# mne.minimum_norm.estimate_snr¶

mne.minimum_norm.estimate_snr(evoked, inv, verbose=None)

Estimate the SNR as a function of time for evoked data

Parameters: evoked : instance of Evoked Evoked instance. inv : instance of InverseOperator The inverse operator. verbose : bool, str, int, or None If not None, override default verbose level (see mne.verbose). snr : ndarray, shape (n_times,) The SNR estimated from the whitened data. snr_est : ndarray, shape (n_times,) The SNR estimated using the mismatch between the unregularized solution and the regularized solution.

Notes

snr_est is estimated by using different amounts of inverse regularization and checking the mismatch between predicted and measured whitened data.

In more detail, given our whitened inverse obtained from SVD:

$\tilde{M} = R^\frac{1}{2}V\Gamma U^T$

The values in the diagonal matrix $$\Gamma$$ are expressed in terms of the chosen regularization $$\lambda\approx\frac{1}{\rm{SNR}^2}$$ and singular values $$\lambda_k$$ as:

$\gamma_k = \frac{1}{\lambda_k}\frac{\lambda_k^2}{\lambda_k^2 + \lambda^2}$

We also know that our predicted data is given by:

$\hat{x}(t) = G\hat{j}(t)=C^\frac{1}{2}U\Pi w(t)$

And thus our predicted whitened data is just:

$\hat{w}(t) = U\Pi w(t)$

Where $$\Pi$$ is diagonal with entries entries:

$\lambda_k\gamma_k = \frac{\lambda_k^2}{\lambda_k^2 + \lambda^2}$

If we use no regularization, note that $$\Pi$$ is just the identity matrix. Here we test the squared magnitude of the difference between unregularized solution and regularized solutions, choosing the biggest regularization that achieves a $$\chi^2$$-test significance of 0.001.

New in version 0.9.0.