We consider the estimation of an unknown regression function from a nonparametric regression model having the feature to have multiplicative noise and additive noise. We focus our attention on wavelet methods ; we develop a linear wavelet estimator and a nonlinear wavelet estimator based on a thresholding of the wavelet coefficients estimators. We prove that they attains fast rates of convergence under the mean integrated square error over Besov spaces. The obtained rates are fast and are obtained under some weak conditions on the model. A numerical study supports the theory.