The goal of this paper is to estimate a denoised phase image from the observed noisy SAR interferogram. We proposed a linear model to obtain a sparse representation of the interferomteric phase image. The main idea is based on the smoothness property of the phases inside interferometric fringes which leads to get a sparse image when applying the gradient operator twice, along x or y direction, on the interferogram. The new sparse representation of the interferometric phase image allows to transform the denoising problem to an optimization one. So the estimated interferogram is achieved using the approximate message passing algorithm. The proposed approach is validated on different cases of simulated and real interferograms.