= Tutorial 12: Signal Space Projections (SSP) =
''Authors: Francois Tadel, Elizabeth Bock, John C Mosher, Sylvain Baillet''

As previously said, the frequency filters are not adapted to remove artifacts that are transient or overlapping in frequency domain with the brain signals of interest. Other approaches exist to correct for those artifacts, based on the  spatial signature of the artifacts.

If an event is very reproducible and  occurs always at the same position (eg. eye blinks and heartbeats), the  sensors will always record the same values when it occurs. We can  identify the topographies corresponding to this artifact (ie spatial  distributions of values at one time point) and remove them from the  recordings. This spatial decomposition is the basic idea behind two  widely used approaches: the '''SSP '''(Signal-Space Projection) and '''ICA '''(Independent Component Analysis) methods.

This introduction tutorial will focus on the SSP approach, as it is a lot simpler and faster but still very efficient for removing blinks and heartbeats from MEG and high-density EEG recordings. You will be able to read later about the ICA decompositions in the advanced tutorials.

<<TableOfContents(2,2)>>

== Overview ==
The general SSP objective is to identify the sensor topragraphies that are typical of a specific artifact, then to create spatial projectors to remove the contributions of these topographies from the recordings.

 1. We start by identifying many examples of the artifact we are trying to remove. This is what we've been doing in the previous tutorial with the creation of the "cardiac" and "blink" events.
 1. We extract a short time window around each of these event markers and concatenate in time all those small blocks of recordings.
 1. We run a principle components analysis (PCA) on the concatenated artifacts in order to get a  decomposition in various spatial components.
 1. We should find in the first few principal components some topographies that are very specific of the type of artifact we are targetting. We select those components to remove.
 1. We compute a linear projector for each spatial component to remove and save them in the database (in the "Link to raw file"). They are not applied immediately to the recordings.
 1. Whenever some data is recordings are read from this file, the SSP projectors will be applied on the fly to them, to remove the artifact contributions. This approach is fast and memory efficient.<<BR>><<BR>> {{attachment:ssp_intro.gif}}

== The order matters ==
This procedure has to be repeated separately for each artifact type. The order in which you process the artifacts matters, because for removing the  second artifact we typically use the recordings cleaned with  the first set of SSP projectors. We have to decide which one to process first.

It works best if each artifact is defined as precisely as  possible, and as independently as possible from the other artifacts. If the two artifacts happen simulateneously,  the SSP projectors  calculated for the blink may contain some of    the  heartbeat topography and vice  versa. When trying to remove the second  artifact,    we might not be  able to isolate it clearly anymore.

Because the heart beats every second or so, there is a high chance that  when the subject blinks there is a heartbeat not too far away in the  recordings. Therefore a   significant  number of the blinks will be contaminated with  heartbeats. But we have usually a lot of "clean" heartbeats, we can start by removing those ones.   To isolate correctly these two common artifacts, we   recommend the following procedure:

 * Remove the markers "cardiac" that are occurring during a blink (done in the previous tutorial),
 * Compute the '''cardiac SSP''' (with no eye movements, because we removed the co-occurring events),
 * Compute the '''blink SSP''' (with no heartbeats, because they've already been taken care of).

If you have multiple modalities recorded simultaneously, for example MEG and EEG, you should run twice thiswhole procedure twice, once for  the EEG only  and once for the MEG only. You will always  get better results if  you  '''process the  different types of sensors  separately'''. Same  thing  when processing  Elekta-Neuromag  recordings, you should process   separately the  magnetometers (MEG  MAG) and the gradiometers (MEG GRAD).

== SSP: Heartbeats ==
Double-click on the link to show the MEG sensors for '''Run #01'''.<<BR>>In the Record tab, select the menu: '''"Artifacts > SSP: Heartbeats"'''.

