This paper presents a new way to address the NP-hard combinatorial l2-l0 problem by minimizing a continuous relaxed functional preserving the minimizers of the initial energy. We propose the Continuous Exact l0 penalty (CEL0), an approximation of the l0 norm leading to a tight continuous relaxation of the l2-l0 criteria whose global minimizers contain those of the l0 penalized least-squares functional. Links between local minimizers of these two functionals are also investigated. This short communication summarizes the main results of our recent work [1].