Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform recovery in infinite-dimensional compressed sensing and
  applications to structured binary sampling   Infinite-dimensional compressed sensing deals with the recovery of analog
signals (functions) from linear measurements, often in the form of integral
transforms such as the Fourier transform. This framework is well-suited to many
real-world inverse problems, which are typically modelled in
infinite-dimensional spaces, and where the application of finite-dimensional
approaches can lead to noticeable artefacts. Another typical feature of such
problems is that the signals are not only sparse in some dictionary, but
possess a so-called local sparsity in levels structure. Consequently, the
sampling scheme should be designed so as to exploit this additional structure.
In this paper, we introduce a series of uniform recovery guarantees for
infinite-dimensional compressed sensing based on sparsity in levels and
so-called multilevel random subsampling. By using a weighted
$\ell^1$-regularizer we derive measurement conditions that are sharp up to log
factors, in the sense they agree with those of certain oracle estimators. These
guarantees also apply in finite dimensions, and improve existing results for
unweighted $\ell^1$-regularization. To illustrate our results, we consider the
problem of binary sampling with the Walsh transform using orthogonal wavelets.
Binary sampling is an important mechanism for certain imaging modalities.
Through carefully estimating the local coherence between the Walsh and wavelet
bases, we derive the first known recovery guarantees for this problem.

28
The categories of this paper are: alg-geom
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
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th