 * '''Event name''': Name of the event to use to calculate the projectors, enter "'''cardiac'''"
 * '''Sensor types''': Type of sensors for which the projection should be calculated ("'''MEG'''").    Note that you will always  get better results if  you  process the different types of sensors  separately.
 * '''Compute using existing SSP projectors''':    You have the option to calculate the projectors from the raw   recordings, or from the recordings filtered with the previously    computed SSP projectors. Unless you have a good reason for not   considering the existing SSP projectors, you should always select this   option. <<BR>><<BR>> {{attachment:ssp_ecg_process.gif}}

After   the computation is done, a new figure is  displayed, that lets you   select the active projectors.

 * '''One the left''': The projector   categories where each row  represents the  result of  an execution of a SSP process  (usually one for  each sensor  type and each artifact).
 * '''On the right''': The spatial components returned by the PCA decomposition. The percentage indicated between brackets is the  singular value for this each component, normalized  for  this decomposition  (percentage = '''S'''i / sum('''S'''i), see details at the end of this page).
 * '''Percentage''': More practically, it indicates  the amount of signal that was captured by this    projector during the decomposition. The highest it is, the more the    projector is representative of the  artifact recordings that were used to    calculate it. In the good  cases, you would typically see one to three    components with values  that are significantly higher that the others.
 * '''Default selection''': The software selects '''the components with values superior to  12%''' and leaves the others unselected. '''This threshold is completely  empirical''' '''and depends on the acquisition device''', you should always  review manually the components that you want to remove.
 * When a  component is selected, it means that it is removed from the recordings. A spatial projector is computed and applied to the  recordings on  the fly  when reading from the continuous file.

=> REPRENDRE A PARTIR D'ICI <=

{{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawSsp?action=AttachFile&do=get&target=sspEcgSelect.gif|sspEcgSelect.gif|height="206",width="386",class="attachment"}}

For   the cardiac event, none of the components show a value superior to  12%,  therefore  the entire "cardiac" projector category was unselected.  This  doesn't  mean that none of those components is actually  interesting for  us, let's  investigate this.

A list of buttons is available to manipulate the projector categories: load, save, rename, delete, and '''display component topography'''.    The last one is one of the most useful tool to understand those    results. Select the category ("cardiac") to enable the list on the   right, click on the first component, then click on the toolbar button to   display its topography. Do it  again for components #2 and #3 (the   components don't need to be  active for that).

The   other  button [No interp] displays the same results without the   magnetic field  smoothing that is applied by default to MEG   topographies. It may help  understand some difficult cases.

{{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawSsp?action=AttachFile&do=get&target=sspEcgCheck.gif|sspEcgCheck.gif|height="207",width="390",class="attachment"}}

{{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawSsp?action=AttachFile&do=get&target=sspEcgComp.gif|sspEcgComp.gif|class="attachment"}}

None   of those topographies can be clearly related to a  cardiac component.   This can have two interpretations: the cardiac  artifact is not very   strong for this subject and  the influence of the  heart activity over   the MEG sensors is completely buried in the noise or  the brain signals,   or the characterization of the artifact that we did  was not so good   and we should refine it by selecting for instance  smaller time windows   around the cardiac peaks. Here, it's probably due  to the subject's   morphology. Some people generate strong artifacts in  the MEG, some   don't.

In this case, it is safer to '''unselect '''this "cardiac" category, rather than removing randomly spatial  components that we are not sure to identify.

== SSP: Eye blinks ==
Let's try the same thing with the eye blinks. Select the process "'''SSP > Compute SSP: Eye blinks'''".  Run it on the event type "blink", that indicate the peaks of the EOG  signal.

{{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawSsp?action=AttachFile&do=get&target=sspEogFile.gif|sspEogFile.gif|class="attachment"}} {{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawSsp?action=AttachFile&do=get&target=sspEog.gif|sspEog.gif|height="214",width="307",class="attachment"}}

In    this specific case, there is one value that is much higher than the    others (21%), and it is selected by default because it is superior to    12%. The first component is most likely a good representation of the    artifact we are trying to remove.

{{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawSsp?action=AttachFile&do=get&target=sspEogSelect.gif|sspEogSelect.gif|height="214",width="384",class="attachment"}}

Select   the cardiac category, and display the topographies for the first three   components. Component #1 is clearly related with the ocular  activity   occurring during the blinks, the others are not as clear.  Conclusion:   the default proposition was good (only component #1  selected).   Setting  this first projector as active removes from the MEG  signals  the  contributions related with the spatial topography we can see  in  the  first figure, ie. a spatial distribution of sensor values  related   specifically to the eye blinks.

