

.. _ch_mne:

=====================
The current estimates
=====================

Overview
########

This Chapter describes the computation of the minimum-norm
estimates. This is accomplished with two programs: *mne_inverse_operator* and *mne_make_movie*.
The chapter starts with a mathematical description of the method,
followed by description of the two software modules. The interactive
program for inspecting data and inverse solutions, mne_analyze ,
is covered in :ref:`ch_interactive_analysis`.

.. _CBBDJFBJ:

Minimum-norm estimates
######################

This section describes the mathematical details of the calculation
of minimum-norm estimates. In Bayesian sense, the ensuing current
distribution is the maximum a posteriori (MAP) estimate under the
following assumptions:

- The viable locations of the currents
  are constrained to the cortex. Optionally, the current orientations
  can be fixed to be normal to the cortical mantle.

- The amplitudes of the currents have a Gaussian prior distribution
  with a known source covariance matrix.

- The measured data contain additive noise with a Gaussian distribution with
  a known covariance matrix. The noise is not correlated over time.

The linear inverse operator
===========================

The measured data in the source estimation procedure consists
of MEG and EEG data, recorded on a total of N channels. The task
is to estimate a total of M strengths of sources located on the
cortical mantle. If the number of source locations is P, M = P for
fixed-orientation sources and M = 3P if the source orientations
are unconstrained. The regularized linear inverse operator following
from the Bayesian approach is given by the :math:`M \times N` matrix

.. math::    M = R' G^T (G R' G^T + C)^{-1}\ ,

where G is the gain matrix relating the source strengths
to the measured MEG/EEG data, :math:`C` is the data noise-covariance matrix
and :math:`R'` is the source covariance matrix.
The dimensions of these matrices are :math:`N \times M`, :math:`N \times N`,
and :math:`M \times M`, respectively. The :math:`M \times 1` source-strength
vector is obtained by multiplying the :math:`N \times 1` data
vector by :math:`M`.

The expected value of the current amplitudes at time *t* is
then given by :math:`\hat{j}(t) = Mx(t)`, where :math:`x(t)` is
a vector containing the measured MEG and EEG data values at time *t*.

.. _CBBHAAJJ:

Regularization
==============

The a priori variance of the currents is, in practise, unknown.
We can express this by writing :math:`R' = R/ \lambda^2`,
which yields the inverse operator

.. math::    M = R G^T (G R G^T + \lambda^2 C)^{-1}\ ,

where the unknown current amplitude is now interpreted in
terms of the regularization parameter :math:`\lambda^2`.
Small :math:`\lambda^2` corresponds to large current amplitudes
and complex estimate current patterns while a large :math:`\lambda^2` means the
amplitude of the current is limited and a simpler, smooth, current
estimate is obtained.

We can arrive in the regularized linear inverse operator
also by minimizing the cost function

.. math::    S = \tilde{e}^T \tilde{e} + \lambda^2 j^T R^{-1} j\ ,

where the first term consists of the difference between the
whitened measured data (see :ref:`CHDDHAGE`) and those predicted
by the model while the second term is a weighted-norm of the current
estimate. It is seen that, with increasing :math:`\lambda^2`,
the source term receive more weight and larger discrepancy between
the measured and predicted data is tolerable.

.. _CHDDHAGE:

Whitening and scaling
=====================

The MNE software employs data whitening so that a 'whitened' inverse operator
assumes the form

.. math::    \tilde{M} = R \tilde{G}^T (\tilde{G} R \tilde{G}^T + I)^{-1}\ ,

where :math:`\tilde{G} = C^{-^1/_2}G` is the spatially
whitened gain matrix. The expected current values are :math:`\hat{j} = Mx(t)`,
where :math:`x(t) = C^{-^1/_2}x(t)` is a the whitened measurement
vector at *t*. The spatial whitening operator
is obtained with the help of the eigenvalue decomposition :math:`C = U_C \Lambda_C^2 U_C^T` as :math:`C^{-^1/_2} = \Lambda_C^{-1} U_C^T`.
In the MNE software the noise-covariance matrix is stored as the
one applying to raw data. To reflect the decrease of noise due to
averaging, this matrix, :math:`C_0`, is scaled
by the number of averages, :math:`L`, *i.e.*, :math:`C = C_0 / L`.

As shown above, regularization of the inverse solution is
equivalent to a change in the variance of the current amplitudes
in the Bayesian *a priori* distribution.

Convenient choice for the source-covariance matrix :math:`R` is
such that :math:`\text{trace}(\tilde{G} R \tilde{G}^T) / \text{trace}(I) = 1`. With this choice we
can approximate :math:`\lambda^2 \sim 1/SNR`, where SNR is
the (power) signal-to-noise ratio of the whitened data.

.. note:: The definition of the signal to noise-ratio/ :math:`\lambda^2` relationship    given above works nicely for the whitened forward solution. In the    un-whitened case scaling with the trace ratio :math:`\text{trace}(GRG^T) / \text{trace}(C)` does not make sense, since the diagonal elements summed have, in general,    different units of measure. For example, the MEG data are expressed    in T or T/m whereas the unit of EEG is Volts.

.. _CBBHEGAB:

Regularization of the noise-covariance matrix
=============================================

Since finite amount of data is usually available to compute
an estimate of the noise-covariance matrix :math:`C`,
the smallest eigenvalues of its estimate are usually inaccurate
and smaller than the true eigenvalues. Depending on the seriousness
of this problem, the following quantities can be affected:

- The model data predicted by the current
  estimate,

- Estimates of signal-to-noise ratios, which lead to estimates
  of the required regularization, see :ref:`CBBHAAJJ`,

- The estimated current values, and

- The noise-normalized estimates, see :ref:`CBBEAICH`.

Fortunately, the latter two are least likely to be affected
due to regularization of the estimates. However, in some cases especially
the EEG part of the noise-covariance matrix estimate can be deficient, *i.e.*,
it may possess very small eigenvalues and thus regularization of
the noise-covariance matrix is advisable.

