.. _sphx_glr_auto_examples_linear_model_plot_omp.py:


===========================
Orthogonal Matching Pursuit
===========================

Using orthogonal matching pursuit for recovering a sparse signal from a noisy
measurement encoded with a dictionary



.. code-block:: python

    print(__doc__)

    import matplotlib.pyplot as plt
    import numpy as np
    from sklearn.linear_model import OrthogonalMatchingPursuit
    from sklearn.linear_model import OrthogonalMatchingPursuitCV
    from sklearn.datasets import make_sparse_coded_signal

    n_components, n_features = 512, 100
    n_nonzero_coefs = 17

    # generate the data
    ###################

    # y = Xw
    # |x|_0 = n_nonzero_coefs

    y, X, w = make_sparse_coded_signal(n_samples=1,
                                       n_components=n_components,
                                       n_features=n_features,
                                       n_nonzero_coefs=n_nonzero_coefs,
                                       random_state=0)

    idx, = w.nonzero()

    # distort the clean signal







.. code-block:: python

    y_noisy = y + 0.05 * np.random.randn(len(y))

    # plot the sparse signal







.. code-block:: python

    plt.figure(figsize=(7, 7))
    plt.subplot(4, 1, 1)
    plt.xlim(0, 512)
    plt.title("Sparse signal")
    plt.stem(idx, w[idx])

    # plot the noise-free reconstruction



.. image:: /auto_examples/linear_model/images/sphx_glr_plot_omp_001.png
    :align: center





.. code-block:: python


    omp = OrthogonalMatchingPursuit(n_nonzero_coefs=n_nonzero_coefs)
    omp.fit(X, y)
    coef = omp.coef_
    idx_r, = coef.nonzero()
    plt.subplot(4, 1, 2)
    plt.xlim(0, 512)
    plt.title("Recovered signal from noise-free measurements")
    plt.stem(idx_r, coef[idx_r])

    # plot the noisy reconstruction



.. image:: /auto_examples/linear_model/images/sphx_glr_plot_omp_002.png
    :align: center





.. code-block:: python

    omp.fit(X, y_noisy)
    coef = omp.coef_
    idx_r, = coef.nonzero()
    plt.subplot(4, 1, 3)
    plt.xlim(0, 512)
    plt.title("Recovered signal from noisy measurements")
    plt.stem(idx_r, coef[idx_r])

    # plot the noisy reconstruction with number of non-zeros set by CV



.. image:: /auto_examples/linear_model/images/sphx_glr_plot_omp_003.png
    :align: center





.. code-block:: python

    omp_cv = OrthogonalMatchingPursuitCV()
    omp_cv.fit(X, y_noisy)
    coef = omp_cv.coef_
    idx_r, = coef.nonzero()
    plt.subplot(4, 1, 4)
    plt.xlim(0, 512)
    plt.title("Recovered signal from noisy measurements with CV")
    plt.stem(idx_r, coef[idx_r])

    plt.subplots_adjust(0.06, 0.04, 0.94, 0.90, 0.20, 0.38)
    plt.suptitle('Sparse signal recovery with Orthogonal Matching Pursuit',
                 fontsize=16)
    plt.show()



.. image:: /auto_examples/linear_model/images/sphx_glr_plot_omp_004.png
    :align: center




**Total running time of the script:** ( 0 minutes  0.313 seconds)



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  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_omp.py <plot_omp.py>`



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