Factoring wavelet transforms into lifting steps

Factoring wavelet transforms into lifting steps (1998)

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by Ingrid Daubechies , Wim Sweldens

Venue:	J. Fourier Anal. Appl
Citations:	336 - 7 self

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Datum	Value	Source
TITLE	Factoring wavelet transforms into lifting steps	INFERENCE
AUTHOR NAME	Ingrid Daubechies	SVM HeaderParse 0.2
AUTHOR NAME	Wim Sweldens	SVM HeaderParse 0.2
ABSTRACT	ABSTRACT. This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filter-ing steps, which we call lifting steps but that are also known as ladder structures. This decomposition corresponds to a factorization of the polyphase matrix of the wavelet or subband filters into elementary matrices. That such a factorization is possible is well-known to algebraists (and expressed by the formula); it is also used in linear systems theory in the electrical engineering community. We present here a self-contained derivation, building the decomposition from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering. This factorization provides an alternative for the lattice factorization, with the advantage that it can also be used in the biorthogonal, i.e, non-unitary case. Like the lattice factorization, the decomposition presented here asymptotically re-duces the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining a wavelet-like transform that maps integers to integers. 1.	SVM HeaderParse 0.2
YEAR	1998	INFERENCE
VENUE	J. Fourier Anal. Appl	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	247--269	INFERENCE
VOLUME	4	INFERENCE
TECH	Technical report	INFERENCE
CITATIONS	59 found	ParsCit 1.0