riecovest.covariance_estimation.est_manifold_frob_whitened_by_true_noise

riecovest.covariance_estimation.est_manifold_frob_whitened_by_true_noise(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 using the ‘true’ noise covariance matrix.

This is equivalent to est_manifold_frob_whitened, except that the whitening parameter is extracted from the optimization variable Rv instead of the sample covariance matrix. This should lead to the same solution, see [vanRompaeyGEVD2018].

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].

  • start_value (tuple of ndarrays, optional) – Initial value for the optimization. If None, the optimization starts from a random point.

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

[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.