A Dereverberation Formulation Based on Sparsity

Abstract

Considering we have the knowledge of the room impulse response, we aim to estimate the original signal from reverbed observations. We make us of a sparsity constrained minimization problem for dereverberation, using Short Time Fourier Transform of signals are sparse. We solve the problem in STFT domain in order to decreases the computational time. Our experiments show that using this method (bypassing transformations) is highly beneficial [.pdf in TR]

Experiments

1st Example

We synthetically produce a reverbed signal and aim to estimate the original form from this observation.

Observation is modified to have signal to noise ratio (SNR) '30'. Noise is added after reverb effects. However because of the low quality of the original signal we have defects in the estimate.

Spectrograms for observation and estimate are given below respectively.

2nd Example

Similar to the first example, we now use a better quality speech signal and add reverb synthetically and trying to estimate the original form.

Observation has a defect. The reverb is seemed to end unnatural. This is because RIR (samples close to 0) is cropped in order to reduce the computational time. Estimate clearly shows that the original speech is obtained.

3rd Example

In addition to speech signals we test the method on a musical instrument. Synthetically adding reverb to a viola signal and trying to estimate the original form.

It is clear that observation has reverb. It is also clear that the metgod managed to produce an estimate which is reverb free.