Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: RIPless compressed sensing from anisotropic measurements   Compressed sensing is the art of reconstructing a sparse vector from its
inner products with respect to a small set of randomly chosen measurement
vectors. It is usually assumed that the ensemble of measurement vectors is in
isotropic position in the sense that the associated covariance matrix is
proportional to the identity matrix. In this paper, we establish bounds on the
number of required measurements in the anisotropic case, where the ensemble of
measurement vectors possesses a non-trivial covariance matrix. Essentially, we
find that the required sampling rate grows proportionally to the condition
number of the covariance matrix. In contrast to other recent contributions to
this problem, our arguments do not rely on any restricted isometry properties
(RIP's), but rather on ideas from convex geometry which have been
systematically studied in the theory of low-rank matrix recovery. This allows
for a simple argument and slightly improved bounds, but may lead to a worse
dependency on noise (which we do not consider in the present paper).

8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an