k h k h k Gamma2n = ae 2 for n = 0 0 otherwise (2.7) If the N coefficients satisfy equations (2.6) and (2. 7) that uses N=2 1 degrees of freedom leaving N=2 Gamma 1 for optimization [9, 17]. Indeed one of the features that distinguishes wavelet systems from most other orthonormal basis sets is having parameters to tailor the system to a particular problem. A general parameterization has been given in [2, 18, 21] Daubechies [5, 6] used these to maximize the number of vanishing ....
J. E. Odegard, R. A. Gopinath, and C. S. Burrus. Optimal wavelets for signal decomposition and the existence of scale limited signals. In Proceedings of the IEEE international conference on signal processing, pages 597--600. ICASSP-92, 1992.
Optimal Wavelet Representation Of Signals And The.. - Gopinath, Odegard.. (1994) (11 citations) Self-citation (Odegard Gopinath Burrus) (Correct)
.... been constructed and compactly supported M band wavelets have been parameterized [15, 12, 32, 17] This paper gives the theory and algorithms for obtaining the optimal wavelet multiresolution analysis for the representation of a given signal at a predetermined scale in a variety of error norms [23]. Moreover, for classes of signals, this paper gives the theory and algorithms for designing the robust wavelet multiresolution analysis that minimizes the worst case approximation error among all signals in the class. All results are derived for the general M band multiresolution analysis. An ....
....of the L 2 case, we present the general results (with examples) In wavelet analysis resolution or scale plays a role analogous to frequency in Fourier analysis. A natural question is whether a notion similar to bandlimitedness exists in wavelet analysis. This question has been investigated in [23], where the authors introduce the notion of essentially scalelimited signals. Our solution to Problem 2 shows that all bandlimited signals are essentially scalelimited (i.e. the class of essentially scalelimited signals is rich) Practically wavelet expansion coefficients are computed as follows: ....
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J. E. Odegard, R. A. Gopinath, and C. S. Burrus. Optimal wavelets for signal decomposition and the existence of scale limited signals. In Proc. Int. Conf. Acoust., Speech, Signal Processing, volume 4, pages IV 597--600, San Francisco, CA, March 1992. IEEE. Also Tech. Report CML TR91-07.
On Cosine-Modulated Wavelet Orthonormal Bases - Gopinath, Burrus (1993) (1 citation) Self-citation (Gopinath Burrus) (Correct)
.... by AFOSR under grant 90 0334 funded by DARPA and Bell Northern Research 1 Introduction Recently orthonormal bases of compactly supported wavelets have received considerable attention in the signal processing community, both as a tool for signal analysis ( 5, 6, 7, 8] and signal representation ([9, 10, 11, 12, 13, 14]) Several authors have tried to use wavelets for image compression [10, 15] It is well known that image coding using wavelets is a special case of subband coding using particular sets of filters called scaling and wavelet vectors. However, this specialization and the mathematical theory of ....
....WTFs, one can pick a tight frame that is suited to any particular application. This involves choosing the scaling function, and then the wavelets. In the wavelet literature there has been some recent work on the choice of optimal and robust scaling function or equivalently the scaling vector [12, 13, 11]. The scaling vector is generically of length N = MK, and determined by (M Gamma 1) K Gamma 1) parameters. All properties of the multiresolution analysis is determined by the scaling function. However, when M 2, to get a WTF one has to design the wavelets too. For large M the design of the WTF ....
[Article contains additional citation context not shown here]
J. E. Odegard, R. A. Gopinath, and C. S. Burrus. Optimal wavelets for signal decomposition and the existence of scale limited signals. In Proc. Int. Conf. Acoust., Speech, Signal Processing, volume 4, pages IV 597--600, San Francisco, CA, March 1992. IEEE.
On the Correlation Structure of Multiplicity M Scaling . . . - Gopinath, al. (1992) (1 citation) (Correct)
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J. E. Odegard, R. A. Gopinath, and C. S. Burrus. Op- timal Wavelets for Signal Decomposition and the Existence of Scale-Limited Signals. In Proceedings of the ICASSP '92, San Francisco. IEEE, March 1992.
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