The MNE software accomplishes the regularization by replacing
a noise-covariance matrix estimate :math:`C` with

.. math::    C' = C + \sum_k {\varepsilon_k \bar{\sigma_k}^2 I^{(k)}}\ ,

where the index :math:`k` goes across
the different channel groups (MEG planar gradiometers, MEG axial
gradiometers and magnetometers, and EEG), :math:`\varepsilon_k` are
the corresponding regularization factors, :math:`\bar{\sigma_k}` are
the average variances across the channel groups, and :math:`I^{(k)}` are
diagonal matrices containing ones at the positions corresponding
to the channels contained in each channel group. The values :math:`\varepsilon_k` can
be adjusted with the regularization options ``--magreg`` , ``--gradreg`` ,
and ``--eegreg`` specified at the time of the inverse operator
decomposition, see :ref:`CBBDDBGF`. The convenience script mne_do_inverse_solution has
the ``--magreg`` and ``--gradreg`` combined to
a single option, ``--megreg`` , see :ref:`CIHCFJEI`.
Suggested range of values for :math:`\varepsilon_k` is :math:`0.05 \dotso 0.2`.

.. _CHDBEHBC:

Computation of the solution
===========================

The most straightforward approach to calculate the MNE is
to employ expression for the original or whitened inverse operator
directly. However, for computational convenience we prefer to take
another route, which employs the singular-value decomposition (SVD)
of the matrix

.. math::    A = \tilde{G} R^{^1/_2} = U \Lambda V^T

where the superscript :math:`^1/_2` indicates a
square root of :math:`R`. For a diagonal matrix,
one simply takes the square root of :math:`R` while
in the more general case one can use the Cholesky factorization :math:`R = R_C R_C^T` and
thus :math:`R^{^1/_2} = R_C`.

With the above SVD it is easy to show that

.. math::    \tilde{M} = R^{^1/_2} V \Gamma U^T

where the elements of the diagonal matrix :math:`\Gamma` are

.. math::    \gamma_k = \frac{1}{\lambda_k} \frac{\lambda_k^2}{\lambda_k^2 + \lambda^2}\ .

With :math:`w(t) = U^T C^{-^1/_2} x(t)` the expression for
the expected current is

.. math::    \hat{j}(t) = R^C V \Gamma w(t) = \sum_k {\bar{v_k} \gamma_k w_k(t)}\ ,

where :math:`\bar{v_k} = R^C v_k`, :math:`v_k` being
the :math:`k` th column of :math:`V`. It is thus seen that the current estimate is
a weighted sum of the 'modified' eigenleads :math:`v_k`.

It is easy to see that :math:`w(t) \propto \sqrt{L}`.
To maintain the relation :math:`(\tilde{G} R \tilde{G}^T) / \text{trace}(I) = 1` when :math:`L` changes
we must have :math:`R \propto 1/L`. With this approach, :math:`\lambda_k` is
independent of  :math:`L` and, for fixed :math:`\lambda`,
we see directly that :math:`j(t)` is independent
of :math:`L`.

.. _CBBEAICH:

Noise normalization
===================

The noise-normalized linear estimates introduced by Dale
et al. require division of the expected current amplitude by its
variance. Noise normalization serves three purposes:

- It converts the expected current value
  into a dimensionless statistical test variable. Thus the resulting
  time and location dependent values are often referred to as dynamic
  statistical parameter maps (dSPM).

- It reduces the location bias of the estimates. In particular,
  the tendency of the MNE to prefer superficial currents is eliminated.

- The width of the point-spread function becomes less dependent
  on the source location on the cortical mantle. The point-spread
  is defined as the MNE resulting from the signals coming from a point
  current source (a current dipole) located at a certain point on
  the cortex.

In practice, noise normalization requires the computation
of the diagonal elements of the matrix

.. math::    M C M^T = \tilde{M} \tilde{M}^T\ .

With help of the singular-value decomposition approach we
see directly that

.. math::    \tilde{M} \tilde{M}^T\ = \bar{V} \Gamma^2 \bar{V}^T\ .

Under the conditions expressed at the end of :ref:`CHDBEHBC`, it follows that the *t*-statistic values associated
with fixed-orientation sources) are thus proportional to :math:`\sqrt{L}` while
the *F*-statistic employed with free-orientation sources is proportional
to :math:`L`, correspondingly.

.. note:: A section discussing statistical considerations    related to the noise normalization procedure will be added to this    manual in one of the subsequent releases.

.. note:: The MNE software usually computes the square    roots of the F-statistic to be displayed on the inflated cortical    surfaces. These are also proportional to :math:`\sqrt{L}`.

.. _CHDCACDC:

Predicted data
==============

Under noiseless conditions the SNR is infinite and thus leads
to :math:`\lambda^2 = 0` and the minimum-norm estimate
explains the measured data perfectly. Under realistic conditions,
however, :math:`\lambda^2 > 0` and there is a misfit
between measured data and those predicted by the MNE. Comparison
of the predicted data, here denoted by :math:`x(t)`,
and measured one can give valuable insight on the correctness of
the regularization applied.

In the SVD approach we easily find

.. math::    \hat{x}(t) = G \hat{j}(t) = C^{^1/_2} U \Pi w(t)\ ,

where the diagonal matrix :math:`\Pi` has
elements :math:`\pi_k = \lambda_k \gamma_k` The predicted data is
thus expressed as the weighted sum of the 'recolored eigenfields' in :math:`C^{^1/_2} U`.

.. _CBBDBHDI:

Cortical patch statistics
=========================

If the ``--cps`` option was used in source space
creation (see :ref:`CIHCHDAE`) or if mne_add_patch_info described
in :ref:`BEHCBCGG` was run manually the source space file
will contain for each vertex of the cortical surface the information
about the source space point closest to it as well as the distance
from the vertex to this source space point. The vertices for which
a given source space point is the nearest one define the cortical
patch associated with with the source space point. Once these data
are available, it is straightforward to compute the following cortical
patch statistics (CPS) for each source location :math:`d`:

- The average over the normals of at the
  vertices in a patch, :math:`\bar{n_d}`,

- The areas of the patches, :math:`A_d`,
  and

- The average deviation of the vertex normals in a patch from
  their average, :math:`\sigma_d`, given in degrees.

