Repairing artifacts with SSP

This tutorial covers the basics of signal-space projection (SSP) and shows how SSP can be used for artifact repair; extended examples illustrate use of SSP for environmental noise reduction, and for repair of ocular and heartbeat artifacts. :depth: 2

We begin as always by importing the necessary Python modules. To save ourselves from repeatedly typing mne.preprocessing we'll directly import a couple functions from that submodule:

What is SSP?

Signal-space projection (SSP) :footcite:UusitaloIlmoniemi1997 is a technique for removing noise from EEG and MEG signals by :term:projecting <projector> the signal onto a lower-dimensional subspace. The subspace is chosen by calculating the average pattern across sensors when the noise is present, treating that pattern as a "direction" in the sensor space, and constructing the subspace to be orthogonal to the noise direction (for a detailed walk-through of projection see tut-projectors-background).

The most common use of SSP is to remove noise from MEG signals when the noise comes from environmental sources (sources outside the subject's body and the MEG system, such as the electromagnetic fields from nearby electrical equipment) and when that noise is stationary (doesn't change much over the duration of the recording). However, SSP can also be used to remove biological artifacts such as heartbeat (ECG) and eye movement (EOG) artifacts. Examples of each of these are given below.

Example: Environmental noise reduction from empty-room recordings

The example data <sample-dataset> was recorded on a Neuromag system, which stores SSP projectors for environmental noise removal in the system configuration (so that reasonably clean raw data can be viewed in real-time during acquisition). For this reason, all the :class:~mne.io.Raw data in the example dataset already includes SSP projectors, which are noted in the output when loading the data:

The example data <sample-dataset> also includes an "empty room" recording taken the same day as the recording of the subject. This will provide a more accurate estimate of environmental noise than the projectors stored with the system (which are typically generated during annual maintenance and tuning). Since we have this subject-specific empty-room recording, we'll create our own projectors from it and discard the system-provided SSP projectors (saving them first, for later comparison with the custom ones):

Notice that the empty room recording itself has the system-provided SSP projectors in it — we'll remove those from the empty room file too.

Visualizing the empty-room noise

Let's take a look at the spectrum of the empty room noise. We can view an individual spectrum for each sensor, or an average (with confidence band) across sensors:

Creating the empty-room projectors

We create the SSP vectors using :func:~mne.compute_proj_raw, and control the number of projectors with parameters n_grad and n_mag. Once created, the field pattern of the projectors can be easily visualized with :func:~mne.viz.plot_projs_topomap. We include the parameter vlim='joint' so that the colormap is computed jointly for all projectors of a given channel type; this makes it easier to compare their relative smoothness. Note that for the function to know the types of channels in a projector, you must also provide the corresponding :class:~mne.Info object:

Notice that the gradiometer-based projectors seem to reflect problems with individual sensor units rather than a global noise source (indeed, planar gradiometers are much less sensitive to distant sources). This is the reason that the system-provided noise projectors are computed only for magnetometers. Comparing the system-provided projectors to the subject-specific ones, we can see they are reasonably similar (though in a different order) and the left-right component seems to have changed polarity.

Visualizing how projectors affect the signal

We could visualize the different effects these have on the data by applying each set of projectors to different copies of the :class:~mne.io.Raw object using :meth:~mne.io.Raw.apply_proj. However, the :meth:~mne.io.Raw.plot method has a proj parameter that allows us to temporarily apply projectors while plotting, so we can use this to visualize the difference without needing to copy the data. Because the projectors are so similar, we need to zoom in pretty close on the data to see any differences:

The effect is sometimes easier to see on averaged data. Here we use an interactive feature of :func:mne.Evoked.plot_topomap to turn projectors on and off to see the effect on the data. Of course, the interactivity won't work on the tutorial website, but you can download the tutorial and try it locally:

Plotting the ERP/F using evoked.plot() or evoked.plot_joint() with and without projectors applied can also be informative, as can plotting with proj='reconstruct', which can reduce the signal bias introduced by projections (see tut-artifact-ssp-reconstruction below).

Example: EOG and ECG artifact repair

Visualizing the artifacts

As mentioned in the ICA tutorial <tut-artifact-ica>, an important first step is visualizing the artifacts you want to repair. Here they are in the raw data:

Repairing ECG artifacts with SSP

MNE-Python provides several functions for detecting and removing heartbeats from EEG and MEG data. As we saw in tut-artifact-overview, :func:~mne.preprocessing.create_ecg_epochs can be used to both detect and extract heartbeat artifacts into an :class:~mne.Epochs object, which can be used to visualize how the heartbeat artifacts manifest across the sensors:

Looks like the EEG channels are pretty spread out; let's baseline-correct and plot again:

To compute SSP projectors for the heartbeat artifact, you can use :func:~mne.preprocessing.compute_proj_ecg, which takes a :class:~mne.io.Raw object as input and returns the requested number of projectors for magnetometers, gradiometers, and EEG channels (default is two projectors for each channel type). :func:~mne.preprocessing.compute_proj_ecg also returns an :term:events array containing the sample numbers corresponding to the onset of each detected heartbeat.

The first line of output tells us that :func:~mne.preprocessing.compute_proj_ecg found three existing projectors already in the :class:~mne.io.Raw object, and will include those in the list of projectors that it returns (appending the new ECG projectors to the end of the list). If you don't want that, you can change that behavior with the boolean no_proj parameter. Since we've already run the computation, we can just as easily separate out the ECG projectors by indexing the list of projectors:

Just like with the empty-room projectors, we can visualize the scalp distribution:

Since no dedicated ECG sensor channel was detected in the :class:~mne.io.Raw object, by default :func:~mne.preprocessing.compute_proj_ecg used the magnetometers to estimate the ECG signal (as stated on the third line of output, above). You can also supply the ch_name parameter to restrict which channel to use for ECG artifact detection; this is most useful when you had an ECG sensor but it is not labeled as such in the :class:~mne.io.Raw file.

