A smooth exact approximation of functional L2-L0 (least squares functional with sparse penalizing term using a L0 norm) is presented. This functional, named CEL0 for Continuous Exact L0 approximation is said exact as it preserves global minimizers and remove some of the local minimizers of the L2-L0 functional. More general results on smooth approximation of the L2-L0 functional are also given, describing a class of continuous functions with the properties of preservation of minimizers as described above. Simulation results are presented.