Background subtraction is a fundamental pre-processing task in computer vision. This task becomes challenging in real scenarios due to variations in the background for both static and moving camera sequences. Several deep learning methods for background subtraction have been proposed in the literature with competitive performances. However, these models show performance degradation when tested on unseen videos; and they require huge amount of data to avoid overfitting. Recently, graph-based algorithms have been successful approaching unsupervised and semi-supervised learning problems. Furthermore, the theory of graph signal processing and semi-supervised learning have been combined leading to new insights in the field of machine learning. In this paper, concepts of recovery of graph signals are introduced in the problem of background subtraction. We propose a new algorithm called Graph BackGround Subtraction (GraphBGS), which is composed of: instance segmentation, background initialization, graph construction, graph sampling, and a semi-supervised algorithm inspired from the theory of recovery of graph signals. Our algorithm has the advantage of requiring less data than deep learning methods while having competitive results on both: static and moving camera videos. GraphBGS outperforms unsupervised and supervised methods in several challenging conditions on the publicly available Change Detection (CDNet2014), and UCSD background subtraction databases.