Symmetric-extension-compatible reversible integer-to-integer wavelet transforms

TitleSymmetric-extension-compatible reversible integer-to-integer wavelet transforms
Publication TypeJournal Article
Year of Publication2003
AuthorsAdams, M. D., and R. K. Ward
JournalSignal Processing, IEEE Transactions on
Pagination2624 - 2636
Date Publishedoct.
Keywordschannel bank filters, filtering theory, finite-length signals, ITI wavelet transforms, per-lifting-step extension, reversible integer-to-integer wavelet transforms, signal coding, symmetric-extension-compatible wavelet transforms, transform coding, uniformly maximally-decimated filterbank, wavelet transforms

Symmetric extension is explored as a means for constructing nonexpansive reversible integer-to-integer (ITI) wavelet transforms for finite-length signals. Two families of reversible ITI wavelet transforms are introduced, and their constituent transforms are shown to be compatible with symmetric extension. One of these families is then studied in detail, and several interesting results concerning its member transforms are presented. In addition, some new reversible ITI structures are derived that are useful in conjunction with techniques like symmetric extension. Last, the relationship between symmetric extension and per-lifting-step extension is explored, and some new results are obtained in this regard.


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