Clouds, together with their shadows, usually occlude ground-cover features in optical remote sensing images. This hinders the utilization of these images for a range of applications such as earth observation, land-cover classification and urban planning. In this work, we propose a deep unfolded and prior-aided robust principal component analysis (DUPA-RPCA) network for removing clouds and recovering ground-cover information in multi-temporal satellite images. We model these cloud-contaminated images as a sum of low rank and sparse elements and then unfold an iterative RPCA algorithm that has been designed for reweighted
minimization. As a result, the activation function in DUPA-RPCA adapts for every input at each layer of the network. Our experimental results on both Landsat and Sentinel images indicate that our method gives better accuracy and efficiency when compared with existing state of the art methods.