The orientation constraints
===========================

The principal sources of MEG and EEG signals are generally
believed to be postsynaptic currents in the cortical pyramidal neurons.
Since the net primary current associated with these microscopic
events is oriented normal to the cortical mantle, it is reasonable
to use the cortical normal orientation as a constraint in source
estimation. In addition to allowing completely free source orientations,
the MNE software implements three orientation constraints based
of the surface normal data:

- Source orientation can be rigidly fixed
  to the surface normal direction (the ``--fixed`` option).
  If cortical patch statistics are available the average normal over
  each patch, :math:`\bar{n_d}`, are used to define
  the source orientation. Otherwise, the vertex normal at the source
  space location is employed.

- A *location independent or fixed loose orientation
  constraint* (fLOC) can be employed (the ``--loose`` option).
  In this approach, a source coordinate system based on the local
  surface orientation at the source location is employed. By default,
  the three columns of the gain matrix G, associated with a given
  source location, are the fields of unit dipoles pointing to the
  directions of the x, y, and z axis of the coordinate system employed
  in the forward calculation (usually the MEG head coordinate frame).
  For LOC the orientation is changed so that the first two source
  components lie in the plane normal to the surface normal at the source
  location and the third component is aligned with it. Thereafter, the
  variance of the source components tangential to the cortical surface are
  reduced by a factor defined by the ``--loose`` option.

- A *variable loose orientation constraint* (vLOC)
  can be employed (the ``--loosevar`` option). This is similar
  to fLOC except that the value given with the ``--loosevar`` option
  will be multiplied by :math:`\sigma_d`, defined above.

.. _CBBDFJIE:

Depth weighting
===============

The minimum-norm estimates have a bias towards superficial
currents. This tendency can be alleviated by adjusting the source
covariance matrix :math:`R` to favor deeper source locations. In the depth
weighting scheme employed in MNE analyze, the elements of :math:`R` corresponding
to the :math:`p` th source location are be
scaled by a factor

.. math::    f_p = (g_{1p}^T g_{1p} + g_{2p}^T g_{2p} + g_{3p}^T g_{3p})^{-\gamma}\ ,

where :math:`g_{1p}`, :math:`g_{2p}`, and :math:`g_{3p}` are the three columns
of :math:`G` corresponding to source location :math:`p` and :math:`\gamma` is
the order of the depth weighting, specified with the ``--weightexp`` option
to mne_inverse_operator . The
maximal amount of depth weighting can be adjusted ``--weightlimit`` option.

.. _CBBDIJHI:

fMRI-guided estimates
=====================

The fMRI weighting in MNE software means that the source-covariance matrix
is modified to favor areas of significant fMRI activation. For this purpose,
the fMRI activation map is thresholded first at the value defined by
the ``--fmrithresh`` option to mne_do_inverse_operator or mne_inverse_operator .
Thereafter, the source-covariance matrix values corresponding to
the the sites under the threshold are multiplied by :math:`f_{off}`, set
by the ``--fmrioff`` option.

It turns out that the fMRI weighting has a strong influence
on the MNE but the noise-normalized estimates are much less affected
by it.

.. _CBBDGIAE:

Effective number of averages
############################

It is often the case that the epoch to be analyzed is a linear
combination over conditions rather than one of the original averages
computed. As stated above, the noise-covariance matrix computed
is originally one corresponding to raw data. Therefore, it has to
be scaled correctly to correspond to the actual or effective number
of epochs in the condition to be analyzed. In general, we have

.. math::    C = C_0 / L_{eff}

where :math:`L_{eff}` is the effective
number of averages. To calculate :math:`L_{eff}` for
an arbitrary linear combination of conditions

.. math::    y(t) = \sum_{i = 1}^n {w_i x_i(t)}

we make use of the the fact that the noise-covariance matrix

.. math::    C_y = \sum_{i = 1}^n {w_i^2 C_{x_i}} = C_0 \sum_{i = 1}^n {w_i^2 / L_i}

which leads to

.. math::    1 / L_{eff} = \sum_{i = 1}^n {w_i^2 / L_i}

An important special case  of the above is a weighted average,
where

.. math::    w_i = L_i / \sum_{i = 1}^n {L_i}

and, therefore

.. math::    L_{eff} = \sum_{i = 1}^n {L_i}

Instead of a weighted average, one often computes a weighted
sum, a simplest case being a difference or sum of two categories.
For a difference :math:`w_1 = 1` and :math:`w_2 = -1` and
thus

.. math::    1 / L_{eff} = 1 / L_1 + 1 / L_2

or

.. math::    L_{eff} = \frac{L_1 L_2}{L_1 + L_2}

Interestingly, the same holds for a sum, where :math:`w_1 = w_2 = 1`.
Generalizing, for any combination of sums and differences, where :math:`w_i = 1` or :math:`w_i = -1`, :math:`i = 1 \dotso n`,
we have

.. math::    1 / L_{eff} = \sum_{i = 1}^n {1/{L_i}}

.. _CBBDDBGF:

Inverse-operator decomposition
##############################

The program ``mne_inverse_operator`` calculates
the decomposition :math:`A = \tilde{G} R^C = U \Lambda \bar{V^T}`, described in :ref:`CHDBEHBC`. It is normally invoked from the convenience
script ``mne_do_inverse_operator`` . This section describes
the options to ``mne_inverse_operator`` should a user need
to invoke it directly for special-purpose processing.

The command-line options of ``mne_inverse_operator`` are:

**\---version**

    Show the program version and compilation date.

**\---help**

    List the command-line options.

**\---meg**

    Employ MEG data in the calculation of the estimates.

**\---eeg**

    Employ EEG data in the calculation of the estimates. Note: The EEG
    computations have not been thoroughly tested at this time.

**\---fixed**

    Use fixed source orientations normal to the cortical mantle. By default,
    the source orientations are not constrained.

