The paper advocates a statistical approach to image denoising based on a maximum a posteriori (MAP) estimation in the wavelet domain. In this framework, a new class of independent identically distributed stochastic image priors is considered to obtain a simple and tractable solution in a closed analytical form. The proposed prior model is considered in the form of a student distribution. The experimental results demonstrate the high fidelity of this model for approximation of the sub-band distributions of wavelet coefficients. The obtained solution is presented in the form of well-studied shrinkage functions