On the Computation of Complex-valued Gradients with Application to Statistically Optimum Beamforming
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.
Cite
@article{arxiv.1701.00392,
title = {On the Computation of Complex-valued Gradients with Application to Statistically Optimum Beamforming},
author = {Christoph Boeddeker and Patrick Hanebrink and Lukas Drude and Jahn Heymann and Reinhold Haeb-Umbach},
journal= {arXiv preprint arXiv:1701.00392},
year = {2019}
}
Comments
Technical Report