Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compressed Sensing with coherent tight frames via $l_q$-minimization for
  $0<q\leq1$   Our aim of this article is to reconstruct a signal from undersampled data in
the situation that the signal is sparse in terms of a tight frame. We present a
condition, which is independent of the coherence of the tight frame, to
guarantee accurate recovery of signals which are sparse in the tight frame,
from undersampled data with minimal $l_1$-norm of transform coefficients. This
improves the result in [1]. Also, the $l_q$-minimization $(0<q<1)$ approaches
are introduced. We show that under a suitable condition, there exists a value
$q_0\in(0,1]$ such that for any $q\in(0,q_0)$, each solution of the
$l_q$-minimization is approximately well to the true signal. In particular,
when the tight frame is an identity matrix or an orthonormal basis, all results
obtained in this paper appeared in [13] and [26].

14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci