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Audio Denoising by Time-Frequency Block Thresholding

 

Summary:

Removing noise from audio signals requires a non-diagonal processing of time-frequency coefficients to avoid producing ``musical noise''. State of the art algorithms perform a parameterized filtering of spectrogram coefficients with empirically fixed parameters. A block thresholding estimation procedure is introduced, which adjusts all parameters adaptively to signal property by minimizing a Stein estimation of the risk. Numerical experiments demonstrate the performance and robustness of this procedure through objective and subjective evaluations.

 

What is "musical noise"?

Musical noise is an artifact that can be often heard in audio signals after denoising. Sounded like random musical notes, it has different nature to original sound and is thus easily perceived. Hear an example.

 

Where comes from "musical noise"?

Lack of time-frequency regularity, diagonal denoising algorithms such power subtraction create some isolated time-frequency coefficients that restore time-frequency structures perceived as musical noise. Hear an example.

 

 

 

How does block thresholding eliminate "musical noise"? 

Time-frequency coefficients are grouped in blocks before being attenuated. Block thresholding regularizes the estimate and does not create isolated coefficients responsible for musical noise. Hear an example.

More examples:

Three audio denoising methods are compared:

  1. Power subtraction (PS) (Berouti et al. 1979)

  2. Ephraim and Malah log-spectrogram amplitude (LSA) suppression rule combined by Cohen's non-causal a priori SNR estimator (LSA-NC) (Cohen 2004, Ephraim and Malan 1985)

  3. Block thresholding (BT) (Yu et al. 2007)

Software:

Download Matlab code.  Unzip the package and see readme for details.

 

 

For more information:

.G. Yu, S. Mallat, E. Bacry, Audio Denoising by Time-Frequency Block Thresholding, IEEE Trans. on Signal Processing, vol 56, no. 5, pp. 1830-1839, May 2008.