Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An asymptotic existence result on compressed sensing matrices   For any rational number $h$ and all sufficiently large $n$ we give a
deterministic construction for an $n\times \lfloor hn\rfloor$ compressed
sensing matrix with $(\ell_1,t)$-recoverability where $t=O(\sqrt{n})$. Our
method uses pairwise balanced designs and complex Hadamard matrices in the
construction of $\epsilon$-equiangular frames, which we introduce as a
generalisation of equiangular tight frames. The method is general and produces
good compressed sensing matrices from any appropriately chosen pairwise
balanced design. The $(\ell_1,t)$-recoverability performance is specified as a
simple function of the parameters of the design. To obtain our asymptotic
existence result we prove new results on the existence of pairwise balanced
designs in which the numbers of blocks of each size are specified.

32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc