New characterizations of wavelet frames inL2(R)
نویسندگان
چکیده
منابع مشابه
Density of Wavelet Frames
Density conditions for wavelet systems with arbitrary sampling points to be frames are studied. We show that for a wavelet system generated by admissible functions and irregular affine lattices to be a frame, the sampling points must have a positive lower Beurling density. The same is true for wavelet systems with arbitrary sampling points and nice generating functions.
متن کاملOn Characterizations of Fourier Frames and Tilings
for all f ∈ H.A and B are called frame bounds.The sequence is called a tight frame if A = B. The sequence is called Bessel if the second inequality above holds. In this case, B is called the Bessel bound. Frames were first introduced by Duffin and Schaeffer [1] in the context of nonharmonic Fourier series, and today they have applications in a wide range of areas. A frame can be considered as a...
متن کاملLearning Steerable Wavelet Frames
We present a functional framework for the adaptive design of dictionaries where the invariance to translation, dilation, and rotation is built upfront into the primary representation space. Our key idea is to build an invariant signal representation prior to the learning stage. By doing so, we focus our effort on adapting the dictionary to the distinctive features of the signal, rather than to ...
متن کاملWavelet-type frames and wavelet-type bases
The concepts of basis and frame are studied in the classical literature of functional analysis, Fourier analysis, and wavelet theory in a wide range. In this paper, we consider an operator-theoretic approach to discrete frame theory on a separable Hilbert space. For this purpose, we define a special type of frames and bases, called wavelet-type frames and wavelet-type bases, obtained by acting ...
متن کاملHilbert Pairs of Wavelet Frames
Recently, research on two distinct types of wavelet frames have emerged, each with its own characteristics. The dual-tree discrete wavelet transform (DWT) [1] is based on the concatenation of two wavelet bases, where the two wavelets are designed to form a Hilbert transform pair, Ãg(t) = HfÃh(t)g [4]. A second type of wavelet frame is based on a single scaling function and two distinct wavelets...
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 Analysis and Applications
سال: 2013
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2012.11.010