$NP/CMP$ Equivalence: A Phenomenon Hidden Among Sparsity Models $l_{0}$ Minimization and $l_{p}$ Minimization for Information Processing

In this paper, we have proved that in 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 l0-norm minimization problem whenever 0 <; p <; p*(A, b). This phenomenon is named NP/CMP equivalence.