{{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawSsp?action=AttachFile&do=get&target=sspEogComp.gif|sspEogComp.gif|class="attachment"}}

While   the recordings are displayed in the file viewer, the selection of the   active projectors interactively updates the recordings. Go to the first   detected "blink" event ('''t=33.600s'''), and select the left frontal sensors ('''Shift+B'''   or right-click > Display setup > CTF LF). Then play with the   checkboxes to change the active projectors, and see how well this first   component of the blink category removes the ocular artifact.

{{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawSsp?action=AttachFile&do=get&target=sspEogMeg.gif|sspEogMeg.gif|class="attachment"}}

Select   the projector category "blink", select the first component, and click   on Save, to validate your changes. Starting from now, all the  successive  operations you apply on this file will integrate this eye  blink  correction, including the calculation of other projectors. After  you  closed this window, you can get back to it by selecting the menu "'''SSP > Select active projector'''" in the Record tab, and change again the selection of active projectors.

We are not going to calculate the SSP for the other category of events identified on the EOG, the group "'''blink2'''".   The events classified in this group could represent eye saccades or   other types of blinks, it is not very clear that they correspond to the   same physiological event. Most of them do not seem to create any  obvious  contamination on the MEG recordings, there is probably no need  to  consider them now.

== Run #02: Running from a script ==
Let's perform the same detection operations on '''Run #02''', using this time the '''Process1''' box.

 * Close everything with the [X] button at the top-right corner of the Brainstorm window.
 * Select the run '''AEF #02''' in the Process1 box, then select the following processes:
 * '''Events > Detect  heartbeats:''' Select channel '''ECG''', check "All file", event name "cardiac".
 * '''Events > Detect eye blinks:''' Select channel '''VEOG''', check "All file", event name "blink".
 * '''Events > Remove simultaneous''': Remove "'''cardiac'''", too close to "'''blink'''", delay '''250ms'''.

Always check visually the results of the SSP cleaning executed from a script.

 * Open the MEG sensors for Run #02.
 * In the Record tab, menu Artifacts > '''Select active projectors'''.

<<TAG(Advanced)>>

== SSP: Generic ==
The calculation of the SSP for the heartbeats and the eye blinks are shortcuts to a more generic algorithm "'''Compute SSP: Generic'''".   We do not need it here, but the illustration of its properties is   interesting to understand the correction of ocular and cardiac   artifacts:

 * '''Event name''': Markers that are used to characterize the artifact
 * '''Time window''':   Time segment to consider before and after each event marker. We want   this time window to be longer than the artifact effect itself, in order   to have a large number of time samples representative of a normal brain   activity. This helps the SVD decomposition to separate the artifact  from  the ongoing brain activity.
 * '''Frequency band''':   Definition of the band-pass filter that is applied to the recordings   before calculating the projector. Usually you would use the same   frequency band as we used for the detection, but you may want to try to   refine this parameter if the results are not satisfying.
 * '''Sensor types or names''': List of sensors for which to calculate the projector. You can get better results if you process one sensor type at a time.

{{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawSsp?action=AttachFile&do=get&target=sspGeneric.gif|sspGeneric.gif|height="328",width="330",class="attachment"}}

<<TAG(Advanced)>>

== Evaluation ==
=== Eye blinks ===
One   efficient way of representing the impact of this artifact correction  is  to epoch the recordings around the artifacts before and after the   correction. Use the same time window as the one used in the SSP options   around each marker, and average all the segments of recordings. Those   operations are detailed in the next tutorial, we are just presenting the   results. You don't need to reproduce them at this time, just remember   that it is doable, in case you need it with your own data. This is what   the database would look like after those operations:

{{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawSsp?action=AttachFile&do=get&target=blinkDb.gif|blinkDb.gif|height="263",width="283",class="attachment"}}

The following image represents the file '''"blink_uncorrected / Avg: blink"''', which is the average of the 18 identified blinks '''before'''   the SSP correction, [-200,+200]ms around the "blink" events. The time   series, the 2D topography at the peak (t = 0ms), and the mapping on the   cortex of those fields, using the basic inverse model calculated in  the  previous tutorial.

