riecovest.covariance_estimation.est_manifold_frob_whitened

riecovest.covariance_estimation.est_manifold_frob_whitened(scm_noisy_signal, scm_noise, rank, alpha=0.5, start_value=None)

Signal and noise covariance estimation using the Frobenius norm distance, with pre-whitening.

This should be equivalent to est_gevd, but with the optimization done on a Riemannian manifold.

Parameters:

  • scm_noisy_signal (ndarray of shape (ambient_dim, ambient_dim)) – Sample covariance matrix of the noisy signal.

  • scm_noise (ndarray of shape (ambient_dim, ambient_dim)) – Sample covariance matrix of the noise.

  • rank (int) – Rank of the signal covariance matrix.

  • alpha (float, optional) – Weighting parameter between the noisy signal and the noise. Default is 0.5. This parameter should not affect the optimal solution, but may affect the convergence of the optimization [vanRompaeyGEVD2018].

Returns:

  • Rx (ndarray of shape (ambient_dim, ambient_dim)) – Estimated signal covariance matrix.

  • Rv (ndarray of shape (ambient_dim, ambient_dim)) – Estimated noise covariance matrix.

References

[serizelLowrank2014] R. Serizel, M. Moonen, B. V. Dijk, and J. Wouters, “Low-rank approximation based multichannel Wiener filter algorithms for noise reduction with application in cochlear implants,” IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 22, no. 4, pp. 785–799, Apr. 2014, doi: 10.1109/TASLP.2014.2304240. [vanRompaeyGEVD2018] R. Van Rompaey and M. Moonen, “GEVD based speech and noise correlation matrix estimation for multichannel Wiener filter based noise reduction,” in 2018 26th European Signal Processing Conference (EUSIPCO), Sep. 2018, pp. 2544–2548. doi: 10.23919/EUSIPCO.2018.8553109.