TY - GEN
T1 - Smooth wavelet frames with application to denoising
AU - Selesnick, Ivan W.
AU - Şendur, Levent
N1 - Funding Information:
This reseach was supported by the NSF under CAREER grant CCR-9875452 oversampled FIR filter banks, for which there is greater design freedom, compared to orthonormal filter banks. We note that in contrast to orthonormal wavelet bases, the number of zero wavelet moments, and the regularity of the scaling function, can be more or less independent. We show that this difference can be utilized to design smoother wavelets for a given support. (The nonlinear design equations that arise are solved using Grobner bases.) Like Kings-bury’s dual-tree DWT, the frames presented in this paper are less shift-sensitive than orthonormal wavelet bases, even though the redundancy rate is only 2, independent of the number of scales over which the signal expansion is performed. Because the frames described in this paper are based on iterated FIR filter banks, a fast discrete frame transform is simple to implement. This paper considers exclusively tzght frames.
Funding Information:
This research was supported by the NSF under CAREER grant CCR-9875452.
Publisher Copyright:
© 2000 IEEE.
PY - 2000
Y1 - 2000
N2 - This paper considers the design and application of wavelet tight frames based on iterated oversampled filter banks. The greater design freedom available makes possible the construction of wavelets with a high degree of smoothness, in comparison with orthonormal wavelet bases. Grobner bases are used to obtain the solutions to the nonlinear design equations. Following the dual-Tree DWT of Kingsbury (see Proceedings of the Eighth IEEE DSP Workshop, Utah, 1998, and Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (ICASSP), Phoenix, 1999), one goal is to keep the redundancy-factor bounded by 2, instead of allowing it to grow as it does for the undecimated DWT (which is exactly shift-invariant). For the tight frame presented here, optimal-Tree based denoising algorithms can be directly applied.
AB - This paper considers the design and application of wavelet tight frames based on iterated oversampled filter banks. The greater design freedom available makes possible the construction of wavelets with a high degree of smoothness, in comparison with orthonormal wavelet bases. Grobner bases are used to obtain the solutions to the nonlinear design equations. Following the dual-Tree DWT of Kingsbury (see Proceedings of the Eighth IEEE DSP Workshop, Utah, 1998, and Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (ICASSP), Phoenix, 1999), one goal is to keep the redundancy-factor bounded by 2, instead of allowing it to grow as it does for the undecimated DWT (which is exactly shift-invariant). For the tight frame presented here, optimal-Tree based denoising algorithms can be directly applied.
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U2 - 10.1109/ICASSP.2000.861887
DO - 10.1109/ICASSP.2000.861887
M3 - Conference contribution
AN - SCOPUS:0033693385
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 129
EP - 132
BT - Signal Processing Theory and Methods I
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 25th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2000
Y2 - 5 June 2000 through 9 June 2000
ER -