{{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawSsp?action=AttachFile&do=get&target=blinkBefore.gif|blinkBefore.gif|height="177",width="533",class="attachment"}}

The next image represents the file  '''"blink_ssp / Avg: blink"''', which is the exact same thing, but '''after '''the   SSP correction. The artifact is gone. If you do this and you can still   see some clear evoked component in the time series figure, the SSP   correction was not efficient: the artifact is not properly identified,   or you should select different components using the "Select active   projectors" window.

{{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawSsp?action=AttachFile&do=get&target=blinkAfter.gif|blinkAfter.gif|height="177",width="533",class="attachment"}}

=== Heartbeats ===
We  can do  the same thing with the heartbeats: epoch [-40,+40]ms around  the   "cardiac" events, average the trials, and review the event-related   fields at three instants:

The peak of the '''P wave''' (t = '''-30ms'''):

{{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawSsp?action=AttachFile&do=get&target=cardiacP.gif|cardiacP.gif|height="178",width="534",class="attachment"}}

The peak of the '''QRS complex''' (t = '''0ms'''):

{{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawSsp?action=AttachFile&do=get&target=cardiacQRS.gif|cardiacQRS.gif|height="178",width="534",class="attachment"}}

The peak of the '''T wave''' (t = '''25ms'''):

{{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawSsp?action=AttachFile&do=get&target=cardiacT.gif|cardiacT.gif|height="178",width="534",class="attachment"}}

Those   peaks may look big, but they are in fact much smaller (300 fT for the   average of 346 repetitions) than what we observed for the eye blinks   (1500 fT for 18 repetitions). You can notice that none of those   topographies are similar to the components we obtained after calculating   the SSP for the cardiac artifact. We don't know how to correct this   artifact, it doesn't look too bad in terms of recordings contamination,   so we just leave it uncorrected.

<<TAG(Advanced)>>

== Troubleshooting ==
You    have calculated the SSP as indicated here but you don't get any good    results. No matter what you do, the topographies don't look like the    targeted artifact. You can try the following:

 * Review one by    one the events indicating the artifacts, remove the ones that are  less   clear or that occur close to another artifact.
 * Select or unselect the option "Compute using existing SSP".
 * Use the process "Compute SSP: Generic" and modify some parameters:
  * Reduce the time window around the peak of the artifact.
  * Use    a narrower frequency band: especially the EOG, if the projectors    capture some of the alpha oscillations, you can limit the frequency band    to [1.5 - 9] Hz.
  * Change the method: Average / SSP.
 * If    you have multiple acquisition runs, you may try to use all the    artifacts from all the runs rather than processing the files one by one.    For that, use the Process2 tab instead of Process1. Put the "Link to    raw file" of all the runs on both side, Files A (what is used to  compute   the SSP) and Files B (where the SSP are applied).

Always   look at what this procedure gives you in output. Most of the time, the  artifact  cleaning will  be an iterative process where to need several  time to  adjust the options  and the order of the different steps in  order to get  good results.

<<TAG(Advanced)>>

== Theory ==
The  Signal-Space Projection (SSP) is one approach to rejection of external  disturbances. Here is a short description of the method by '''Matti Hämäläinen''', from the [[http://www.martinos.org/meg/manuals/MNE-manual-2.7.pdf|MNE 2.7 reference manual]], section 4.16.

Unlike  many other noise-cancellation approaches, SSP does not require  additional reference sensors to record the disturbance fields. Instead,  SSP relies on the fact that the magnetic field distributions generated  by the sources in the brain have spatial distributions sufficiently  different from those generated by external noise sources. Furthermore,  it is implicitly assumed that the linear space spanned by the  significant external noise patterns has a low dimension.

