TY - JOUR
T1 - The double-density dual-tree DWT
AU - Selesnick, Ivan W.
N1 - Funding Information:
Manuscript received July 17, 2001; revised May 28, 2003. This work was supported by the National Science Foundation under CAREER Grant CCR-9875452. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Arnab K. Shaw. The author is with the Department of Electrical and Computer Engineering, Polytechnic University, Brooklyn, NY 11202 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TSP.2004.826174
PY - 2004/5
Y1 - 2004/5
N2 - This paper introduces the double-density dual-tree discrete wavelet transform (DWT), which is a DWT that combines the double-density DWT and the dual-tree DWT, each of which has its own characteristics and advantages. The transform corresponds to a new family of dyadic wavelet tight frames based on two scaling functions and four distinct wavelets. One pair of the four wavelets are designed to be offset from the other pair of wavelets so that the integer translates of one wavelet pair fall midway between the integer translates of the other pair. Simultaneously, one pair of wavelets are designed to be approximate Hilbert transforms of the other pair of wavelets so that two complex (approximately analytic) wavelets can be formed. Therefore, they can be used to implement complex and directional wavelet transforms. The paper develops a design procedure to obtain finite impulse response (FIR) filters that satisfy the numerous constraints imposed. This design procedure employs a fractional-delay allpass filter, spectral factorization, and filterbank completion. The solutions have vanishing moments, compact support, a high degree of smoothness, and are nearly shift-invariant.
AB - This paper introduces the double-density dual-tree discrete wavelet transform (DWT), which is a DWT that combines the double-density DWT and the dual-tree DWT, each of which has its own characteristics and advantages. The transform corresponds to a new family of dyadic wavelet tight frames based on two scaling functions and four distinct wavelets. One pair of the four wavelets are designed to be offset from the other pair of wavelets so that the integer translates of one wavelet pair fall midway between the integer translates of the other pair. Simultaneously, one pair of wavelets are designed to be approximate Hilbert transforms of the other pair of wavelets so that two complex (approximately analytic) wavelets can be formed. Therefore, they can be used to implement complex and directional wavelet transforms. The paper develops a design procedure to obtain finite impulse response (FIR) filters that satisfy the numerous constraints imposed. This design procedure employs a fractional-delay allpass filter, spectral factorization, and filterbank completion. The solutions have vanishing moments, compact support, a high degree of smoothness, and are nearly shift-invariant.
KW - Dual-tree complex wavelet transform
KW - Frame
UR - http://www.scopus.com/inward/record.url?scp=2442598093&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=2442598093&partnerID=8YFLogxK
U2 - 10.1109/TSP.2004.826174
DO - 10.1109/TSP.2004.826174
M3 - Article
AN - SCOPUS:2442598093
SN - 1053-587X
VL - 52
SP - 1304
EP - 1314
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 5
ER -