Study On Subspace Based Speech Enhancement Algorithm With Low Computation Complexity

Since speech signal is inevitably degraded by ambient noise in voice communication systems,speech enhancement is the principal method to reduce and suppress the noise interference for the improvement of communication quality in speech systems,such as speech coding,speech recognition,and speech synthesis,etc.The objective of speech enhancement is to improve intelligibility and articulation of degraded speech signal by extracting original speech from noisy speech signal.As we know that speech enhancement algorithms can suppress or reduce noise interference,in the same time they also bring some distortion for original speech,which results in contradiction in the speech enhancement.Normally,we respect both better noise suppression and less speech distortion.Subspace speech enhancement algorithm has this kind of balance,so that it is our research basis to develop new algorithm.The basic idea of subspace method is that noisy speech signal space can be decomposed into two orthogonal subspaces,namely the signal subspace or the signal-plus-noise subspace,and the noise subspace.Clean speech signal is obtained by removing or nulling the components of the signal in the noise subspace and retaining the components of the speech signal in the signal subspace,such that the clean speech signal can be extracted as much as possible from the signal subspace.Unfortunately,the subspace method requires eigendecomposition of speech data matrix withO(K~3)computational complexity,where K is the frame length of the sampled speech data.In many practical environments,the speech data matrix is time varied,which needs us to solve the instantaneous eigendecomposition of the time-varying speech data matrix.Therefore,to develop adaptive subspace algorithm for speech enhancement in this case has become a focus of our research.Since the generalized subspace approach has large computation burden and is not practical or suitable to its real-time implementation.To reduce this heavy calculation burden and improve performance of the speech enhancement,a new subspace based speech enhancement algorithm with low computation complexity is proposed.This algorithm uses the subspace iteration method,widely used in engineering applications,which is effective to solve large generalized eigenvalue problem.By repeatedly using one-dimensional subspace iteration,all eigenvalues and corresponding eigenvectors of speech data matrix can be iteratively estimated in order to realize speech enhancement.From the derived algorithm we can see that the computational complexity of this speech enhancement algorithm by the derived iterative estimation for the eigenvectors and eigenvalues of speech data matrix reduced toO(K~2).When K is large,the superiority of the low complexity is obvious.In addition,the knowledge of the background noise is not required in the proposed algorithm,so that the proposed algorithm is suitable and effective for all type of noise,which is an optimal estimation algorithm.It is valid for both white and colored noise with better performance in several speech quality evaluation criteria.The low complexity provides more practical implementation in real speech applications.The increase of the frame length can improve the quality of speech enhancement in less number of iterative calculations but will add burden for the generalized speech enhancement algorithm compared.In low SNR,the proposed algorithm performs better and proves its superiority if we consider the balance between SNR and the choice of the frame length to obtain acceptable enhanced speech quality.The speech enhancement with projection approximate subspace tracking can be considered as the classical adaptive subspace speech enhancement algorithm based on several assumptions.In the case of non-stationary noise environment and low SNR,if we use this algorithm as the basis of speech enhancement,the enhancement performance is not satisfied and even unacceptable.In order to overcome the above mentioned shortcomings,a new subspace based speech enhancement algorithm with adaptive discrete cosine transform(DCT)in stead of using Karhunen-Loève transform(KLT)for the estimation of eigenvalues and eigenvectors of noisy speech covariance matrix is proposed.We introduce adaptive DCT in our proposed speech enhancement algorithm to approximate KLT in the estimation for eigenvalues and eigenvectors of noisy speech covariance matrix to realize enhanced speech quality improvement in different respects.From the derived algorithm we can see that the calculation complexity for the estimation of the eigenvalues and the eigenvectors of noisy speech covariance matrix is O(K).Thus the derived adaptive subspace based speech enhancement algorithm is easy to be implemented in real applications.In addition,the proposed algorithm does not make assumptions on the noise stochastic characteristics.Since the proposed algorithm does not rely on the eigendecomposition,it has fast convergence speed and high estimation precision.The simulation results show that this algorithm achieves a better speech enhancement in recursive form under different noise environment and input SNR with lower speech distortion than the classical KLT based algorithm.Especially,for the case of non-stationary noise environment and low SNR,the superiority of the proposed algorithm is more obvious.Maximum likelihood adaptive subspace estimation(MALASE)is a new method to deal with fast adaptive eigendecomposition problem,which is a random algorithm to realize subspace tracking through the maximum likelihood criterion.The tracking results are adaptive or iterative tracking of eigenvalues and eigenvectors of data covariance matrix to realize instantaneous eigendecomposition withO(K~2)computational complexity.Since MALASE algorithm uses a similar Givens rotation,it ensures the orthogonality of the estimated eigenvectors after iteration,which is a very significant advantage of the algorithm.A new subspace speech enhancement algorithm using MALASE with noise eigenvalue estimation is proposed without eigendecomposition and voice activity detection.According to MALASE algorithm,we can obtain the eigenvalues and the eigenvectors of noisy speech covariance matrix,the noise eigenvalue estimation with speech presence probability in subspace domain can be calculated by recursive smoothing.The proposed algorithm can be used for different kinds of noise environment compared with the classical algorithm and MCRA algorithm,and has the advantages of high estimation precision,easy implementation,low voice distortion,small residual noise and good overall quality.It is also suitable for the application of low SNR and non-stationary noise environment.