**排序方式：**共有6条查询结果，搜索用时 108 毫秒

**1**

1.

Factoring wavelet transforms into lifting steps

**总被引：223，自引：0，他引：223**This article 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 filtering 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

*SL*(n;**[z, z***R*^{−1}])=*E*(n;**[z, z***R*^{−1}])); 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 reduces 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. Research Tutorial*Acknowledgements and Notes*. Page 264. 相似文献2.

Biorthogonal Smooth Local Trigonometric Bases

**总被引：3，自引：0，他引：3**In this paper we discuss smooth local trigonometric bases. We present two generalizations of the orthogonal basis of Malvar
and Coifman-Meyer: biorthogonal and equal parity bases. These allow natural representations of constant and, sometimes, linear
components. We study and compare their approximation properties and applicability in data compression. This is illustrated
with numerical examples. 相似文献

3.

A multiresolution analysis of a curve is normal if
each wavelet detail vector with respect to a certain subdivision
scheme lies in the local normal direction. In this paper we study
properties such as regularity, convergence, and stability of a
normal multiresolution analysis. In particular, we show that these
properties critically depend on the underlying subdivision scheme
and that, in general, the convergence of normal multiresolution
approximations equals the convergence of the underlying subdivision
scheme. 相似文献

4.

We present a generalization of the commutation formula to irregular subdivision schemes and wavelets. We show how, in the
noninterpolating case, the divided differences need to be adapted to the subdivision scheme. As an example we include the
construction of an entire family of biorthogonal compactly supported irregular knot B-spline wavelets starting from Lagrangian
interpolation.
September 4, 1998. Date revised: July 27, 1999. Date accepted: November 16, 2000. 相似文献

5.

Given a complete separable σ-finite measure space (X,

*Σ*, μ) and nested partitions of X, we construct unbalanced Haar-like wavelets on X that form an unconditional basis for L_{p}(X,*Σ*, μ) where*1*<p<∞. Our construction and proofs build upon ideas of Burkholder and Mitrea. We show that if(X,*Σ*, μ) is not purely atomic, then the unconditional basis constant of our basis is (*max*(p, q) −*1*). We derive a fast algorithm to compute the coefficients. 相似文献6.

Summary. We generalize earlier results concerning
an asymptotic error expansion of wavelet
approximations. The properties of the monowavelets,
which are the building
blocks for the error expansion, are studied in more
detail, and connections
between spline wavelets and Euler and
Bernoulli polynomials are pointed out.
The expansion is used to compare the
error for different wavelet families.
We prove that the leading terms of the
expansion only depend on the multiresolution
subspaces and not
on how the complementary subspaces
are chosen.
Consequently, for a fixed set of
subspaces , the leading
terms do not depend on the fact whether
the wavelets are orthogonal or not.
We also show that Daubechies' orthogonal wavelets need,
in general, one level more than spline wavelets to obtain an
approximation with a prescribed accuracy.
These results are illustrated with numerical examples.
Received May 3, 1993 / Revised version received January 31, 1994 相似文献

**1**