  Sparsity of representations of signals has been shown to be a key concept of
fundamental importance in fields such as blind source separation, compression,
sampling and signal analysis. The aim of this paper is to compare several
commonlyused sparsity measures based on intuitive attributes. Intuitively, a
sparse representation is one in which a small number of coefficients contain a
large proportion of the energy. In this paper six properties are discussed:
(Robin Hood, Scaling, Rising Tide, Cloning, Bill Gates and Babies), each of
which a sparsity measure should have. The main contributions of this paper are
the proofs and the associated summary table which classify commonly-used
sparsity measures based on whether or not they satisfy these six propositions
and the corresponding proofs. Only one of these measures satisfies all six: The
Gini Index. measures based on whether or not they satisfy these six
propositions and the corresponding proofs. Only one of these measures satisfies
all six: The Gini Index.
