Active-set newton algorithm for non-negative sparse coding of audio

We propose a new algorithm to efficiently obtain non-negative sparse representations for audio. The spectrum of an audio signal is represented as a sparse linear combination of atoms taken from an overcomplete dictionary. The algorithm is based on minimizing the generalized Kullback-Leibler divergence between an observed magnitude spectrum and a non-negative linear combination of atoms, plus an ℓ₁ regularization term. The proposed method consists of an active-set method that iteratively updates a set of active atoms that have non-zero weights, using a Newton step where the weights of the active atoms are updated. The proposed method was evaluated using mixtures of two speakers, and it was shown to yield more than 10 times faster convergence in comparison to an established algorithm based on multiplicative update rules. Moreover, the ℓ₁ regularization was found to decrease the computation time and to improve the source separation performance.