Refinable Function-Based Construction of Weak (Quasi-)Affine Bi-Frames

Jia, H. Y.; Li, Yun‐Zhang

doi:10.1007/s00041-014-9349-y

Cited by 18 publications

(7 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They date back to [5,6,9,10,[12][13][14][15][16]21,22] and references therein. Due to their application potential in signal processing, the study of various extension principles has been attracting many researchers [23][24][25][26][27][28][29][30][31][32].…”

Section: An Overview Of Dual Wavelet Framesmentioning

confidence: 99%

Nonhomogeneous dual wavelet frames and mixed oblique extension principles in Sobolev spaces

Zhang

2017

Applicable Analysis

Self Cite

View full text Add to dashboard Cite

From the literature, it is known that nonhomogeneous dual wavelet frames admit fast wavelet transform as homogeneous ones, and have more designing freedom than homogeneous ones. In this paper, we give a characterization of nonhomogeneous dual wavelet frames in (H s (R d ), H −s (R d )), and using this characterization we derive a mixed oblique extension principle for such dual wavelet frames. ARTICLE HISTORY

show abstract

Section: An Overview Of Dual Wavelet Framesmentioning

confidence: 99%

Nonhomogeneous dual wavelet frames and mixed oblique extension principles in Sobolev spaces

Zhang

2017

Applicable Analysis

Self Cite

View full text Add to dashboard Cite

show abstract

“…Li and Zhou 36 established a frame and dual frame-preservation theorem between affine systems and quasi-affine systems and presented a Fourier-domain characterization of affine dual frames in general reducing subspaces. Jia and Li 37,38 introduced the notion of weak affine dual frames and obtained a construction method under the setting of general reducing subspaces.…”

Section: Then X(ψ) Is a Bessel Sequence With Bound B And If Furthermorementioning

confidence: 99%

Partial affine system–based frames and dual frames

Tian

2017

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

In this paper, we introduce the notion of partial affine system that is a subset of an affine system. It has potential applications in signal analysis. A general affine system has been extensively studied; however, the partial one has not. The main focus of this paper is on partial affine system-based frames and dual frames. We obtain a necessary condition and a sufficient condition for a partial affine system to be a frame and present a characterization of partial affine system-based dual frames. Some examples are also provided. KEYWORDSaffine dual frame, affine frame, affine system, frame, partial affine system It gives a frequency description of f. In signal analysis, noise elimination and data compression are 2 common tasks. For (4), they mean to set the high-frequency coefficients (c k with large k) equal to zero and then, for the left terms, to retain only those coefficients c k that are larger (in absolute value) than some specified tolerance (Boggess and Narcowich 1 ). Similarly, for a wavelet frame expansion of the form Math Meth Appl

show abstract

“…It is natural to ask what are expected from general refinable functions without too many restrictions. For this purpose, Jia and Li in [21] introduced the nation of weak wavelet biframes (weak dual wavelet frames). Starting from a pair of general refinable functions without smoothness restrictions, they obtained a construction of weak dual wavelet frames for reducing subspace FL 2 ðΩÞ of L 2 ðℝ d Þ.…”

Section: Introductionmentioning

confidence: 99%

A Class of Weak Dual Wavelet Frames for Reducing Subspaces of Sobolev Spaces

Zhang

2022

Journal of Function Spaces

View full text Add to dashboard Cite

In recent years, dual wavelet frames derived from a pair of refinable functions have been widely studied by many researchers. However, the requirement of the Bessel property of wavelet systems is always required, which is too technical and artificial. In present paper, we will relax this restriction and only require the integer translation of the wavelet functions (or refinable functions) to form Bessel sequences. For this purpose, we introduce the notion of weak dual wavelet frames. And for generality, we work under the setting of reducing subspaces of Sobolev spaces, we characterize a pair of weak dual wavelet frames, and by using this characterization, we obtain a mixed oblique extension principle for such weak dual wavelet frames.

show abstract

Refinable Function-Based Construction of Weak (Quasi-)Affine Bi-Frames

Cited by 18 publications

References 34 publications

Nonhomogeneous dual wavelet frames and mixed oblique extension principles in Sobolev spaces

Nonhomogeneous dual wavelet frames and mixed oblique extension principles in Sobolev spaces

Partial affine system–based frames and dual frames

A Class of Weak Dual Wavelet Frames for Reducing Subspaces of Sobolev Spaces

Contact Info

Product

Resources

About