@article{025b8c8d49c349a58b0ecc740540b7e4,
title = "Nonseparable Two-and Three-Dimensional Wavelets",
abstract = "We present two-and three-dimensional nonseparable wavelets. They are obtained from discrete-time bases by iterating filter banks. We consider three sampling lattices: quincunx, separable by two in two dimensions, and FCO. The design methods are based either on cascade structures or on the McClellan transformation in the quincunx case. We give a few design examples. In particular, the first example of an orthonormal 2-D wavelet basis with symmetries is constructed.",
author = "Jelena Kova{\v c}evi{\'c} and Martin Vetterli",
note = "Funding Information: The main difference when compared to the 1-D treatment is that multidimensional sampling requires the use of lattices. A lattice is the set of all vectors generated by Dk, k E 2“,w here D is the matrix characterizing the sampling process. Note that D is not unique for a given sampling pattern. Using the expressions given for sampling rate changes, analysis of multidimensional filter banks (see Fig. 1) can be performed in a similar fashion to their 1-D counterparts. One of the basic tools is the polyphase domain representation, where all signals and filters are decomposed into their polyphase components, each one corresponding to one coset of the sampling lattice. The net result of this process is that, effectively, a single-input single-output periodically time-varying system can be analyzed as if it were a multiple-input multiple-output time-invariant system. The results on alias cancellation and perfect reconstruction are very similar to Manuscript received January 12, 1994; revised October 17, 1994. This work was presented at ICASSP 1992 in San Francisco, CA, and ISCAS 1993 in Chicago, IL. This work was supported by the National Science Foundation under grants ECD-88-11111 and MIP 90-14189. J. KovaEeviC is with the Signal Processing Research Department, AT&T Bell Laboratories, Murray Hill, NJ, 07974 USA. M. Vetterli is with the Electrical Engineering and Computer Science Department, Univeristy of California at Berkeley, Berkeley, CA, 94720 USA. IEEE Log Number 9410295.",
year = "1995",
month = may,
doi = "10.1109/78.382414",
language = "English (US)",
volume = "43",
pages = "1269--1273",
journal = "IRE Transactions on Audio",
issn = "1053-587X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "5",
}