Without loss of generality we can always decompose any ''n''-channel measurement '''b'''(''t'') into its signal and noise components as:

 . '''b'''(''t'') = '''b'''<<HTML(<sub>)>>''s''<<HTML(</sub>)>>(''t'') ''+'' '''b'''<<HTML(<sub>)>>''n''<<HTML(</sub>)>>(''t'')

Further, if we know that '''b'''<<HTML(<sub>)>>''n''<<HTML(</sub>)>>(''t'') is well characterized by a few field patterns '''b'''<<HTML(<sub>)>>''1''<<HTML(</sub>)>>...'''b'''<<HTML(<sub>)>>''m''<<HTML(</sub>)>>, we can express the disturbance as

 . '''b'''<<HTML(<sub>)>>''n''<<HTML(</sub>)>>(''t'') = '''Uc'''<<HTML(<sub>)>>''n''<<HTML(</sub>)>>(''t'') ''+'' '''e'''(''t'') ,

where the columns of '''U''' constitute an orthonormal basis for '''b'''<<HTML(<sub>)>>''1''<<HTML(</sub>)>>...'''b'''<<HTML(<sub>)>>''m''<<HTML(</sub>)>>, '''c'''<<HTML(<sub>)>>''n''<<HTML(</sub>)>>(''t'') is an ''m''-component column vector, and the error term '''e'''(''t'') is small and does not exhibit any consistent spatial distributions over time,'' i.e.'', '''C'''<<HTML(<sub>)>>''e''<<HTML(</sub>)>> = ''E''{'''ee'''<<HTML(<sup>)>>''T''<<HTML(</sup>)>>} = '''I'''. Subsequently, we will call the column space of '''U''' the noise subspace. The basic idea of SSP is that we can actually find a small basis set '''b'''<<HTML(<sub>)>>''1''<<HTML(</sub>)>>...'''b'''<<HTML(<sub>)>>''m''<<HTML(</sub>)>> such that the conditions described above are satisfied. We can now construct the orthogonal complement operator

 . '''P'''<<HTML(<sub>)>>⊥<<HTML(</sub>)>> = '''I''' - '''UU'''<<HTML(<sup>)>>T<<HTML(</sup>)>>

and apply it to '''b'''(''t'') yielding

 . '''b'''(''t'') ≈ '''P'''<<HTML(<sub>)>>⊥<<HTML(</sub>)>>'''b'''<<HTML(<sub>)>>''s''<<HTML(</sub>)>>(''t'') ,

since '''P'''<<HTML(<sub>)>>⊥<<HTML(</sub>)>>'''b'''<<HTML(<sub>)>>''n''<<HTML(</sub>)>>(''t'') = '''P'''<<HTML(<sub>)>>⊥<<HTML(</sub>)>>'''Uc'''<<HTML(<sub>)>>''n''<<HTML(</sub>)>>(''t'') ≈ 0. The projection operator '''P'''<<HTML(<sub>)>>⊥<<HTML(</sub>)>>  is called the signal-space projection operator and generally provides  considerable rejection of noise, suppressing external disturbances by a  factor of 10 or more. The effectiveness of SSP depends on two factors:

 1. The basis set '''b'''<<HTML(<sub>)>>''1''<<HTML(</sub>)>>...'''b'''<<HTML(<sub>)>>''m''<<HTML(</sub>)>> should be able to characterize the disturbance field patterns completely and
 1. The angles between the noise subspace space spanned by '''b'''<<HTML(<sub>)>>''1''<<HTML(</sub>)>>...'''b'''<<HTML(<sub>)>>''m''<<HTML(</sub>)>> and the signal vectors '''b'''<<HTML(<sub>)>>''s''<<HTML(</sub>)>>(''t'') should be as close to π/2 as possible.

If the first requirement is not satisfied, some noise will leak through because '''P'''<<HTML(<sub>)>>⊥<<HTML(</sub>)>>'''b'''<<HTML(<sub>)>>''n''<<HTML(</sub>)>>(''t'') ≠ 0. If the any of the brain signal vectors '''b'''<<HTML(<sub>)>>''s''<<HTML(</sub>)>>(''t'') is close to the noise subspace not only the noise but also the signal will be attenuated by the application of '''P'''<<HTML(<sub>)>>⊥<<HTML(</sub>)>> and, consequently, there might by little gain in signal-to-noise ratio.

