Abstract
This paper addresses the estimation of Relative Transfer Function (RTF) between microphones from noisy recordings. We utilize an incomplete initial measurement of the RTF, which is known for only several frequency bins. The measurement is completed by finding its sparsest representation in the time domain. We propose to perform this reconstruction by solving a Second-Order Cone Program (SOCP). Free parameters of this formulation represent distance of the completed RTF from the initial estimate. We select these parameters based on the theoretical performance of the initial estimate. In experiments with real-world data, this approach achieves a significant refinement of the RTF, especially in scenarios with low signal-to-noise ratios.
This work was supported by The Czech Sciences Foundation through Project No. 14-11898S.
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Notes
- 1.
The right channel \(X_\mathrm{R}\) as well as H are typically delayed by a few samples due to possible acausality of \(H_\mathrm{RTF}\). We omit this detail here for the sake of simplicity of the notation.
- 2.
The variance of FD under the model is also derived in [2] and could be taken into account. The bias, however, seems to have a larger influence on the entire accuracy of FD; we therefore focus on the bias.
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The kurtosis-based selection appears to be efficient when the frequency components of the target signal have non-Gaussian distribution while those of the noise are Gaussian; see Sect. 5 in [5]. In real-world situations, this is often satisfied when the target signal is speech and the noise is quasi-stationary.
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Koldovský, Z., Málek, J., Tichavský, P. (2015). Improving Relative Transfer Function Estimates Using Second-Order Cone Programming. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2015. Lecture Notes in Computer Science(), vol 9237. Springer, Cham. https://doi.org/10.1007/978-3-319-22482-4_26
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