  In this paper, we consider the exact continuous relaxation model of $l_0$
regularization problem which was given by Bian and Chen (SIAM J. Numer. Anal
58(1): 858-883, 2020) and propose a smoothing proximal gradient algorithm with
extrapolation (SPGE) for this kind of problem. We show that any accumulation
point of the sequence generated by SPGE algorithm is a lifted stationary point
of the relaxation model for a fairly general choice of extrapolation parameter.
Moreover, it is shown that the whole sequence generated by SPGE algorithm
converges to a lifted stationary point of the relaxation model. The convergence
rate of $o(\frac{1}{k^{1-\sigma}})(\sigma\in(0,1))$ with respect to squared
proximal residual is established. Finally, we conduct three important numerical
experiments to illustrate the faster efficiency of the SPGE algorithm compared
with the smoothing proximal gradient(SPG) algorithm proposed by Bian and Chen
(SIAM J. Numer. Anal 58(1):858-883, 2020).
