Fast Implementation of KLT-Based Speech Enhancement Using Vector Quantization

We propose a new method for implementing Karhunen–Loeve transform (KLT)-based speech enhancement to exploit vector quantization (VQ). The method is suitable for real-time processing. The proposed method consists of a VQ learning stage and a filtering stage. In the VQ learning stage, the autocorrelation vectors comprising the first
$K$
elements of the autocorrelation function are extracted from learning data. The autocorrelation vectors are used as codewords in the VQ codebook. Next, the KLT bases that correspond to all the codeword vectors are estimated through eigendecomposition (ED) of the empirical Toeplitz covariance matrices constructed from the codeword vectors. In the filtering stage, the autocorrelation vectors that are estimated from the input signal are compared to the codewords. The nearest one is chosen in each frame. The precomputed KLT bases corresponding to the chosen codeword are used for filtering instead of performing ED, which is computationally intensive. Speech quality evaluation using objective measures shows that the proposed method is comparable to a conventional KLT-based method that performs ED in the filtering process. Results of subjective tests also support this result. In addition, processing time is reduced to about 1/66 that of the conventional method in the case where a frame length of 120 points is used. This complexity reduction is attained after the computational cost in the learning stage and a corresponding increase in the associated memory requirement. Nevertheless, these results demonstrate that the proposed method reduces computational complexity while maintaining the speech quality of the KLT-based speech enhancement.