**\---loose <*amount*>**

    Employ a loose orientation constraint (LOC). This means that the source
    covariance matrix entries corresponding to the current component
    normal to the cortex are set equal to one and the transverse components
    are set to <*amount*> . Recommended
    value of amount is 0.2...0.6.

**\---loosevar <*amount*>**

    Use an adaptive loose orientation constraint. This option can be
    only employed if the source spaces included in the forward solution
    have the patch information computed, see :ref:`CIHCHDAE`. Blaa
    blaa...***what???**

**\---fwd <*name*>**

    Specifies the name of the forward solution to use.

**\---noisecov <*name*>**

    Specifies the name of the noise-covariance matrix to use. If this
    file contains a projection operator, attached by mne_browse_raw and mne_process_raw ,
    no additional projection vectors can be added with the ``--proj`` option. For
    backward compatibility, ``--senscov`` can be used as a synonym for ``--noisecov``.

**\---noiserank <*value*>**

    Specifies the rank of the noise covariance matrix explicitly rather than
    trying to reduce it automatically. This option is seldom needed,

**\---gradreg <*value*>**

    Regularize the planar gradiometer section (channels for which the unit
    of measurement is T/m) of the noise-covariance matrix by the given
    amount. The value is restricted to the range 0...1. For details, see :ref:`CBBHEGAB`.

**\---magreg <*value*>**

    Regularize the magnetometer and axial gradiometer section (channels
    for which the unit of measurement is T) of the noise-covariance matrix
    by the given amount. The value is restricted to the range 0...1.
    For details, see :ref:`CBBHEGAB`.

**\---eegreg <*value*>**

    Regularize the EEG section of the noise-covariance matrix by the given
    amount. The value is restricted to the range 0...1. For details, see :ref:`CBBHEGAB`.

**\---diagnoise**

    Omit the off-diagonal terms from the noise-covariance matrix in
    the computations. This may be useful if the amount of signal-free
    data has been insufficient to calculate a reliable estimate of the
    full noise-covariance matrix.

**\---srccov <*name*>**

    Specifies the name of the diagonal source-covariance matrix to use.
    By default the source covariance matrix is a multiple of the identity matrix.
    This option can be employed to incorporate the fMRI constraint.
    The software to create a source-covariance matrix file from fMRI
    data will be provided in a future release of this software package.

**\---depth**

    Employ depth weighting. For details, see :ref:`CBBDFJIE`.

**\---weightexp <*value*>**

    This parameter determines the steepness of the depth weighting function
    (default = 0.8). For details, see :ref:`CBBDFJIE`.

**\---weightlimit <*value*>**

    Maximum relative strength of the depth weighting (default = 10). For
    details, see :ref:`CBBDFJIE`.

**\---fmri <*name*>**

    With help of this w file, an *a priori* weighting
    can be applied to the source covariance matrix. The source of the
    weighting is usually fMRI but may be also some other data, provided
    that the weighting  can be expressed as a scalar value on the cortical
    surface, stored in a w file. It is recommended that this w file
    is appropriately smoothed (see :ref:`CHDEBAHH`) in mne_analyze , tksurfer or
    with mne_smooth_w to contain
    nonzero values at all vertices of the triangular tessellation of
    the cortical surface. The name of the file given is used as a stem of
    the w files. The actual files should be called <*name*> ``-lh.pri`` and <*name*> ``-rh.pri`` for
    the left and right hemsphere weight files, respectively. The application
    of the weighting is discussed in :ref:`CBBDIJHI`.

**\---fmrithresh <*value*>**

    This option is mandatory and has an effect only if a weighting function
    has been specified with the ``--fmri`` option. If the value
    is in the *a priori* files falls below this value
    at a particular source space point, the source covariance matrix
    values are multiplied by the value specified with the ``--fmrioff`` option
    (default 0.1). Otherwise it is left unchanged.

**\---fmrioff <*value*>**

    The value by which the source covariance elements are multiplied
    if the *a priori* weight falls below the threshold
    set with ``--fmrithresh`` , see above.

**\---bad <*name*>**

    A text file to designate bad channels, listed one channel name on each
    line of the file. If the noise-covariance matrix specified with the ``--noisecov`` option
    contains projections, bad channel lists can be included only if
    they specify all channels containing non-zero entries in a projection
    vector. For example, bad channels can usually specify all magnetometers
    or all gradiometers since the projection vectors for these channel
    types are completely separate. Similarly, it is possible to include
    MEG data only or EEG data only by using only one of ``--meg`` or ``--eeg`` options
    since the projection vectors for MEG and EEG are always separate.

**\---surfsrc**

    Use a source coordinate system based on the local surface orientation
    at the source location. By default, the three dipole components are
    pointing to the directions of the x, y, and z axis of the coordinate system
    employed in the forward calculation (usually the MEG head coordinate
    frame). This option changes the orientation so that the first two
    source components lie in the plane normal to the surface normal
    at the source location and the third component is aligned with it.
    If patch information is available in the source space, the normal
    is the average patch normal, otherwise the vertex normal at the source
    location is used. If the ``--loose`` or ``--loosevar`` option
    is employed, ``--surfsrc`` is implied.

**\---exclude <*name*>**

    Exclude the source space points defined by the given FreeSurfer 'label' file
    from the source reconstruction. This is accomplished by setting
    the corresponding entries in the source-covariance matrix equal
    to zero. The name of the file should end with ``-lh.label``
    if it refers to the left hemisphere and with ``-rh.label`` if
    it lists points in the right hemisphere, respectively.

**\---proj <*name*>**

    Include signal-space projection (SSP) information from this file. For information
    on SSP, see :ref:`CACCHABI`. If the projections are present in
    the noise-covariance matrix, the ``--proj`` option is
    not allowed.

**\---csd**

    Compute the inverse operator for surface current densities instead
    of the dipole source amplitudes. This requires the computation of patch
    statistics for the source space. Since this computation is time consuming,
    it is recommended that the patch statistics are precomputed and
    the source space file containing the patch information is employed
    already when the forward solution is computed, see :ref:`CIHCHDAE` and :ref:`BABCHEJD`.
    For technical details of the patch information, please consult :ref:`CBBDBHDI`. This option is considered experimental at
    the moment.

**\---inv <*name*>**

    Save the inverse operator decomposition here.

.. _CBBECEDE:

Producing movies and snapshots
##############################

mne_make_movie is a program
for producing movies and snapshot graphics frames without any graphics
output to the screen. In addition, mne_make_movie can
produce stc or w files which contain the numerical current estimate
data in a simple binary format for postprocessing. These files can
be displayed in mne_analyze ,
see :ref:`ch_interactive_analysis`, utilized in the cross-subject averaging
process, see :ref:`ch_morph`, and read into Matlab using the MNE
Matlab toolbox, see :ref:`ch_matlab`.

The command-line options to mne_make_movie are
explained in the following subsections.

General options
===============

**\---version**

    Show the program version and compilation date.

**\---help**

    List the command-line options.

Input files
===========

**\---inv <*name*>**

    Load the inverse operator decomposition from here.

**\---meas <*name*>**

    Load the MEG or EEG data from this file.

**\---set <*number*>**

    The data set (condition) number to load. This is the sequential
    number of the condition. You can easily see the association by looking
    at the condition list in mne_analyze when
    you load the file.

**\---stcin <*name*>**

    Specifies an stc file to read as input.

Times and baseline
==================

**\---tmin <*time/ms*>**

    Specifies the starting time employed in the analysis. If ``--tmin`` option
    is missing the analysis starts from the beginning of the epoch.

**\---tmax <*time/ms*>**

    Specifies the finishing time employed in the analysis. If ``--tmax`` option
    is missing the analysis extends to the end of the epoch.

**\---tstep <*step/ms*>**

    Time step between consequtive movie frames, specified in milliseconds.

**\---integ  <*:math:`\Delta`t/ms*>**

    Integration time for each frame. Defaults to zero. The integration will
    be performed on sensor data. If the time specified for a frame is :math:`t_0`,
    the integration range will be :math:`t_0 - \Delta t/2 \leq t \leq t_0 + \Delta t/2`.

**\---pick <*time/ms*>**

    Pick a time for the production of rgb, tif, jpg, png, or w files.
    Several pick options may be present. The time must be with in the
    analysis interval, indicated by the ``--tmin`` and ``--tmax`` options.
    The ``--rgb`` , ``--tif`` , ``--jpg`` , ``--png`` , and ``--w`` options
    control which file types are actually produced. When a ``--pick`` option
    is encountered, the effect of any preceding ``--pickrange`` option
    is ignored.

**\---pickrange**

    All previous ``-pick`` options will be ignored. Instead,
    snapshots are produced as indicated by the ``--tmin`` , ``--tmax`` ,
    and ``--tstep`` options. This is useful, *e.g.*,
    for producing input for scripts merging the individual graphics
    snapshots into a composite "filmstrip" reprensentation.
    However, such scripts are not yet part of the MNE software.

**\---bmin <*time/ms*>**

    Specifies the starting time of the baseline. In order to activate
    baseline correction, both ``--bmin`` and ``--bmax`` options
    must be present.

**\---bmax <*time/ms*>**

    Specifies the finishing time of the baseline.

**\---baselines <*file_name*>**

    Specifies a file which contains the baseline settings. Each line
    of the file should contain a name of a channel, followed by the
    baseline value, separated from the channel name by a colon. The
    baseline values must be specified in basic units, i.e., Teslas/meter
    for gradiometers, Teslas for magnetometers, and Volts for EEG channels.
    If some channels are missing from the baseline file, warning messages are
    issued: for these channels, the ``--bmin`` and ``--bmax`` settings will
    be used.

Options controlling the estimates
=================================

**\---nave <*value*>**

    Specifies the effective number of averaged epochs in the input data, :math:`L_{eff}`,
    as discussed in :ref:`CBBDGIAE`. If the input data file is
    one produced by mne_browse_raw or mne_process_raw , the
    number of averages is correct in the file. However, if subtractions
    or some more complicated combinations of simple averages are produced,
    e.g., by  using the xplotter software,
    the number of averages should be manually adjusted along the guidelines
    given in :ref:`CBBDGIAE`. This is accomplished either by
    employing this flag or by adjusting the number of averages in the
    data file with help of the utility mne_change_nave .

**\---snr <*value*>**

    An estimate for the amplitude SNR. The regularization parameter will
    be set as :math:`\lambda^2 = 1/SNR^2`. The default value is
    SNR = 3. Automatic selection of the regularization parameter is
    currently not supported.

**\---spm**

    Calculate the dSPM instead of the expected current value.

**\---sLORETA**

    Calculate the noise-normalized estimate using the sLORETA approach.
    sLORETA solutions have in general a smaller location bias than either
    the expected current (MNE) or the dSPM.

**\---signed**

    Indicate the current direction with respect to the cortex outer
    normal by sign. Currents flowing out of the cortex are thus considered
    positive (warm colors) and currents flowing into the cortex negative (cold
    colors).

**\---picknormalcomp**

    The components of the estimates corresponding to directions tangential
    with the cortical mantle are zeroed out.

.. _CBBBBHIF:

Visualization options
=====================

**\---subject <*subject*>**

    Specifies the subject whose MRI data is employed in the visualization.
    This must be the same subject that was used for computing the current
    estimates. The environment variable SUBJECTS_DIR must be set to
    point to a locations where the subjects are to be found.

**\---morph <*subject*>**

    Morph the data to to the cortical surface of another subject. The Quicktime
    movie, stc-file, graphics snapshot, and w-file outputs are affected
    by this option, *i.e.*, they will take the morphing
    into account and will represent the data on the cortical surface
    of the subject defined with this option. The stc files morphed to
    a single subject's cortical surface are used by mne_average_estimates to
    combine data from different subjects, see :ref:`CHDFDIFE`.
    If morphing is selected appropriate smoothing must be specified
    with the ``--smooth`` option. The morphing process can
    be made faster by precomputing the necessary morphing maps with mne_make_morph_maps ,
    see :ref:`CHDBBHDH`. More information about morphing and averaging
    can be found in :ref:`ch_morph`.

**\---morphgrade <*number*>**

    Adjusts the number of vertices in the stc files produced when morphing
    is in effect. By default the number of vertices is 10242 corresponding
    to --morphgrade value 5. Allowed values are 3, 4, 5, and 6 corresponding
    to 642, 2562, 10242, and 40962 vertices, respectively.

**\---surface <*surface name*>**

    Name of the surface employed in the visualization. The default is inflated .

**\---curv <*name*>**

    Specify a nonstandard curvature file name. The default curvature files
    are ``lh.curv`` and ``rh.curv`` . With this option,
    the names become ``lh.`` <*name*> and ``rh.`` <*name*> .

**\---patch <*name*> [: <*angle/deg*> ]**

    Specify the name of a surface patch to be used for visualization instead
    of the complete cortical surface. A complete name of a patch file
    in the FreeSurface surf directory must be given. The name should
    begin with lh or rh to allow association of the patch with a hemisphere.
    Maximum of two ``--patch`` options can be in effect, one patch for each
    hemisphere. If the name refers to a flat patch, the name can be
    optionally followed by a colon and a rotation angle in degrees.
    The flat patch will be then rotated counterclockwise by this amount
    before display. You can check a suitable value for the rotation
    angle by loading the patch interactively in mne_analyze .

**\---width <*value*>**

    Width of the graphics output frames in pixels. The default width
    is 600 pixels.

**\---height <*value*>**

    Height of the graphics output frames in pixels. The default height
    is 400 pixels.

**\---mag <*factor*>**

    Magnify the the visualized scene by this factor.

**\---lh**

    Select the left hemisphere for graphics output. By default, both hemisphere
    are processed.

**\---rh**

    Select the right hemisphere for graphics output. By default, both hemisphere
    are processed.

**\---view <*name*>**

    Select the name of the view for mov, rgb, and tif graphics output files.
    The default viewnames, defined in ``$MNE_ROOT/share/mne/mne_analyze/eyes`` ,
    are *lat* (lateral), *med* (medial), *ven* (ventral),
    and *occ* (occipital). You can override these
    defaults by creating the directory .mne under your home directory
    and copying the eyes file there. Each line of the eyes file contais
    the name of the view, the viewpoint for the left hemisphere, the
    viewpoint for the right hemisphere, left hemisphere up vector, and
    right hemisphere up vector. The entities are separated by semicolons.
    Lines beginning with the pound sign (#) are considered to be comments.

**\---smooth <*nstep*>**

    Number of smoothsteps to take when producing the output frames. Depending
    on the source space decimation, an appropriate number is 4 - 7.
    Smoothing does not have any effect for the original brain if stc
    files are produced. However, if morphing is selected smoothing is
    mandatory even with stc output. For details of the smoothing procedure,
    see :ref:`CHDEBAHH`.

**\---nocomments**

    Do not include the comments in the image output files or movies.

**\---noscalebar**

    Do not include the scalebar in the image output files or movies.

**\---alpha <*value*>**

    Adjust the opacity of maps shown on the cortical surface (0 = transparent,
    1 = totally opaque). The default value is 1.

Thresholding
============

**\---fthresh <*value*>**

    Specifies the threshold for the displayed colormaps. At the threshold,
    the overlayed color will be equal to the background surface color.
    For currents, the value will be multiplied by :math:`1^{-10}`.
    The default value is 8.

**\---fmid <*value*>**

    Specifies the midpoint for the displayed colormaps. At this value, the
    overlayed color will be read (positive values) or blue (negative values).
    For currents, the value will be multiplied by :math:`1^{-10}`.
    The default value is 15.

**\---fmax <*value*>**

    Specifies the maximum point for the displayed colormaps. At this value,
    the overlayed color will bright yellow (positive values) or light
    blue (negative values). For currents, the value will be multiplied
    by :math:`1^{-10}`. The default value is 20.

**\---fslope <*value*>**

    Included for backwards compatibility. If this option is specified
    and ``--fmax`` option is *not* specified, :math:`F_{max} = F_{mid} + 1/F_{slope}`.

Output files
============

**\---mov <*name*>**

    Produce QuickTime movie files. This is the 'stem' of
    the ouput file name. The actual name is derived by stripping anything
    up to and including the last period from the end of <*name*> .
    According to the hemisphere, ``-lh`` or ``-rh`` is
    then appended. The name of the view is indicated with ``-`` <*viename*> .
    Finally, ``.mov`` is added to indicate a QuickTime output
    file. The movie is produced for all times as dictated by the ``--tmin`` , ``--tmax`` , ``--tstep`` ,
    and ``--integ`` options.

**\---qual <*value*>**

    Quality of the QuickTime movie output. The default quality is 80 and
    allowed range is 25 - 100. The size of the movie files is a monotonously
    increasing function of the movie quality.

**\---rate <*rate*>**

    Specifies the frame rate of the QuickTime movies. The default value is :math:`1/(10t_{step})`,
    where :math:`t_{step}` is the time between subsequent
    movie frames produced in seconds.

**\---rgb <*name*>**

    Produce rgb snapshots. This is the 'stem' of the
    ouput file name. The actual name is derived by stripping anything
    up to and including the last period from the end of <*name*> .
    According to the hemisphere, ``-lh`` or ``-rh`` is
    then appended. The name of the view is indicated with ``-`` <*viename*> .
    Finally, ``.rgb`` is added to indicate an rgb output file.
    Files are produced for all picked times as dictated by the ``--pick`` and ``--integ`` options.

**\---tif <*name*>**

    Produce tif snapshots. This is the 'stem' of the
    ouput file name. The actual name is derived by stripping anything
    up to and including the last period from the end of <*name*> .
    According to the hemisphere, ``-lh`` or ``-rh`` is
    then appended. The name of the view is indicated with ``-`` <*viename*> .
    Finally, ``.tif`` is added to indicate an rgb output file.
    Files are produced for all picked times as dictated by the ``--pick`` and ``--integ`` options.
    The tif output files are *not* compressed. Pass
    the files through an image processing program to compress them.

**\---jpg <*name*>**

    Produce jpg snapshots. This is the 'stem' of the
    ouput file name. The actual name is derived by stripping anything
    up to and including the last period from the end of <*name*> .
    According to the hemisphere, ``-lh`` or ``-rh`` is
    then appended. The name of the view is indicated with ``-`` <*viename*> .
    Finally, ``.jpg`` is added to indicate an rgb output file.
    Files are produced for all picked times as dictated by the ``--pick`` and ``--integ`` options.

**\---png <*name*>**

    Produce png snapshots. This is the 'stem' of the
    ouput file name. The actual name is derived by stripping anything
    up to and including the last period from the end of <*name*> .
    According to the hemisphere, ``-lh`` or ``-rh`` is
    then appended. The name of the view is indicated with ``-`` <*viename*> .
    Finally, ``.png`` is added to indicate an rgb output file.
    Files are produced for all picked times as dictated by the ``--pick`` and ``--integ`` options.

**\---w <*name*>**

    Produce w file snapshots. This is the 'stem' of
    the ouput file name. The actual name is derived by stripping anything
    up to and including the last period from the end of <*name*> .
    According to the hemisphere, ``-lh`` .w or ``-rh`` .w
    is then appended. Files are produced for all picked times as dictated
    by the ``--pick`` and ``--integ`` options.

**\---stc <*name*>**

    Produce stc files for either the original subject or the one selected with
    the ``--morph`` option. These files will contain data only
    for the decimated locations. If morphing is selected, appropriate
    smoothing is mandatory. The morphed maps will be decimated with
    help of a subdivided icosahedron so that the morphed stc files will
    always contain 10242 vertices. These morphed stc files can be easily
    averaged together, e.g., in Matlab since they always contain an
    identical set of vertices.

**\---norm <*name*>**

    Indicates that a separate w file
    containing the noise-normalization values will be produced. The
    option ``--spm`` must also be present. Nevertheless, the
    movies and stc files output will
    contain MNE values. The noise normalization data files will be called <*name*>- <*SNR*> ``-lh.w`` and <*name*>- <*SNR*> ``-rh.w`` .

.. _CBBHHCEF:

Label processing
================

**\---label <*name*>**

    Specifies a label file to process. For each label file, the values
    of the computed estimates are listed in text files. The label files
    are produced by tksurfer or mne_analyze and
    specify regions of interests (ROIs). A label file name should end
    with ``-lh.label`` for left-hemisphere ROIs and with ``-rh.label`` for
    right-hemisphere ones. The corresponding output files are tagged
    with ``-lh-`` <*data type*> ``.amp`` and ``-rh-`` <*data type*> ``.amp``, respectively. <*data type*> equals ``'mne`` ' for
    expected current data and ``'spm`` ' for
    dSPM data. Each line of the output file contains the waveform of
    the output quantity at one of the source locations falling inside
    the ROI. For more information about the label output formats, see :ref:`CACJJGFA`.

**\---labelcoords**

    Include coordinates of the vertices in the output. The coordinates will
    be listed in millimeters in the coordinate system which was specified
    for the forward model computations. This option cannot be used with
    stc input files (``--stcin`` ) because the stc files do
    not contain the coordinates of the vertices.

**\---labelverts**

    Include vertex numbers in the output. The numbers refer to the complete
    triangulation of the corresponding surface and are zero based. The
    vertex numbers are by default on the first row or first column of the
    output file depending on whether or not the ``--labeltimebytime`` option
    is present.

**\---labeltimebytime**

    Output the label data time by time instead of the default vertex-by-vertex
    output.

**\---labeltag <*tag*>**

    End the output files with the specified tag. By default, the output files
    will end with ``-mne.amp`` or ``-spm.amp`` depending
    on whether MNE or one of the noise-normalized estimates (dSPM or sLORETA)
    was selected.

**\---labeloutdir <*directory*>**

    Specifies the directory where the output files will be located.
    By default, they will be in the current working directory.

**\---labelcomments**

    Include comments in the output files. The comment lines begin with the
    percent sign to make the files compatible with Matlab.

**\---scaleby <*factor*>**

    By default, the current values output to the files will be in the
    actual physical units (Am). This option allows scaling of the current
    values to other units. mne_analyze typically
    uses 1e10 to bring the numbers to a human-friendly scale.

Using stc file input
====================

The ``--stcin`` option allows input of stc files.
This feature has several uses:

- QuickTime movies can be produced from
  existing stc files without having to resort to EasyMeg.

- Graphics snapshot can be produced from existing stc files.

- Existing stc files can be temporally resampled with help of
  the ``--tmin`` , ``--tmax`` , ``--tstep`` ,
  and ``--integ`` options.

- Existing stc files can be morphed to another cortical surface
  by specifying the ``--morph`` option.

- Timecourses can be inquired and stored into text files with
  help of the ``--label`` options, see above.

.. _CBBCGHAH:

Computing inverse from raw and evoked data
##########################################

The purpose of the utility mne_compute_raw_inverse is
to compute inverse solutions from either evoked-response or raw
data at specified ROIs (labels) and to save the results in a fif
file which can be viewed with mne_browse_raw ,
read to Matlab directly using the MNE Matlab Toolbox, see :ref:`ch_matlab`,
or converted to Matlab format using either mne_convert_mne_data , mne_raw2mat ,
or mne_epochs2mat , see :ref:`ch_convert`.

.. _CHDEIHFA:

Command-line options
====================

**\---version**

    Show the program version and compilation date.

**\---help**

    List the command-line options.

**\---in <*filename*>**

    Specifies the input data file. This can be either an evoked data
    file or a raw data file.

**\---bmin <*time/ms*>**

    Specifies the starting time of the baseline. In order to activate
    baseline correction, both ``--bmin`` and ``--bmax`` options
    must be present. This option applies to evoked data only.

**\---bmax <*time/ms*>**

    Specifies the finishing time of the baseline. This option applies
    to evoked data only.

**\---set <*number*>**

    The data set (condition) number to load. This is the sequential
    number of the condition. You can easily see the association by looking
    at the condition list in mne_analyze when
    you load the file.

