Minimum Mean-Square Error Estimation of Mel-Frequency Cepstral Features–A Theoretically Consistent Approach

In this work, we consider the problem of feature enhancement for noise-robust automatic speech recognition (ASR). We propose a method for minimum mean-square error (MMSE) estimation of mel-frequency cepstral features, which is based on a minimum number of well-established, theoretically consistent statistical assumptions. More specifically, the method belongs to the class of methods relying on the statistical framework proposed in Ephraim and Malah's original work (“Speech enhancement using a minimum mean-square error short-time spectral amplitude estimator,” IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-32, no. 6, 1984). The method is general in that it allows MMSE estimation of mel-frequency cepstral coefficients (MFCC's), cepstral-mean subtracted (CMS-) MFCC's, autoregressive-moving-average (ARMA)-filtered CMS-MFCC's, velocity, and acceleration coefficients. In addition, the method is easily modified to take into account other compressive non-linearities than the logarithm traditionally used for MFCC computation. In terms of MFCC estimation performance, as measured by MFCC mean-square error, the proposed method shows performance which is identical to or better than other state-of-the-art methods. In terms of ASR performance, no statistical difference could be found between the proposed method and the state-of-the-art methods. We conclude that existing state-of-the-art MFCC feature enhancement algorithms within this class of algorithms, while theoretically suboptimal or based on theoretically inconsistent assumptions, perform close to optimally in the MMSE sense.