In this paper, we propose a speech enhancement method based on spectral magnitude estimation. We modify the noise estimation from the minimum statistics method and combine with a maximum a posterior (MAP) decomposition, using the Rice-conditional probability and a non-Gaussian statistic model of the speech. We derive two versions of magnitude decomposition and magnitude-phase decomposition and compare to spectral subtraction and other MAP methods based on the Gaussian statistic (MMSE, LSA). The experiments show the advantage of the proposed method in the improvement of both SNR (up to 12 dB) and recognition accuracy rate (up to 21 % to base line).