**\---inv <*name*>**

    Load the inverse operator decomposition from here.

**\---nave <*value*>**

    Specifies the effective number of averaged epochs in the input data, :math:`L_{eff}`,
    as discussed in :ref:`CBBDGIAE`. If the input data file is
    one produced by mne_browse_raw or mne_process_raw ,
    the number of averages is correct in the file. However, if subtractions
    or some more complicated combinations of simple averages are produced,
    e.g., by  using the xplotter software,
    the number of averages should be manually adjusted along the guidelines
    given in :ref:`CBBDGIAE`. This is accomplished either by
    employing this flag or by adjusting the number of averages in the
    data file with help of the utility mne_change_nave .

**\---snr <*value*>**

    An estimate for the amplitude SNR. The regularization parameter will
    be set as :math:`\lambda^2 = 1/SNR^2`. The default value is
    SNR = 1. Automatic selection of the regularization parameter is
    currently not supported.

**\---spm**

    Calculate the dSPM instead of the expected current value.

**\---picknormalcomp**

    The components of the estimates corresponding to directions tangential
    with the cortical mantle are zeroed out.

**\---mricoord**

    Provide source locations and orientations in the MRI coordinate frame
    instead of the default head coordinate frame.

**\---label <*name*>**

    Specifies a label file to process. For each label file, the values
    of the computed estimates stored in a fif file. For more details,
    see :ref:`CBBHJDAI`. The label files are produced by tksurfer
    or mne_analyze and specify regions
    of interests (ROIs). A label file name should end with ``-lh.label`` for
    left-hemisphere ROIs and with ``-rh.label`` for right-hemisphere
    ones. The corresponding output files are tagged with ``-lh-`` <*data type*> ``.fif`` and ``-rh-`` <*data type*> ``.fif`` , respectively. <*data type*> equals ``'mne`` ' for expected
    current data and ``'spm`` ' for dSPM data.
    For raw data, ``_raw.fif`` is employed instead of ``.fif`` .
    The output files are stored in the same directory as the label files.

**\---labelselout**

    Produces additional label files for each label processed, containing only
    those vertices within the input label which correspond to available
    source space vertices in the inverse operator. These files have the
    same name as the original label except that ``-lh`` and ``-rh`` are replaced
    by ``-sel-lh`` and ``-sel-rh`` , respectively.

**\---align_z**

    Instructs the program to try to align the waveform signs within
    the label. For more information, see :ref:`CBBHJDAI`. This
    flag will not have any effect if the inverse operator has been computed
    with the strict orientation constraint active.

**\---labeldir <*directory*>**

    All previous ``--label`` options will be ignored when this
    option is encountered. For each label in the directory, the output
    file defined with the ``--out`` option will contain a summarizing
    waveform which is the average of the waveforms in the vertices of
    the label. The ``--labeldir`` option implies ``--align_z`` and ``--picknormalcomp`` options.

**\---orignames**

    This option is used with the ``--labeldir`` option, above.
    With this option, the output file channel names will be the names
    of the label files, truncated to 15 characters, instead of names
    containing the vertex numbers.

**\---out <*name*>**

    Required with ``--labeldir`` . This is the output file for
    the data.

**\---extra <*name*>**

    By default, the output includes the current estimate signals and
    the digital trigger channel, see ``--digtrig`` option,
    below. With the ``--extra`` option, a custom set of additional
    channels can be included. The extra channel text file should contain
    the names of these channels, one channel name on each line. With
    this option present, the digital trigger channel is not included
    unless specified in the extra channel file.

**\---noextra**

    No additional channels will be included with this option present.

**\---digtrig <*name*>**

    Name of the composite digital trigger channel. The default value
    is 'STI 014'. Underscores in the channel name
    will be replaced by spaces.

**\---split <*size/MB*>**

    Specifies the maximum size of the raw data files saved. By default, the
    output is split into files which are just below 2 GB so that the
    fif file maximum size is not exceed.

.. note:: The digital trigger channel can also be set with    the MNE_TRIGGER_CH_NAME environment variable. Underscores in the variable    value will *not* be replaced with spaces by mne_compute_raw_inverse .    Using the ``--digtrig`` option supersedes the MNE_TRIGGER_CH_NAME    environment variable.

.. _CBBHJDAI:

Implementation details
======================

The fif files output from mne_compute_raw_inverse have
various fields of the channel information set to facilitate interpretation
by postprocessing software as follows:

**channel name**

    Will be set to J[xyz] <*number*> ,
    where the source component is indicated by the coordinat axis name
    and number is the vertex number, starting from zero, in the complete
    triangulation of the hemisphere in question.

**logical channel number**

    Will be set to is the vertex number, starting from zero, in the
    complete triangulation of the hemisphere in question.

**sensor location**

    The location of the vertex in head coordinates or in MRI coordinates,
    determined by the ``--mricoord`` flag.

**sensor orientation**

    The *x*-direction unit vector will point to the
    direction of the current. Other unit vectors are set to zero. Again,
    the coordinate system in which the orientation is expressed depends
    on the ``--mricoord`` flag.

The ``--align_z`` flag tries to align the signs
of the signals at different vertices of the label. For this purpose,
the surface normals within the label are collected into a :math:`n_{vert} \times 3` matrix.
The preferred orientation will be taken as the first right singular
vector of this matrix, corresponding to its largest singular value.
If the dot product of the surface normal of a vertex is negative,
the sign of the estimates at this vertex are inverted. The inversion
is reflected in the current direction vector listed in the channel
information, see above.

.. note:: The raw data files output by mne_compute_raw_inverse can be converted to mat files with mne_raw2mat, see :ref:`convert_to_matlab`. Alternatively, the files can be read directly from Matlab using the routines in the MNE Matlab toolbox, see :ref:`ch_matlab`. The evoked data output can be easily read directly from Matlab using the fiff_load_evoked routine in the MNE Matlab toolbox. Both raw data and evoked output files can be loaded into mne_browse_raw, see :ref:`ch_browse`.
