Tutorial 22: Source estimation


Authors: Francois Tadel, Elizabeth Bock, Rey R Ramirez, John C Mosher, Richard Leahy, Sylvain Baillet

You have in your database a forward model matrix that explains how the cortical sources determine the values on the sensors. This is useful for simulations, but what we need is to build the inverse information: how to estimate the sources when we have the recordings. This tutorials introduces the tools available in Brainstorm for solving this inverse problem.

Ill-posed problem

Our goal is to estimate the activity of the 45,000 dipoles described by our forward model. However we only have a few hundreds of variables (the number of sensors). This inverse problem is ill-posed, there is an infinity of combinations of source activity that can generate exactly the same sensor topography. Inverting the forward problem directly is impossible, unless we add some strong priors in our model.

Wikipedia says: "Inverse problems are some of the most important and well-studied mathematical problems in science and mathematics because they tell us about parameters that we cannot directly observe. They have wide application in optics, radar, acoustics, communication theory, signal processing, medical imaging, computer vision, geophysics, oceanography, astronomy, remote sensing, natural language processing, machine learning, nondestructive testing, and many other fields."

Many solutions have been proposed in the literature, based on different assumptions on the way the brain works and depending on the amount of information we already have on the effects we are studying. Among the hundreds of methods available, two classes of inverse models have been widely used in MEG/EEG source imaging in the past years: minimum-norm solutions and beamformers.

Both approaches have the advantage of being linear: the activity of the sources is a linear recombination of the MEG/EEG recordings. It is possible to solve the inverse problem independently of the recordings, making the data manipulation a lot easier and faster.

Both are available in Brainstorm, so you can use the one the most adapted to your recordings or to your own personal expertise. Only the minimum norm estimates will be described in this tutorial, but the other solutions work exactly in the same way.

Source estimation options [TODO]

Before we start estimating the sources for the recordings available in our database, let's start with an overview of the options available. The screen capture below represents the basic options for the minimum norm estimates. The options for the other methods will be described in advanced tutorials.




The minimum norm estimates are a measure of the current density flowing at the surface of the cortex. To visualize these results and compare them between subjects, we can normalize the MNE values to get a standardized level of activation with respect to the noise or baseline level (dSPM, sLORETA, MNp).

Source orientation

Sources for a single data file (constrained)

Display: Cortex surface

Display: MRI Viewer

Display: MRI 3D

Sign of constrained minimum norm values

You should pay attention to a property of the current amplitudes that are given by the minimum norm method: they can be positive of negative, and they oscillate around zero. If you display the sources of the surface again, then configure the colormap to show relative values (uncheck the "Absolute values" option), you would see those typical stripes of positive and negative values around the sulci. Double-click on the colorbar after testing this to reset the colormap.

This pattern is due to the orientation constraint imposed on the dipoles. On both sides of a sulcus, we have defined dipoles that are very close to each other, but with opposite orientations. If we observe a pattern of activity on one side of a suclus that can be assimilated to an electric dipole (green arrow), the minimum norm model will try to explain it with the dipoles that are available in the head model (red and blue arrows). Because of the dipoles orientations, it translates into positive values (red arrows) on one side of the sulcus and negative on the other side (blue arrows).

When displaying the cortical maps at one time point, we are usually not interested by the sign of the minimum norm values but rather by their amplitude. This is why we always display them by default with the colormap option "absolute values" selected.

However, we cannot simply discard the sign of these values because we need them for other types of analysis, typically time-frequency decompositions and connectivity analysis. For estimating frequency measures on those source maps, we need to keep the oscillations around zero.

Computing sources for multiple data files

Because the minimum norm model is linear, we can compute an inverse model independently from the recordings and apply it on the recordings when needed. We will now illustrate how to compute a shared inverse model for all the imported epochs. For illustration purpose, we will use this time an unconstrained source model.

Source map normalization

The current density values returned by the minimum norm method have a few problems:

Normalizing the current density maps with respect with a baseline (noise recordings or resting state) can help with all these issues at the same time. Some normalizations can be computed independently from the recordings, and saved as part of the linear source model (dSPM, sLORETA, MNp). An other way of proceeding is to compute a Z-score baseline correction from the current density maps.

All the normalizations options do not change your results, they are just different ways at looking at the same minimum norm maps. If you look at the time series associated with one source, it would be exactly the same for all the normalizations, except for a scaling factor. What changes is only the relative weights between the sources, and these weights do not change over time.



