Simple alternatives to the Ephraim and Malah suppression rule for speech enhancement

Short-time spectral attenuation is a common form of audio signal enhancement in which a time-varying filter, or suppression rule, is applied to the frequency-domain transform of a corrupted signal. The suppression rule (see Ephraim, Y. and Malah, D., IEEE Trans. on Acoustics, Speech and Signal Proc., vol.ASSP-32, no.6, p.1109-21, 1984) for speech enhancement is both optimal in the minimum mean-square error sense and well-known for its associated colourless residual noise; however, it requires the computation of exponential and Bessel functions. We show that, under the same modelling assumptions, alternative Bayesian approaches lead to suppression rules exhibiting almost identical behaviour. We derive three such rules and show that they are efficient to implement and yield a more intuitive interpretation.