Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Aspects of 2D-Adaptive Fourier Decompositions   As a new type of series expansion, the so-called one-dimensional adaptive
Fourier decomposition (AFD) and its variations (1D-AFDs) have effective
applications in signal analysis and system identification. The 1D-AFDs have
considerable influence to the rational approximation of one complex variable
and phase retrieving problems, etc. In a recent paper, Qian developed 2D-AFDs
for treating square images as the essential boundary of the 2-torus embedded
into the space of two complex variables. This paper studies the numerical
aspects of multi-dimensional AFDs, and in particular 2D-AFDs, which mainly
include (i) Numerical algorithms of several types of 2D-AFDs in relation to
image representation; (ii) Perform experiments for the algorithms with
comparisons between 5 types of image reconstruction methods in the Fourier
category; and (iii) New and sharper estimations for convergence rates of
orthogonal greedy algorithm and pre-orthogonal greedy algorithm. The comparison
shows that the 2D-AFD methods achieve optimal results among the others.

12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga