.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "generated/tutorials/megin/00_signal_space_projection.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_generated_tutorials_megin_00_signal_space_projection.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_generated_tutorials_megin_00_signal_space_projection.py:


.. _tut-artifact-ssp:

Create Signal Space Projectors
==============================

.. include:: ../../../links.inc

.. important::

    This example requires the ``meg_wiki`` package to download the sample dataset. This
    package can be installed with ``pip``:

    .. code-block:: bash

        $ pip install git+https://github.com/fcbg-platforms/meg-wiki

Background on projection
------------------------

Signal-Space Projection (SSP)\ :footcite:p:`ssp_1997` is a way of estimating a
projection matrix to remove noise from a recording by comparing measurements with and
without the signal of interest. An empty-room recording is typically used to estimate
the direction(s) of environmental noise in sensor space. Once the noise vector(s) are
known, you can create an orthogonal hyperplane and construct a projection matrix to
project your recording onto that hyperplane. It should be clear that SSP reduces the
dimensionality of your data and thus sensors will not retain linear independency.

Additional information on projections and on Signal-Space Projection (SSP) can be found
in `MNE's background on projectors and projections`_.

MNE's Python geometric example projecting from 3-dimensional space to the (x, y) plane:

.. GENERATED FROM PYTHON SOURCE LINES 34-68

.. code-block:: Python


    import numpy as np
    from matplotlib import pyplot as plt

    ax = plt.axes(projection="3d")
    ax.view_init(azim=-105, elev=20)
    ax.set(xlabel="x", ylabel="y", zlabel="z", xlim=(-1, 5), ylim=(-1, 5), zlim=(0, 5))

    # plot the vector (3, 2, 5)
    origin = np.zeros((3, 1))
    point = np.array([[3, 2, 5]]).T
    vector = np.hstack([origin, point])
    ax.plot(*vector, color="k")
    ax.plot(*point, color="k", marker="o")

    # project the vector onto the x,y plane and plot it
    xy_projection_matrix = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 0]])
    projected_point = xy_projection_matrix @ point
    projected_vector = xy_projection_matrix @ vector
    ax.plot(*projected_vector, color="C0")
    ax.plot(*projected_point, color="C0", marker="o")

    # add dashed arrow showing projection
    arrow_coords = np.concatenate([point, projected_point - point]).flatten()
    ax.quiver3D(
        *arrow_coords,
        length=0.96,
        arrow_length_ratio=0.1,
        color="C1",
        linewidth=1,
        linestyle="dashed",
    )
    plt.show()




.. image-sg:: /generated/tutorials/megin/images/sphx_glr_00_signal_space_projection_001.png
   :alt: 00 signal space projection
   :srcset: /generated/tutorials/megin/images/sphx_glr_00_signal_space_projection_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 69-79

Default projectors
------------------

The default set of projectors is available `on our GitHub <sample dataset ssp_>`_.
Those projectors were obtained by combining projectors from the wideband PCA and from
the narrowband PCA (bandpass filter between 15 and 18 Hz).
The narrowband PCA improves the correction of the 16.7 Hz artifact, typical from a 15
kV AC railway electrification system.

Let's have a look at the projectors in 68° position when IAS is disabled.

.. GENERATED FROM PYTHON SOURCE LINES 79-86

.. code-block:: Python


    from mne import read_proj

    from meg_wiki.datasets import sample

    projs = read_proj(sample.data_path() / "ssp" / "200123" / "ssp_68_200123_proj.fif")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

        Read a total of 14 projection items:
            ssp_68_magn.fif : PCA-v1 (1 x 306)  idle
            ssp_68_magn.fif : PCA-v2 (1 x 306)  idle
            ssp_68_magn.fif : PCA-v3 (1 x 306)  idle
            ssp_68_magn.fif : PCA-v4 (1 x 306)  idle
            ssp_68_magn.fif : PCA-v5 (1 x 306)  idle
            ssp_68_magn.fif : PCA-v6 (1 x 306)  idle
            ssp_68_magn.fif : PCA-v1 (1 x 306)  idle
            ssp_68_magn.fif : PCA-v2 (1 x 306)  idle
            ssp_68_magn.fif : PCA-v3 (1 x 306)  idle
            ssp_68_grad.fif : PCA-v1 (1 x 306)  idle
            ssp_68_grad.fif : PCA-v2 (1 x 306)  idle
            ssp_68_grad.fif : PCA-v3 (1 x 306)  idle
            ssp_68_grad.fif : PCA-v1 (1 x 306)  idle
            ssp_68_grad.fif : PCA-v2 (1 x 306)  idle




.. GENERATED FROM PYTHON SOURCE LINES 87-89

To visualize the projector as topographic maps, we need information about the sensors
location and orientation. Those information are stored in every raw recording.

.. GENERATED FROM PYTHON SOURCE LINES 89-97

.. code-block:: Python


    from mne.io import read_info

    info = read_info(
        sample.data_path() / "meas_info" / "measurement-info.fif", verbose=False
    )
    info






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        <td>mne_anonymize</td>
    
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                102
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        <td>Gradiometers</td>
        <td>
            <button class="channel-names-btn" onclick="alert('Good Gradiometers:\n\nMEG0112, MEG0113, MEG0122, MEG0123, MEG0132, MEG0133, MEG0142, MEG0143, MEG0212, MEG0213, MEG0222, MEG0223, MEG0232, MEG0233, MEG0242, MEG0243, MEG0312, MEG0313, MEG0322, MEG0323, MEG0332, MEG0333, MEG0342, MEG0343, MEG0412, MEG0413, MEG0422, MEG0423, MEG0432, MEG0433, MEG0442, MEG0443, MEG0512, MEG0513, MEG0522, MEG0523, MEG0532, MEG0533, MEG0542, MEG0543, MEG0612, MEG0613, MEG0622, MEG0623, MEG0632, MEG0633, MEG0642, MEG0643, MEG0712, MEG0713, MEG0722, MEG0723, MEG0732, MEG0733, MEG0742, MEG0743, MEG0812, MEG0813, MEG0822, MEG0823, MEG0912, MEG0913, MEG0922, MEG0923, MEG0932, MEG0933, MEG0942, MEG0943, MEG1012, MEG1013, MEG1022, MEG1023, MEG1032, MEG1033, MEG1042, MEG1043, MEG1112, MEG1113, MEG1122, MEG1123, MEG1132, MEG1133, MEG1142, MEG1143, MEG1212, MEG1213, MEG1222, MEG1223, MEG1232, MEG1233, MEG1242, MEG1243, MEG1312, MEG1313, MEG1322, MEG1323, MEG1332, MEG1333, MEG1342, MEG1343, MEG1412, MEG1413, MEG1422, MEG1423, MEG1432, MEG1433, MEG1442, MEG1443, MEG1512, MEG1513, MEG1522, MEG1523, MEG1532, MEG1533, MEG1542, MEG1543, MEG1612, MEG1613, MEG1622, MEG1623, MEG1632, MEG1633, MEG1642, MEG1643, MEG1712, MEG1713, MEG1722, MEG1723, MEG1732, MEG1733, MEG1742, MEG1743, MEG1812, MEG1813, MEG1822, MEG1823, MEG1832, MEG1833, MEG1842, MEG1843, MEG1912, MEG1913, MEG1922, MEG1923, MEG1932, MEG1933, MEG1942, MEG1943, MEG2012, MEG2013, MEG2022, MEG2023, MEG2032, MEG2033, MEG2042, MEG2043, MEG2112, MEG2113, MEG2122, MEG2123, MEG2132, MEG2133, MEG2142, MEG2143, MEG2212, MEG2213, MEG2222, MEG2223, MEG2232, MEG2233, MEG2242, MEG2243, MEG2312, MEG2313, MEG2322, MEG2323, MEG2332, MEG2333, MEG2342, MEG2343, MEG2412, MEG2413, MEG2422, MEG2423, MEG2432, MEG2433, MEG2442, MEG2443, MEG2512, MEG2513, MEG2522, MEG2523, MEG2532, MEG2533, MEG2542, MEG2543, MEG2612, MEG2613, MEG2622, MEG2623, MEG2632, MEG2633, MEG2642, MEG2643')" title="(Click to open in popup)&#13;&#13;MEG0112, MEG0113, MEG0122, MEG0123, MEG0132, MEG0133, MEG0142, MEG0143, MEG0212, MEG0213, MEG0222, MEG0223, MEG0232, MEG0233, MEG0242, MEG0243, MEG0312, MEG0313, MEG0322, MEG0323, MEG0332, MEG0333, MEG0342, MEG0343, MEG0412, MEG0413, MEG0422, MEG0423, MEG0432, MEG0433, MEG0442, MEG0443, MEG0512, MEG0513, MEG0522, MEG0523, MEG0532, MEG0533, MEG0542, MEG0543, MEG0612, MEG0613, MEG0622, MEG0623, MEG0632, MEG0633, MEG0642, MEG0643, MEG0712, MEG0713, MEG0722, MEG0723, MEG0732, MEG0733, MEG0742, MEG0743, MEG0812, MEG0813, MEG0822, MEG0823, MEG0912, MEG0913, MEG0922, MEG0923, MEG0932, MEG0933, MEG0942, MEG0943, MEG1012, MEG1013, MEG1022, MEG1023, MEG1032, MEG1033, MEG1042, MEG1043, MEG1112, MEG1113, MEG1122, MEG1123, MEG1132, MEG1133, MEG1142, MEG1143, MEG1212, MEG1213, MEG1222, MEG1223, MEG1232, MEG1233, MEG1242, MEG1243, MEG1312, MEG1313, MEG1322, MEG1323, MEG1332, MEG1333, MEG1342, MEG1343, MEG1412, MEG1413, MEG1422, MEG1423, MEG1432, MEG1433, MEG1442, MEG1443, MEG1512, MEG1513, MEG1522, MEG1523, MEG1532, MEG1533, MEG1542, MEG1543, MEG1612, MEG1613, MEG1622, MEG1623, MEG1632, MEG1633, MEG1642, MEG1643, MEG1712, MEG1713, MEG1722, MEG1723, MEG1732, MEG1733, MEG1742, MEG1743, MEG1812, MEG1813, MEG1822, MEG1823, MEG1832, MEG1833, MEG1842, MEG1843, MEG1912, MEG1913, MEG1922, MEG1923, MEG1932, MEG1933, MEG1942, MEG1943, MEG2012, MEG2013, MEG2022, MEG2023, MEG2032, MEG2033, MEG2042, MEG2043, MEG2112, MEG2113, MEG2122, MEG2123, MEG2132, MEG2133, MEG2142, MEG2143, MEG2212, MEG2213, MEG2222, MEG2223, MEG2232, MEG2233, MEG2242, MEG2243, MEG2312, MEG2313, MEG2322, MEG2323, MEG2332, MEG2333, MEG2342, MEG2343, MEG2412, MEG2413, MEG2422, MEG2423, MEG2432, MEG2433, MEG2442, MEG2443, MEG2512, MEG2513, MEG2522, MEG2523, MEG2532, MEG2533, MEG2542, MEG2543, MEG2612, MEG2613, MEG2622, MEG2623, MEG2632, MEG2633, MEG2642, MEG2643">
                204
            </button>

        
        </td>
    </tr>


    <tr class="repr-element channels-e2140867-715d-4ce5-9465-934f7505ef9c ">
        <td class="repr-section-toggle-col"></td>
        <td>Head & sensor digitization</td>
    
        <td>Not available</td>
    
    </tr>
    







    <tr class="repr-section-header filters-53f9d90a-216b-47b5-9f09-c7c7742d2a6b"  title="Hide section" 
        onclick="toggleVisibility('filters-53f9d90a-216b-47b5-9f09-c7c7742d2a6b')">
        <th class="repr-section-toggle-col">
            <button>
            
                <span class="collapse-uncollapse-caret"></span>
            </button>
        </th>
        <th colspan="2">
            <strong>Filters</strong>
        </th>
    </tr>

    <tr class="repr-element filters-53f9d90a-216b-47b5-9f09-c7c7742d2a6b ">
        <td class="repr-section-toggle-col"></td>
        <td>Highpass</td>
        <td>0.10 Hz</td>
    </tr>


    <tr class="repr-element filters-53f9d90a-216b-47b5-9f09-c7c7742d2a6b ">
        <td class="repr-section-toggle-col"></td>
        <td>Lowpass</td>
        <td>330.00 Hz</td>
    </tr>


    <tr class="repr-element filters-53f9d90a-216b-47b5-9f09-c7c7742d2a6b ">
        <td class="repr-section-toggle-col"></td>
        <td>Projections</td>
        <td>
        
            ssp_68_magn.fif : PCA-v1 (off)
            <br />
        
            ssp_68_magn.fif : PCA-v2 (off)
            <br />
        
            ssp_68_magn.fif : PCA-v3 (off)
            <br />
        
            ssp_68_magn.fif : PCA-v4 (off)
            <br />
        
            ssp_68_magn.fif : PCA-v5 (off)
            <br />
        
            ssp_68_magn.fif : PCA-v6 (off)
            <br />
        
            ssp_68_magn.fif : PCA-v1 (off)
            <br />
        
            ssp_68_magn.fif : PCA-v2 (off)
            <br />
        
            ssp_68_magn.fif : PCA-v3 (off)
            <br />
        
            ssp_68_grad.fif : PCA-v1 (off)
            <br />
        
            ssp_68_grad.fif : PCA-v2 (off)
            <br />
        
            ssp_68_grad.fif : PCA-v3 (off)
            <br />
        
            ssp_68_grad.fif : PCA-v1 (off)
            <br />
        
            ssp_68_grad.fif : PCA-v2 (off)
        
