On the EM algorithm for the estimation of speech AR parameters in noise

In this paper, the estimation of speech AR parameters under noisy conditions is revisited. The EM algorithm serving this purpose was first proposed by Gannot et al. We present an extensive experimental study along with a new approach to implement the E-step of the algorithm. The new realization of the E-step uses matrix computations instead of a Kalman filter. By appropriate rearrangement of the E-step, the complexity O(P(p +q)³)of the Kalman filter approach has been reduced to O(P log P), where P is the frame length, p is the speech order and q is the noise order. In practice, a speed up of the E-step of at least two orders of magnitude has been achieved. An extensive evaluation of the algorithm shows that EM algorithm in its base form is unable to improve over a recent speech enhancement method proposed by Heusdens et al. and over an established Spectral Subtraction with Minimum Statistics method, as measured by various quality measures. However, with some modification it was possible to improve over these methods in terms of spectral distortion.