Traditional mammography can be positively complemented by phase contrast and scattering x-ray imaging, because they can detect subtle differences in the electron density of a material and measure the local small-angle scattering power generated by the microscopic density fluctuations in the specimen, respectively. The grating-based x-ray interferometry technique can produce absorption, differential phase contrast (DPC) and scattering signals of the sample, in parallel, and works well with conventional X-ray sources; thus, it constitutes a promising method for more reliable breast cancer screening and diagnosis. Recently, our team proved that this novel technology can provide images superior to conventional mammography. This new technology was used to image whole native breast samples directly after mastectomy. The images acquired show high potential, but the noise level associated to the DPC and scattering signals is significant, so it is necessary to remove it in order to improve image quality and visualization. The noise models of the three signals have been investigated and the noise variance can be computed. In this work, a wavelet-based denoising algorithm using these noise models is proposed. It was evaluated with both simulated and experimental mammography data. The outcomes demonstrated that our method offers a good denoising quality, while simultaneously preserving the edges and important structural features. Therefore, it can help improve diagnosis and implement further post-processing techniques such as fusion of the three signals acquired.