Cepstrum Domain Laplace Denoising

This paper introduces the Laplace algorithm for de-noising in the cepstrum domain with applications to speech recognition. Our method uses Gaussian mixture priors for clean speech and noise cepstra and assumes that speech and noise mix linearly in the spectrum domain. The Laplace algorithm involves two steps (a) computing the posterior mode of the observed noisy cepstra and (b) Gaussian approximation of the posterior around the mode. We show that the Algonquin algorithm is a special case of our approach where a Newton method is used for (a). Interestingly, this observation also proves that the Algonquin algorithm does not converge in general. We propose the use of the BFGS method for (a) which also allows us to efficiently apply the Laplace algorithm in the cepstral domain. De-noising in the cepstral domain gives more than 31% relative reduction in word error rate on average on the Aurora 2 task.