Graph models provide flexible tools for the representation and analysis of signals defined over irregular domains such as social or sensor networks. However, in real applications data observations are often not available over the whole graph, due to practical problems such as sensor failure or connection loss. In this paper, we study the estimation of partially observed graph signals on multiple graphs. We learn a sparse representation of partially observed graph signals over spectrally concentrated graph dictionaries. Our dictionary model consists of several sub-dictionaries each of which is generated from a Gaussian kernel centered at a certain graph frequency in order to capture a particular spectral component of the graph signals at hand. The problem of jointly learning the spectral kernels and the sparse codes is solved with an alternating optimization approach. Finally, the incomplete entries of the given graph signals are estimated using the learnt dictionaries and the sparse coefficients. Experimental results on synthetic and real graph data sets suggest that the proposed method yields promising performance in comparison to reference solutions.