In this article we propose an extension of non-negative matrix factorization (NMF) based on a source/filter underlying model which permits to well decompose audio signals which contain redundant sounds with strong spectral variations. Our algorithm permits notably to use only one atom per musical event (such as a note) for such non-stationary sounds whereas NMF needs several atoms to represent a non-stationary sound. We have tested our algorithm on real audio data and shown how the proposed decomposition provides a smarter representation of audio spectrograms than standard NMF.