Sparse Regression with Structured Priors: Application to Audio Denoising

We describe in this paper a fully Bayesian approach for sparse audio signal regression in an union of two bases, with application to audio denoising. One basis aims at modeling tonal parts and the other at modeling transients. The noisy signal is decomposed as a linear combination of atoms from the two basis, plus a residual part containing the noise. Conditionally upon an indicator variable which is either 0 or 1, one source coefficient is set to zero or given a hierarchical prior. Various priors can be considered for the indicator variables. In addition to non-structured Bernoulli priors we study the performance of structured priors which favor horizontal time-frequency structures for tonals and vertical structures for transients. A Gibbs sampler is used to sample from the parameters of the model. We present results over denoising of a piano sequence using a MDCT basis with long time resolution to model the tonals and a MDCT with short time resolution to model the transients