Delete your experiments

Typical recommendations

Average in source space


Display: Contact sheets and movies

A good way to represent what is happening in time is to generate contact sheets or videos. Right-click on any figure and go to the menu Snapshot to check out all the possible options. For a nicer result, take some time to adjust the size of the figure, the amplitude threshold and the colormap options (hiding the colorbar can be a good option for contact sheets).

A time stamp is added to the captured figure. The size of the text font is fixed, so if you want it to be reable in the contact sheet, you should make you figure very small before starting the capture.


Advanced options

Right-click on the deviant average for Run#01 > Compute sources [2015].
Click on the button [Show details] to bring up all the advanced minimum norm options.

Depth weighting

The minimum-norm estimates have a bias towards superficial currents. This tendency can be alleviated by adjusting these parameters. To understand how to set these parameters, please refer to the MNE manual (options --depth, --weightexp and --weightlimit).

Noise covariance regularization

LCMV beamformer

Dipole fitting

Output mode

Signal properties

Noise covariance matrix



TODO: John


Rey on sLORETA

Yes in sLORETA the noise covariance is not used at all for the standardization process. It can be used modeling correlated noise and whitening, but that is optional.

I have noticed that a lot of folks are confused about this and I have seen many statements in papers spreading this awful confusion. The sLORETA is standardized by the resolution matrix (diagonal for dipole orientations constraints, or block diagonals for free orientations).

That is why sLORETA has zero localization bias for ALL point-spread functions, and why I always prefer sLORETA over dSPM, MNE, or any beamformer. This is all in the math .... but ..... just so that you know Fas Hsuan Lin's paper comparing sLORETA with dSPM, and MNE has a big mistake, the assumed source covariance matrix is not the identity matrix, and that violates the beauty of the math and results in non-zero localization bias. That's why in Brainstorm the prior source covariance matrix used for sLORETA automatically uses no depth bias compensation (identity matrix). sLORETA accomplishes depth bias compensation via the resolution matrix, NOT via the prior source covariance matrix. Trying to use a depth exponent of 0.7 or 0.8 like we do for MNE and dSPM will mess up sLORETA.You will not find this in a paper, but I checked it all out many years ago. This is critical.

Explain sLORETA units (see email exchanges from Feb 2015)


Issues with dSPM average

Average(dSPM) is NOT equal to dSPM(Average).

There is no problem for the MNE and sLORETA solutions, because the scaling of the noise covariance matrix doesn't impact the results.
    wMNE(Data, NoiseCov) = wMNE(Data, NoiseCov / N)
So when we average we get:
    Average(wMNE(Trials, NoiseCov)) = wMNE(Average, NoiseCov) = wMNE(Average, NoiseCov / N)

But for dSPM we have:
    dSPM(Data, NoiseCov) = dSPM(Data, NoiseCov / N) ./ sqrt(N)
So when we average we get:
    Average(dSPM(Trials, NoiseCov)) = dSPM(Average, NoiseCov) = dSPM(Average, NoiseCov / N) ./ sqrt(N)

Rey: "Basically, the dSPM value at each location is equal to the wMNE value divided by the projection of the estimated noise covariance matrix onto each source point. After whitening, the operational noise covariance matrix is by definition the identity matrix, and hence the projection of the noise is equal to the L2 norm of the row vector of the wMNE inverse operator (in the case of fixed dipole orientations). So, dSPM is what you get when the rows of the wMNE inverse operator all have unit norm (i.e., they all point in different directions but lie in a unit hyper-sphere)."

Rey: "dSPM is really a source mapping of SNR, not of activity. Hence, it's not all so surprising that the single trial SNR maps are smaller...

"Rey: "Perhaps, dSPM should be used only for averaged data (i.e., ERF, ERP), at least until it's all figure out. In a way, dSPM is just MNE followed by the noise normalization. Thus, you could do all the single trial processing with the MNE algorithm, and only do the noise normalization when needed (e.g., after averaging or on single trials only if they are not going to be averaged)."

On the hard drive

Document file tags

Document file structure

Differences for kernel vs. sources

Differences for constrained vs. unconstrained

in_bst_results to get the full sources or apply any process

Links: These links are not saved as files but as specific strings in the database: "link|kernel_file|data_file". This means that to represent them, one should load the shared kernel, load the recordings, and multiply them.


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Tutorials/SourceEstimation (last edited 2015-08-13 22:47:36 by FrancoisTadel)