A Multichannel Audio Denoising Formulation Based on Spectral Sparsity

We consider the estimation of an audio source from multiple noisy observations, where the correlation between noise in the different observations is low. We propose a two-stage method for this estimation problem. The method does not require any information about noise and assumes that the signal of interest has a sparse time-frequency representation. The first stage uses this assumption to obtain the best linear combination of the observations. The second stage estimates the amount of remaining noise and applies a post-filter to further enhance the reconstruction. We discuss the optimality of this method under a specific model and demonstrate its usefulness on synthetic and real data.