Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A null space analysis of the L1 synthesis method in dictionary-based
  compressed sensing   An interesting topic in compressed sensing aims to recover signals with
sparse representations in a dictionary. Recently the performance of the
L1-analysis method has been a focus, while some fundamental problems for the
L1-synthesis method are still unsolved. For example, what are the conditions
for it to stably recover compressible signals under noise? Whether coherent
dictionaries allow the existence of sensing matrices that guarantee good
performances of the L1-synthesis method? To answer these questions, we build up
a framework for the L1-synthesis method. In particular, we propose a
dictionary-based null space property DNSP which, to the best of our knowledge,
is the first sufficient and necessary condition for the success of L1-synthesis
without measurement noise. With this new property, we show that when the
dictionary D is full spark, it cannot be too coherent otherwise the method
fails for all sensing matrices. We also prove that in the real case, DNSP is
equivalent to the stability of L1-synthesis under noise.

8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org