Sparse Linear Regression With Structured Priors and Application to Denoising of Musical Audio

Abstract--We describe in this paper an audio denoising technique based on sparse linear regression with structured priors. The noisy signal is decomposed as a linear combination of atoms belonging to two modified discrete cosine transform (MDCT) bases, plus a residual part containing the noise. One MDCT basis has a long time resolution, and thus high frequency resolution, and is aimed at modeling tonal parts of the signal, while the other MDCT basis has short time resolution and is aimed at modeling transient parts (such as attacks of notes). The problem is formulated within a Bayesian setting. Conditional upon an indicator variable which is either 0 or 1, one expansion coefficient is set to zero or given a hierarchical prior. Structured priors are employed for the indicator variables; using two types of Markov chains, persistency along the time axis is favored for expansion coefficients of the tonal layer, while persistency along the frequency axis is favored for the expansion coeffic...

• Type: Journal
• Year: 2008
• Where: TASLP
• Authors: Cédric Févotte, Bruno Torrésani, Laurent Daudet, Simon J. Godsill
• Keywords: Expansion Coefficients, MDCT Basis, TASLP 2008, Time Resolution