Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximately dual pairs of wavelet frames   This paper deals with structural issues concerning wavelet frames and their
dual frames. It is known that there exist wavelet frames $\{a^{j/2}\psi(
a^j\cdot -kb)\}_{j,k\in \mathbb Z}$ in $L^2(\mathbb R)$ for which no dual frame
has wavelet structure. We first generalize this result by proving that there
exist wavelet frames for which no approximately dual frame has wavelet
structure. Motivated by this we show that by imposing a very mild decay
condition on the Fourier transform of the generator $\psi\in L^2(\mathbb R),$ a
certain oversampling $\{a^{j/2}\psi( a^j\cdot -kb/N)\}_{j,k\in \mathbb Z}$
indeed has an approximately dual wavelet frame; most importantly, by choosing
the parameter $N\in \mathbb N$ sufficiently large we can get as close to
perfect reconstruction as desired, which makes the approximate dual frame pairs
perform equally well as the classical dual frame pairs in applications.

20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin