$NP\mathrm{/}CLP$ Equivalence: A Phenomenon Hidden Among Sparsity Models for Information Processing

It is proved in this paper that to every underdetermined linear system $Ax=b$ there corresponds a constant $p(A,b)>0$ such that every solution to the $l_p$-norm minimization problem also solves the $l_0$-norm minimization problem whenever $0<p<p(A,b)$. This phenomenon is named $NP\mathrm{/}CLP$ equivalence.