Unitary Extension Principle for Nonuniform Wavelet Frames in L2(?)
نویسندگان
چکیده
We study the construction of nonuniform tight wavelet frames for Lebesgue space $L^2(\mathbb{R})$, where related translation set is not necessary a group. The main purpose this paper to prove unitary extension principle (UEP) and oblique (OEP) multi-generated $L^2(\mathbb{R})$. Some examples are also given illustrate results.
منابع مشابه
Irregular wavelet frames on L2(R)
If the wavelet system {aψ(a ·−bk)}j,k∈Z forms a frame onL(R) for some a > 1 and b > 0, then it is called a (regular) wavelet frame. In this case we can reconstruct any f from the sampled values (Wψf)(a , abk). In practice the sampling points may be irregular. We need to know for which wavelet ψ and parameters {(sj , bk)}j,k , the wavelet system {s j ψ(sj · −bk)}j,k∈Z forms a frame on L (R). In ...
متن کاملA Local Construction for Nonuniform Spline Tight Wavelet Frames
We present a construction for tight wavelet frames for nonuniform spline type spaces. Our basic requirement is that the twoscale matrices are row stochastic as this admits the local construction of a set of framelets for each scaling function. The framelets have one vanishing moment, small support, and can be designed to have symmetry properties. We apply our method to univariate splines and to...
متن کاملDual Gramian analysis: Duality principle and unitary extension principle
Abstract. Dual Gramian analysis is one of the fundamental tools developed in a series of papers [37, 40, 38, 39, 42] for studying frames. Using dual Gramian analysis, the frame operator can be represented as a family of matrices composed of the Fourier transforms of the generators of (generalized) shiftinvariant systems, which allows us to characterize most properties of frames and tight frames...
متن کاملExtension Principles for Tight Wavelet Frames of Periodic Functions
A unitary extension principle for constructing normalized tight wavelet frames of periodic functions of one or higher dimensions is established. While the wavelets are nonstationary, the method much simplifies their construction by reducing it to a matrix extension problem that involves finite rows of complex numbers. Further flexibility is achieved by reformulating the result as an oblique ext...
متن کاملOn B-Spline Framelets Derived from the Unitary Extension Principle
Spline wavelet tight frames of [20] have been used widely in frame based image analysis and restorations (see, e.g. survey articles [15, 22]). However, except for the tight frame property and the approximation order of the truncated series (see [13,20]), there are few other properties of this family of spline wavelet tight frames to be known. This paper is to present a few new properties of thi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics Analysis Geometry
سال: 2021
ISSN: ['1812-9471', '1817-5805']
DOI: https://doi.org/10.15407/mag17.01.079