Given the raw absorption and differential phase-contrast images obtained from a grating-based x-ray radiography, we formulate the joint denoising of the absorption image and retrieval of the non-differential phase image as a regularized inverse problem. The choice of the regularizer is driven by the existing correlation between absorption and differential phase; it leads to the linear combination of a total-variation norm with a total-variation nuclear norm. We then develop the corresponding algorithm to efficiently solve this inverse problem. We evaluate our method using different experiments, including mammography data. We conclude that our method provides useful information in the context of mammography screening and diagnosis.