NP-hardness of $\ell$0 minimization problems: revision and extension to the non-negative setting
Résumé
Sparse approximation arises in many applications and often leads to a constrained or penalized l0 minimization problem, which was proved to be NP-hard. This paper proposes a revision of existing analyses of NP-hardness of the penalized l0 problem and it introduces a new proof adapted from Natarajan's construction (1995). Moreover, we prove that l0 minimization problems with non-negativity constraints are also NP-hard.
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