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Techniques based on non-negative matrix factorization (NMF) can be used to efficiently decompose a magnitude spectrogram into a set of template (column) vectors and activation (row) vectors. To better control this decomposition, NMF has been extended using prior knowledge and parametric models. In this paper, we present such an extended approach that uses additional score information to guide the decomposition process. Here, opposed to previous methods, our main idea is to impose constraints on both the template as well as the activation side. We show that using such double constraints results in musically meaningful decompositions similar to parametric approaches, while being computationally less demanding and easier to implement. Furthermore, additional onset constraints can be incorporated in a straightforward manner without sacrificing robustness. We evaluate our approach in the context of separating note groups (e. g. the left or right hand) from monaural piano recordings.