On the Computation of Complex-valued Gradients with Application to Statistically Optimum Beamforming

C. Boeddeker, P. Hanebrink, L. Drude, J. Heymann, R. Haeb-Umbach, On the Computation of Complex-Valued Gradients with Application to Statistically Optimum Beamforming, 2017.

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Abstract
This report describes the computation of gradients by algorithmic differentiation for statistically optimum beamforming operations. Especially the derivation of complex-valued functions is a key component of this approach. Therefore the real-valued algorithmic differentiation is extended via the complex-valued chain rule. In addition to the basic mathematic operations the derivative of the eigenvalue problem with complex-valued eigenvectors is one of the key results of this report. The potential of this approach is shown with experimental results on the CHiME-3 challenge database. There, the beamforming task is used as a front-end for an ASR system. With the developed derivatives a joint optimization of a speech enhancement and speech recognition system w.r.t. the recognition optimization criterion is possible.
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Boeddeker C, Hanebrink P, Drude L, Heymann J, Haeb-Umbach R. On the Computation of Complex-Valued Gradients with Application to Statistically Optimum Beamforming.; 2017.
Boeddeker, C., Hanebrink, P., Drude, L., Heymann, J., & Haeb-Umbach, R. (2017). On the Computation of Complex-valued Gradients with Application to Statistically Optimum Beamforming.
@book{Boeddeker_Hanebrink_Drude_Heymann_Haeb-Umbach_2017, title={On the Computation of Complex-valued Gradients with Application to Statistically Optimum Beamforming}, author={Boeddeker, Christoph and Hanebrink, Patrick and Drude, Lukas and Heymann, Jahn and Haeb-Umbach, Reinhold}, year={2017} }
Boeddeker, Christoph, Patrick Hanebrink, Lukas Drude, Jahn Heymann, and Reinhold Haeb-Umbach. On the Computation of Complex-Valued Gradients with Application to Statistically Optimum Beamforming, 2017.
C. Boeddeker, P. Hanebrink, L. Drude, J. Heymann, and R. Haeb-Umbach, On the Computation of Complex-valued Gradients with Application to Statistically Optimum Beamforming. 2017.
Boeddeker, Christoph, et al. On the Computation of Complex-Valued Gradients with Application to Statistically Optimum Beamforming. 2017.

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