        
        </td>
    </tr>

    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 98-114

.. code-block:: Python


    from matplotlib import pyplot as plt

    f, ax = plt.subplots(2, 3, figsize=(6, 6))
    for k, proj in enumerate(projs[0:6]):
        proj.plot_topomap(info, axes=ax[k // 3, k % 3])
        ax[k // 3, k % 3].set_title(f"PCA-v{k+1}")
    plt.suptitle("Magnetometers - Wideband PCA")

    f, ax = plt.subplots(1, 3, figsize=(6, 6))
    for k, proj in enumerate(projs[6:9]):
        proj.plot_topomap(info, axes=ax[k])
        ax[k].set_title(f"PCA-v{k+1}")
    plt.suptitle("Magnetometers - Narrowband PCA")
    plt.show()




.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /generated/tutorials/megin/images/sphx_glr_00_signal_space_projection_002.png
         :alt: Magnetometers - Wideband PCA, PCA-v1, PCA-v2, PCA-v3, PCA-v4, PCA-v5, PCA-v6
         :srcset: /generated/tutorials/megin/images/sphx_glr_00_signal_space_projection_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /generated/tutorials/megin/images/sphx_glr_00_signal_space_projection_003.png
         :alt: Magnetometers - Narrowband PCA, PCA-v1, PCA-v2, PCA-v3
         :srcset: /generated/tutorials/megin/images/sphx_glr_00_signal_space_projection_003.png
         :class: sphx-glr-multi-img





.. GENERATED FROM PYTHON SOURCE LINES 115-131

.. code-block:: Python


    from matplotlib import pyplot as plt

    f, ax = plt.subplots(1, 3, figsize=(6, 6))
    for k, proj in enumerate(projs[9:12]):
        proj.plot_topomap(info, axes=ax[k])
        ax[k].set_title(f"PCA-v{k+1}")
    plt.suptitle("Gradiometers - Wideband PCA")

    f, ax = plt.subplots(1, 2, figsize=(6, 6))
    for k, proj in enumerate(projs[12:14]):
        proj.plot_topomap(info, axes=ax[k])
        ax[k].set_title(f"PCA-v{k+1}")
    plt.suptitle("Gradiometers - Narrowband PCA")
    plt.show()




.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /generated/tutorials/megin/images/sphx_glr_00_signal_space_projection_004.png
         :alt: Gradiometers - Wideband PCA, PCA-v1, PCA-v2, PCA-v3
         :srcset: /generated/tutorials/megin/images/sphx_glr_00_signal_space_projection_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /generated/tutorials/megin/images/sphx_glr_00_signal_space_projection_005.png
         :alt: Gradiometers - Narrowband PCA, PCA-v1, PCA-v2
         :srcset: /generated/tutorials/megin/images/sphx_glr_00_signal_space_projection_005.png
         :class: sphx-glr-multi-img





.. GENERATED FROM PYTHON SOURCE LINES 132-140

Empty room recording
--------------------

Projectors are determined from an empty-room recording. They are specific to a gantry
position (up-right 68°, up-right 60°, supine 0°) and to an
:ref:`meg-settings:Internal Active Shielding (IAS)` state (``ON`` or ``OFF``). The
empty-room recording loaded below was measured with the gantry in the 68° position and
with IAS disabled.

.. GENERATED FROM PYTHON SOURCE LINES 140-149

.. code-block:: Python


    from mne.io import read_raw_fif

    raw = read_raw_fif(
        sample.data_path() / "empty-room" / "empty-room-raw.fif", verbose=False
    )
    raw.del_proj("all")  # remove the default projectors
    raw.info["bads"] = ["MEG1343"]  # bad channel with flux jumps








.. GENERATED FROM PYTHON SOURCE LINES 150-156

Noise level
~~~~~~~~~~~

The power spectral density can be used to visualize the noise level. See
:footcite:t:`msr-noise_2013` and this `MNE-Python example`_ for additional
information.

.. GENERATED FROM PYTHON SOURCE LINES 156-167

.. code-block:: Python


    raw.compute_psd(verbose=False).plot(
        average=True,
        spatial_colors=False,
        dB=False,
        xscale="log",
        picks="data",
        exclude="bads",
    )
    plt.show()




.. image-sg:: /generated/tutorials/megin/images/sphx_glr_00_signal_space_projection_006.png
   :alt: Gradiometers, Magnetometers
   :srcset: /generated/tutorials/megin/images/sphx_glr_00_signal_space_projection_006.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Plotting power spectral density (dB=False).




.. GENERATED FROM PYTHON SOURCE LINES 168-174

References
----------

.. footbibliography::

.. _MNE-Python example: https://mne.tools/stable/auto_examples/visualization/sensor_noise_level.html


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 7.609 seconds)

**Estimated memory usage:**  1051 MB


.. _sphx_glr_download_generated_tutorials_megin_00_signal_space_projection.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: 00_signal_space_projection.ipynb <00_signal_space_projection.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: 00_signal_space_projection.py <00_signal_space_projection.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: 00_signal_space_projection.zip <00_signal_space_projection.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_