For array-based acoustic source enhancement, variants of multi-channel Wiener filters are commonly used. The approach includes a Wiener post-filter that requires the simultaneous estimation of the power spectral density (PSD) of the target source and of noise sources for each time-frame. Conventional methods generally do not exploit prior knowledge , such as sparsity of the source, in solving this simultaneous estimation problem. We show that, for common scenarios, the simultaneous PSD estimation with consideration of prior knowledge can be formulated as a convex optimization problem with linear constraints. We use monotone operator splitting (MOS) to solve the constrained optimization problem. Our experiments confirm that the proposed method improves the accuracy of the noise PSD estimation, and that the resulting enhanced target signal is of higher quality.