**排序方式：**共有15条查询结果，搜索用时 97 毫秒

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.

Regularity of refinable function vectors

**总被引：10，自引：0，他引：10** Albert Cohen Ingrid Daubechies Gerlind Plonka 《Journal of Fourier Analysis and Applications》1997,3(3):295-324

We study the existence and regularity of compactly supported solutions φ = (φ

_{v})_{v=0 }^{/r−1 }of vector refinement equations. The space spanned by the translates of φ_{v}can only provide approximation order if the refinement mask**P**has certain particular factorization properties. We show, how the factorization of**P**can lead to decay of |̸_{v}(u)| as |u| → ∞. The results on decay are used to prove uniqueness of solutions and convergence of the cascade algorithm. 相似文献3.

Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints

**总被引：2，自引：0，他引：2** Ingrid Daubechies Massimo Fornasier Ignace Loris 《Journal of Fourier Analysis and Applications》2008,14(5-6):764-792

Regularization of ill-posed linear inverse problems via

*?*_{1}penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an*?*_{1}penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to*?*_{1}-constraints, using a gradient method, with projection on*?*_{1}-balls. The corresponding algorithm uses again iterative soft-thresholding, now with a variable thresholding parameter. We also propose accelerated versions of this iterative method, using ingredients of the (linear) steepest descent method. We prove convergence in norm for one of these projected gradient methods, without and with acceleration. 相似文献4.

In this paper we show that there exist wavelet frames that have nice dual wavelet frames, but for which the

*canonical*dual frame does not consist of wavelets, i.e., cannot be generated by the translates and dilates of a single function. 相似文献5.

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

6.

Starting from any two compactly supported refinable functions in L

_{2}(R) with dilation factor d,we show that it is always possible to construct 2d wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L_{2}(R). Moreover, the number of vanishing moments of each of these wavelet frames is equal to the approximation order of the dual MRA; this is the highest possible. In particular, when we consider symmetric refinable functions, the constructed dual wavelets are also symmetric or antisymmetric. As a consequence, for any compactly supported refinable function in L_{2}(R), it is possible to construct, explicitly and easily, wavelets that are finite linear combinations of translates (d · – k), and that generate a wavelet frame with an arbitrarily preassigned number of vanishing moments.We illustrate the general theory by examples of such pairs of dual wavelet frames derived from B-spline functions. 相似文献7.

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

8.

9.

If the mask of a refinable function has infinitely many coefficients, or if the coefficients are irrational, then it is often replaced by a finite mask with coefficients with terminating decimal expansions when it comes to applications. This note studies how such truncation affects the refinable function.Communicated by Charles A. Micchelli 相似文献

10.

Ingrid Daubechies H.J. Landau Zeph Landau 《Journal of Fourier Analysis and Applications》1994,1(4):437-478

Gabor time-frequency lattices are sets of functions of the form
generated from a given function
by discrete translations in time and frequency. They are potential tools for the decomposition and handling of signals that,
like speech or music, seem over short intervals to have well-defined frequencies that, however, change with time. It was recently
observed that the behavior of a lattice
can be connected to that of a dual lattice
Here we establish this interesting relationship and study its properties. We then clarify the results by applying the theory
of von Neumann algebras. One outcome is a simple proof that for
to span
the lattice
must have at least unit density. Finally, we exploit the connection between the two lattices to construct expansions having
improved convergence and localization properties. 相似文献