  Traditional NMF-based signal decomposition relies on the factorization of
spectral data, which is typically computed by means of short-time frequency
transform. In this paper we propose to relax the choice of a pre-fixed
transform and learn a short-time orthogonal transform together with the
factorization. To this end, we formulate a regularized optimization problem
reminiscent of conventional NMF, yet with the transform as additional unknown
parameters, and design a novel block-descent algorithm enabling to find
stationary points of this objective function. The proposed joint transform
learning and factorization approach is tested for two audio signal processing
experiments, illustrating its conceptual and practical benefits.
