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:

evokedinstance of Evoked

Evoked instance.

invinstance of InverseOperator

The inverse operator.

verbosebool | str | int | None

Control verbosity of the logging output. If None, use the default verbosity level. See the logging documentation and mne.verbose() for details. Should only be passed as a keyword argument.

Returns:

snrndarray, shape (n_times,)

The SNR estimated from the whitened data (i.e., GFP of whitened data).

snr_estndarray, 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:

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

The values in the diagonal matrix $\mathrm{\Gamma }$ are expressed in terms of the chosen regularization ${\lambda }^2\sim 1/{\mathrm{S}\mathrm{N}\mathrm{R}}^2$ 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:

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

And thus our predicted whitened data is just:

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

Where $\mathrm{\Pi }$ 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 $\mathrm{\Pi }$ 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.