Ten lectures on wavelets
Multirate systems and filter banks
Multirate systems and filter banks
Wavelets and subband coding
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
JPEG 2000: Image Compression Fundamentals, Standards and Practice
JPEG 2000: Image Compression Fundamentals, Standards and Practice
CREW: Compression with Reversible Embedded Wavelets
DCC '95 Proceedings of the Conference on Data Compression
Gain normalization of lifted filter banks
Signal Processing
Group lifting structures for multirate filter banks II: linear phase filter banks
IEEE Transactions on Signal Processing
A wreath product group approach to signal and image processing .I.Multiresolution analysis
IEEE Transactions on Signal Processing
Symmetric-extension-compatible reversible integer-to-integer wavelet transforms
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
The polyphase-with-advance representation and linear phase lifting factorizations
IEEE Transactions on Signal Processing - Part I
Group lifting structures for multirate filter banks II: linear phase filter banks
IEEE Transactions on Signal Processing
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Group lifting structures are introduced to provide an algebraic framework for studying lifting factorizations of two-channel perfect reconstruction finite-impulse-response (FIR) filter banks. The lifting factorizations generated by a group lifting structure are characterized by Abelian groups of lower and upper triangular lifting matrices, an Abelian group of unimodular gain scaling matrices, and a set of base filter banks. Examples of group lifting structures are given for linear phase lifting factorizations of the two nontrivial classes of two-channel linear phase FIR filter banks, the whole- and half-sample symmetric classes, including both the reversible and irreversible cases. This covers the lifting specifications for whole-sample symmetric filter banks in Parts 1 and 2 of the ISO/IEC JPEG 2000 still image coding standard. The theory is used to address the uniqueness of lifting factorizations. With no constraints on the lifting process, it is shown that lifting factorizations are highly nonunique. When certain hypotheses developed in the paper are satisfied, however, lifting factorizations generated by a group lifting structure are shown to be unique. A companion paper applies the uniqueness results proven in this paper to the linear phase group lifting structures for whole- and half-sample symmetric filter banks.