Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On asymptotic structure in compressed sensing   This paper demonstrates how new principles of compressed sensing, namely
asymptotic incoherence, asymptotic sparsity and multilevel sampling, can be
utilised to better understand underlying phenomena in practical compressed
sensing and improve results in real-world applications. The contribution of the
paper is fourfold:
  First, it explains how the sampling strategy depends not only on the signal
sparsity but also on its structure, and shows how to design effective sampling
strategies utilising this.
  Second, it demonstrates that the optimal sampling strategy and the efficiency
of compressed sensing also depends on the resolution of the problem, and shows
how this phenomenon markedly affects compressed sensing results and how to
exploit it.
  Third, as the new framework also fits analog (infinite dimensional) models
that govern many inverse problems in practice, the paper describes how it can
be used to yield substantial improvements.
  Fourth, by using multilevel sampling, which exploits the structure of the
signal, the paper explains how one can outperform random Gaussian/Bernoulli
sampling even when the classical $l^1$ recovery algorithm is replaced by
modified algorithms which aim to exploit structure such as model based or
Bayesian compressed sensing or approximate message passaging. This final
observation raises the question whether universality is desirable even when
such matrices are applicable.
  Examples of practical applications investigated in this paper include
Magnetic Resonance Imaging (MRI), Electron Microscopy (EM), Compressive Imaging
(CI) and Fluorescence Microscopy (FM). For the latter, a new compressed sensing
approach is also presented.

35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th