Noise Reduction Based Random Matrix Theory

In speech enhancement literature, the signal subspace based method gains a lot of attention because of its simplicity in analytical formulations. The original idea in this method is based on the assumption that clean speech signal occupies a certain low dimensional space, while the noise signal which is a white additive noise spread the whole observation space. In this method, accurate estimation of the noise power (or variance) is required. However, in real applications, the noise power can only be estimated with some degree of uncertainty. This uncertainty will degrade the signal subspace based speech enhancement algorithms, especially in heavy noisy situations since it does not take this uncertainty into consideration. In this study, we took the uncertainty of the estimation of noise power into consideration by using the statistical property of noise based on random matrix theory. The noise statistical property (eigenvalue distribution) was analytically formulated based on the maximum and minimum eigenvalues of the noise random matrix. Based on the statistical property of the eigenvalues of noise, we reduced the part contributed by noise from the covariance matrix of noisy speech. We tested our method for speech enhancement using AURORA-2J speech corpus. Our initial experiments showed that the proposed method performed better than the traditional signal subspace based speech enhancement method.