✦ LIBER ✦

On Frame Wavelets Associated with Frame Multiresolution Analysis

✍ Scribed by Hong Oh Kim; Jae Kun Lim

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 108 KB
Volume: 10
Category: Article
ISSN: 1063-5203
DOI: 10.1006/acha.2000.0322

No coin nor oath required. For personal study only.

✦ Synopsis

We present some necessary and sufficient conditions for a frame multiresolution analysis (FMRA) to admit a frame wavelet whose dyadic dilations and integer translates generate a frame for L 2 (R) and propose a construction of a wavelet, if it exists, which reduces to the classical orthonormal wavelet in the case of orthonormal multiresolution analysis. We also show that there always exists a frame for the detail space W 0 of a frame MRA consisting of the integer translates of two functions and give an explicit construction of them.

📜 SIMILAR VOLUMES

On Dual Wavelet Tight Frames

✍ Bin Han 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 489 KB

A characterization of multivariate dual wavelet tight frames for any general dilation matrix is presented in this paper. As an application, Lawton's result on wavelet tight frames in L 2 ‫)ޒ(‬ is generalized to the n-dimensional case. Two ways of constructing certain dual wavelet tight frames in L 2

Smooth Wavelet Tight Frames with Zero Mo

Smooth Wavelet Tight Frames with Zero Moments

✍ Ivan W. Selesnick 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 354 KB

This paper considers the design of wavelet tight frames based on iterated oversampled filter banks. The greater design freedom available makes possible the construction of wavelets with a high degree of smoothness, in comparison with orthonormal wavelet bases. In particular, this paper takes up the

Homogeneous approximation property for w

Homogeneous approximation property for wavelet frames with matrix dilations

✍ Wenchang Sun 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 201 KB

## Abstract The homogeneous approximation property (HAP) for wavelet frames was studied recently. The HAP is useful in practice since it means that the number of building blocks involved in a reconstruction of a function up to some error is essentially invariant under time‐scale shifts. In this pap

Orthonormal Wavelets and Tight Frames wi

Orthonormal Wavelets and Tight Frames with Arbitrary Real Dilations

✍ Charles K Chui; Xianliang Shi 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 170 KB

The objective of this paper is to establish a complete characterization of tight frames, and particularly of orthonormal wavelets, for an arbitrary dilation factor a > 1, that are generated by a family of finitely many functions in L 2 := L 2 (R). This is a generalization of the fundamental work of

Characterizations of Biorthogonal Wavele

Characterizations of Biorthogonal Wavelets Which Are Associated with Biorthogonal Multiresolution Analyses

✍ Hong Oh Kim; Rae Young Kim; Jae Kun Lim 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 130 KB

We first characterize the Riesz wavelets which are associated with multiresolution analyses (MRAs) and the Riesz wavelets whose duals are also Riesz wavelets. The characterizations show that if a Riesz wavelet is associated with an MRA, then it has a dual Riesz wavelet. We then improve Wang's charac

Matrix analysis of frames with shear wal

Matrix analysis of frames with shear walls

✍ B.K. Goyal; S.P. Sharma 📂 Article 📅 1968 🏛 Elsevier Science ⚖ 413 KB

The stiffness matrix approach has been used to solve frames with or without shear walls. In case of shear walls it is assumed that between the centre line and edge of the shear wall the beam is infinitely rigid. An experimental investigation has been conducted to test the validity of the assumption.