• In this paper, a new probabilistic method for image enhancement is presented based on a simultaneous estimation of illumination and reflectance in the linear domain. • We show that the linear domain model can better represent prior information for better estimation of reflectance and illumination than the logarithmic domain. • A maximum a posteriori (MAP) formulation is employed with priors of both illumination and reflectance. • To estimate illumination and reflectance effectively, an alternating direction method of multipliers is adopted to solve the MAP problem. • The experimental results show the satisfactory performance of the proposed method to obtain reflectance and illumination with visually pleasing enhanced results and a promising convergence rate. • Compared with other testing methods, the proposed method yields comparable or better results on both subjective and objective assessments.