Since  the signal-space projection modifies the signal vectors originating in  the brain, it is necessary to apply the projection to the forward  solution in the course of inverse computations.

<<TAG(Advanced)>>

== Algorithm ==
We  have now 346 examples of heartbeats, 18 examples of blinks, and 12  examples of saccades. Those are sufficient numbers of repetitions to  calculate reliable signal-space projections. The logic of the  computation is the following:

 1. Take a small time  window around each marker to capture the full effect of the artifact,  plus some clean brain signals before and after. The default time window  is [-200,+200]ms for eye blinks, and [-40,+40]ms for the heartbeats.
 1. Filter the MEG or EEG signals in a frequency band of interest, in which the artifact is the most visible.
 1. Concatenate all those time blocks into a big matrix '''A''' = ['''b'''<<HTML(<sub>)>>''1''<<HTML(</sub>)>>, ..., '''b'''<<HTML(<sub>)>>''m''<<HTML(</sub>)>>]
 1. Compute the singular value decomposition of this matrix '''A''': ['''U''','''S''','''V'''] = '''svd'''('''A''', 'econ')
 1. The singular vectors '''U'''i with the highest singular values '''S'''i  are an orthonormal basis of the artifact subspace that we want to  subtract from the recordings. The software selects by default the  vectors with eigenvalues above a certain threshold: '''S'''i > 12% * sum('''S'''i)<<BR>>Then it is possible to redefine interactively the selected components.
 1. Calculate the projection operator:''' P'''<<HTML(<sub>)>>⊥i<<HTML(</sub>)>> = '''I''' - '''U'''i'''U'''i<<HTML(<sup>)>>T<<HTML(</sup>)>>
 1. Apply this projection on the MEG or EEG recordings '''F''': '''F''' = '''P'''<<HTML(<sub>)>>⊥i<<HTML(</sub>)>>'''F'''
 1. The process has to be repeated '''separately '''several times:
  * for each sensor type (EEG, MEG magnetometers, MEG gradiometers) and
  * for  each artifact, starting with the one that leads to the strongest  contamination in amplitude on the sensors (in the case: the eye blinks)
  * If  you have difficulties removing one artifact or the other, you may try  to process them in a different order. You may also try removing some of  the artifact markers in the case of co-occurring artifacts. If a lot of  the blinks happen at the same time as heartbeats, you may end up  calculating projectors that mix both effects, but that do not remove  efficiently one or the other. In this case, remove all the markers that  happen in the segments contaminated by multiple artifacts.

Steps #1 to #5 are done automatically by the processes "SSP > Compute SSP" in the Record tab: the results, the vectors '''U'''i, are saved in the database link ("Link to raw file") and in the channel file.

Steps  #6 and #7 are calculated on the fly when reading a block of recordings  from the continuous file: when using the raw viewer, running a process a  process on the continuous file, or importing epochs in the database.

Step  #8 is the manual control of the process. Take some time to understand  what you are trying to remove and how to do it. Never trust blindly any  fully automated artifact cleaning algorithm, always check manually what  is removed from the recordings, and do not give up if the first results  are not satisfying.

<<TAG(Advanced)>>

== References ==
For more information on the SSP method, please consult the following publications:

 * C.   D. Tesche, M. A. Uusitalo, R. J. Ilmoniemi, M. Huotilainen, M. Kajola,   and O. Salonen, "Signal-space projections of MEG data characterize  both  distributed and well-localized neuronal sources,"  Electroencephalogr  Clin Neurophysiol, vol. 95, pp. 189-200, 1995.
 * M.  A. Uusitalo  and R. J. Ilmoniemi, "Signal-space projection method for  separating MEG  or EEG into components," Med Biol Eng Comput, vol. 35,  pp. 135-40, 1997.

<<TAG(Advanced)>>

== Additional documentation ==
 * Forum: [[http://neuroimage.usc.edu/forums/showthread.php?1272|Refining the pre-processing pipeline]]
 * McGill guidelines
 * SSP cookbook
 * Alpha and cardiac overlapping?

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