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Kalman Filter with Sensitivity Tuning for Improved Noise Reduction in Speech

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Abstract

In this paper, we will present a Kalman filtering algorithm that achieves better noise reduction in a single-channel speech enhancement application. The proposed method aims to tune the Kalman filter gain in order to offset the bias that is inherent when estimating speech parameters from noise-corrupted speech. After analysing the Kalman recursion equations and the filter gain, the sensitivity metric was shown to be useful in tuning the Kalman filter to achieve better noise reduction. Speech enhancement experiments were performed on the commonly available NOIZEUS database corrupted with white Gaussian noise, and the proposed method was evaluated and compared with recent speech enhancement methods, such as the STSA estimator with wavelet thresholding on multi-tapered spectra (or STSA-WT) and generalised subspace method. The proposed method was shown to produce better quality speech than the STSA-WT estimator, while being competitive with the generalised subspace method. Spectrogram analysis demonstrated that the proposed method could achieve similar levels of noise reduction to the Kalman filter in the oracle case.

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Notes

  1. The MATLAB code and sample speech output files are available and can be downloaded at http://tiny.cc/speech_enhancement.

  2. Note that we will use the ‘negative sign’ convention, as is commonly used in linear prediction analysis [3].

  3. We used bold variables to denote matrix/vector quantities, as opposed to unbolded variables for scalar quantities.

  4. In this study, we are assuming the effects of the white noise on the estimates of \(a_k\) are negligible, in comparison with the variance of the measurement noise \(\sigma _v^2\), i.e. \(\tilde{a}_k\approx a_k\).

  5. The MATLAB code and sample speech output files are available and can be downloaded at http://tiny.cc/speech_enhancement.

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Acknowledgments

We would like to thank the anonymous reviewers of this manuscript. Their feedback was extremely helpful in improving the clarity and quality of the manuscript.

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Authors and Affiliations

  1. Signal Processing Laboratory, Griffith School of Engineering, Griffith University, Brisbane, QLD, 4111, Australia

    Stephen So, Aidan E. W. George & Kuldip K. Paliwal

  2. Department of Instrumentation and Electronics Engineering, Jadavpur University, Kolkata, 700084, India

    Ratna Ghosh

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  1. Stephen So
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  2. Aidan E. W. George
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  3. Ratna Ghosh
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  4. Kuldip K. Paliwal
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Correspondence to Stephen So.

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So, S., George, A.E.W., Ghosh, R. et al. Kalman Filter with Sensitivity Tuning for Improved Noise Reduction in Speech. Circuits Syst Signal Process 36, 1476–1492 (2017). https://doi.org/10.1007/s00034-016-0363-y

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