The next few lines of the output describe the filter used to isolate ECG events. The default settings are usually adequate, but the filter can be customized via the parameters ecg_l_freq, ecg_h_freq, and filter_length (see the documentation of :func:~mne.preprocessing.compute_proj_ecg for details).

.. TODO what are the cases where you might need to customize the ECG filter? infants? Heart murmur?

Once the ECG events have been identified, :func:~mne.preprocessing.compute_proj_ecg will also filter the data channels before extracting epochs around each heartbeat, using the parameter values given in l_freq, h_freq, filter_length, filter_method, and iir_params. Here again, the default parameter values are usually adequate.

.. TODO should advice for filtering here be the same as advice for filtering raw data generally? (e.g., keep high-pass very low to avoid peak shifts? what if your raw data is already filtered?)

By default, the filtered epochs will be averaged together before the projection is computed; this can be controlled with the boolean average parameter. In general this improves the signal-to-noise (where "signal" here is our artifact!) ratio because the artifact temporal waveform is fairly similar across epochs and well time locked to the detected events.

To get a sense of how the heartbeat affects the signal at each sensor, you can plot the data with and without the ECG projectors:

Finally, note that above we passed reject=None to the :func:~mne.preprocessing.compute_proj_ecg function, meaning that all detected ECG epochs would be used when computing the projectors (regardless of signal quality in the data sensors during those epochs). The default behavior is to reject epochs based on signal amplitude: epochs with peak-to-peak amplitudes exceeding 50 µV in EEG channels, 250 µV in EOG channels, 2000 fT/cm in gradiometer channels, or 3000 fT in magnetometer channels. You can change these thresholds by passing a dictionary with keys eeg, eog, mag, and grad (though be sure to pass the threshold values in volts, teslas, or teslas/meter). Generally, it is a good idea to reject such epochs when computing the ECG projectors (since presumably the high-amplitude fluctuations in the channels are noise, not reflective of brain activity); passing reject=None above was done simply to avoid the dozens of extra lines of output (enumerating which sensor(s) were responsible for each rejected epoch) from cluttering up the tutorial.

While :func:~mne.preprocessing.compute_proj_ecg conveniently combines several operations into a single function, MNE-Python also provides functions for performing each part of the process. Specifically:

• :func:mne.preprocessing.find_ecg_events for detecting heartbeats in a :class:~mne.io.Raw object and returning a corresponding :term:events array

• :func:mne.preprocessing.create_ecg_epochs for detecting heartbeats in a :class:~mne.io.Raw object and returning an :class:~mne.Epochs object

• :func:mne.compute_proj_epochs for creating projector(s) from any :class:~mne.Epochs object

See the documentation of each function for further details.

Repairing EOG artifacts with SSP

Once again let's visualize our artifact before trying to repair it. We've seen above the large deflections in frontal EEG channels in the raw data; here is how the ocular artifacts manifests across all the sensors:

Just like we did with the heartbeat artifact, we can compute SSP projectors for the ocular artifact using :func:~mne.preprocessing.compute_proj_eog, which again takes a :class:~mne.io.Raw object as input and returns the requested number of projectors for magnetometers, gradiometers, and EEG channels (default is two projectors for each channel type). This time, we'll pass no_proj parameter (so we get back only the new EOG projectors, not also the existing projectors in the :class:~mne.io.Raw object), and we'll ignore the events array by assigning it to _ (the conventional way of handling unwanted return elements in Python).

Just like with the empty-room and ECG projectors, we can visualize the scalp distribution:

Now we repeat the plot from above (with empty room and ECG projectors) and compare it to a plot with empty room, ECG, and EOG projectors, to see how well the ocular artifacts have been repaired:

Notice that the small peaks in the first to magnetometer channels (MEG 1411 and MEG 1421) that occur at the same time as the large EEG deflections have also been removed.

Choosing the number of projectors

In the examples above, we used 3 projectors (all magnetometer) to capture empty room noise, and saw how projectors computed for the gradiometers failed to capture global patterns (and thus we discarded the gradiometer projectors). Then we computed 3 projectors (1 for each channel type) to capture the heartbeat artifact, and 3 more to capture the ocular artifact. How did we choose these numbers? The short answer is "based on experience" — knowing how heartbeat artifacts typically manifest across the sensor array allows us to recognize them when we see them, and recognize when additional projectors are capturing something else other than a heartbeat artifact (and thus may be removing brain signal and should be discarded).

Visualizing SSP sensor-space bias via signal reconstruction

.. sidebar:: SSP reconstruction

Internally, the reconstruction is performed by effectively using a
minimum-norm source localization to a spherical source space with the
projections accounted for, and then projecting the source-space data
back out to sensor space.

Because SSP performs an orthogonal projection, any spatial component in the data that is not perfectly orthogonal to the SSP spatial direction(s) will have its overall amplitude reduced by the projection operation. In other words, SSP typically introduces some amount of amplitude reduction bias in the sensor space data.

When performing source localization of M/EEG data, these projections are properly taken into account by being applied not just to the M/EEG data but also to the forward solution, and hence SSP should not bias the estimated source amplitudes. However, for sensor space analyses, it can be useful to visualize the extent to which SSP projection has biased the data. This can be explored by using proj='reconstruct' in evoked plotting functions, for example via :meth:evoked.plot() <mne.Evoked.plot>:

Note that here the bias in the EEG and magnetometer channels is reduced by the reconstruction. This suggests that the application of SSP has slightly reduced the amplitude of our signals in sensor space, but that it should not bias the amplitudes in source space.

References

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