Persistent Time-Frequency Shrinkage for Audio Denoising

Natural audio signals are known to be highly structured. Incorporating knowledge about this inherent structure helps to improve audio restoration algorithms. In this article audio denoising is addressed as a problem of structured sparse atomic decomposition. A class of time-frequency shrinkage operators is introduced that generalizes some well-known thresholding operators such as the empirical Wiener filter and basis pursuit denoising. The general framework allows for the exploitation of structural properties, in particular the persistence inherent to most natural audio signals. Fast iterative shrinkage algorithms are reviewed and their convergence is numerically evaluated. The denoising performance of the proposed persistent shrinkage operators is evaluated on real-life audio signals. The novel approach shows competitive performance to the state of the art when evaluated by means of signal to noise ratio and appears to have beneficial perceptual properties.