Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mathematics of Sparsity and Entropy: Axioms, Core Functions and Sparse
  Recovery   Sparsity and entropy are pillar notions of modern theories in signal
processing and information theory. However, there is no clear consensus among
scientists on the characterization of these notions. Previous efforts have
contributed to understand individually sparsity or entropy from specific
research interests. This paper proposes a mathematical formalism, a joint
axiomatic characterization, which contributes to comprehend (the beauty of)
sparsity and entropy. The paper gathers and introduces inherent and first
principles criteria as axioms and attributes that jointly characterize sparsity
and entropy. The proposed set of axioms is constructive and allows to derive
simple or \emph{core functions} and further generalizations. Core sparsity
generalizes the Hoyer measure, Gini index and $pq$-means. Core entropy
generalizes the R\'{e}nyi entropy and Tsallis entropy, both of which generalize
Shannon entropy. Finally, core functions are successfully applied to compressed
sensing and to minimum entropy given sample moments. More importantly, the
(simplest) core sparsity adds theoretical support to the $\ell_1$-minimization
approach in compressed sensing.

25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat