We consider a deconvolution problem with a random noise. The noise is a product of a Gaussian stationary random process by a weight function εh ∈ L₂(R¹) with constant ε > 0. We study the asymptotically minimax and Bayes settings (ε → 0). In the minimax model a priori information is given that the solution belongs to a ball in Sobolev space W₂^β(R¹). For such a priori information we find an asymptotically minimax estimator of the solution. In the Bayes setting the noise is the same. The solution is a realization of a random process defined as a product of a Gaussian stationary random process by a weight function h₁ ∈ L₂(R¹). We show that the standard Wiener filters remain asymptotically Bayes estimators for this modification of Wiener filtration. The introduction of weight functions h, h₁ ∈ L₂(R¹) is the main difference from the standard settings. This allows us not to make the traditional assumptions that the powers of noise and solutions are infinite or tend to infinity.