A novel image denoising algorithm has been proposed for quantum noise reduction in digital mammography. The method uses the Anscombe transformation to stabilize noise variance and convert the signal-dependent Poisson noise into an approximately signal-independent Gaussian additive noise. In the Anscombe domain, noise is removed through an adaptive Wiener filter, whose parameters are obtained considering local image statistics. Thus, the method does not require any a priori knowledge about the original signal, because all the necessary parameters are estimated directly from the noisy image. The method was applied on synthetic mammograms generated based upon an anthropomorphic software breast phantom with different levels of simulated quantum noise. The evaluation of the proposed method was performed by calculating the peak signal-to-noise ratio (PSNR) and the mean structural similarity index (MSSIM) before and after denoising. Results show that the proposed algorithm improves image quality by reducing image noise without significantly affecting image sharpness.