In this paper, we address the problem of estimating sparse communication channels in OFDM systems. We consider the case where carrier frequency offset is present. The problem of estimation is then approached by maximizing a regularized (modified) likelihood function. This regularized likelihood function includes a new term accounting for the a priori probability density function for the parameters, represented by a Gaussian mean-variance mixture. The maximization of the regularized likelihood function is carried out by using the Expectation-Maximization (EM) algorithm. We show that the E-step in the proposed algorithm has a closed-form solution, and in the M-step, the cost function is concentrated in one variable (carrier frequency offset).