Existing denoising algorithms based on a simplified signal-dependent noise model are valid under the assumption of the predefined parameters. Consequently, these methods fail if the predefined conditions are not satisfied. An adaptive method for eliminating random noise from the simplified signal-dependent noise model is presented in this paper. A linear mapping function between multiplicative noise and noiseless image data is established using the Maclaurin formula. Through demonstrations of the cross-correlation between random variables and independent random variable functions, the mapping function between the variances of multiplicative noise and noiseless image data is acquired. Accordingly, the adaptive denoising model of simplified signal-dependent noise in the wavelet domain is built. The experimental results confirm that the proposed method outperforms conventional ones.