.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/06_denoise/06_03_3d_volume_smoothing.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_06_denoise_06_03_3d_volume_smoothing.py>`
        to download the full example code. or to run this example in your browser via JupyterLite or Binder

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

.. _sphx_glr_auto_examples_06_denoise_06_03_3d_volume_smoothing.py:


3D Volume Smoothing
===================

We use the smooth module to smooth N-dimensional data.

.. GENERATED FROM PYTHON SOURCE LINES 13-15

Imports
-------

.. GENERATED FROM PYTHON SOURCE LINES 15-20

.. code-block:: Python


    import numpy as np
    import matplotlib.pyplot as plt
    from splineops.denoise.smoothing_spline import smoothing_spline_nd








.. GENERATED FROM PYTHON SOURCE LINES 21-23

Sinusoid 3D Data
----------------

.. GENERATED FROM PYTHON SOURCE LINES 23-101

.. code-block:: Python


    def demo_3d_sinusoid():
        # Desired cutoff frequency
        cutoff_freq = 0.1  # Adjusted cutoff frequency
        gamma = 2.0        # Order of the spline operator

        # Compute lambda_ based on cutoff frequency
        lambda_ = (1 / (2 * np.pi * cutoff_freq)) ** (2 * gamma)

        snr_db = 10.0   # Desired SNR in dB

        # Create a 3D clean volume (sinusoid)
        x = np.linspace(0, 1, 64)
        y = np.linspace(0, 1, 64)
        z = np.linspace(0, 1, 64)
        X, Y, Z = np.meshgrid(x, y, z, indexing='ij')
        clean_volume = np.sin(8 * np.pi * X) + np.sin(8 * np.pi * Y) + np.sin(8 * np.pi * Z)
        clean_volume = (clean_volume - clean_volume.min()) / (clean_volume.max() - clean_volume.min())  # Normalize to [0, 1]

        # Add noise
        signal_power = np.mean(clean_volume ** 2)
        sigma = np.sqrt(signal_power / (10 ** (snr_db / 10)))
        noise = np.random.randn(*clean_volume.shape) * sigma
        noisy_volume = clean_volume + noise

        # Apply smoothing spline
        smoothed_volume = smoothing_spline_nd(noisy_volume, lambda_, gamma)

        # Compute SNRs
        snr_noisy = compute_snr(clean_volume, noisy_volume)
        snr_smoothed = compute_snr(clean_volume, smoothed_volume)
        snr_improvement = snr_smoothed - snr_noisy

        print("3D Sinusoid Volume:")
        print(f"SNR of noisy volume: {snr_noisy:.2f} dB")
        print(f"SNR after smoothing: {snr_smoothed:.2f} dB")
        print(f"SNR improvement: {snr_improvement:.2f} dB\n")

        # Visualize one slice of the volume (middle slice)
        slice_index = clean_volume.shape[2] // 2

        plt.figure(figsize=(12, 4))

        plt.subplot(1, 3, 1)
        plt.imshow(clean_volume[:, :, slice_index], cmap='gray')
        plt.title('Clean Volume Slice')
        plt.axis('off')

        plt.subplot(1, 3, 2)
        plt.imshow(noisy_volume[:, :, slice_index], cmap='gray')
        plt.title(f'Noisy Slice (SNR={snr_noisy:.2f} dB)')
        plt.axis('off')

        plt.subplot(1, 3, 3)
        plt.imshow(smoothed_volume[:, :, slice_index], cmap='gray')
        plt.title(f'Smoothed Slice (SNR={snr_smoothed:.2f} dB)')
        plt.axis('off')

        plt.tight_layout()
        plt.show()

    def compute_snr(clean_signal, noisy_signal):
        """
        Compute the Signal-to-Noise Ratio (SNR).

        Parameters:
        clean_signal (np.ndarray): Original clean signal.
        noisy_signal (np.ndarray): Noisy signal.

        Returns:
        float: SNR value in decibels (dB).
        """
        signal_power = np.mean(clean_signal ** 2)
        noise_power = np.mean((noisy_signal - clean_signal) ** 2)
        snr = 10 * np.log10(signal_power / noise_power)
        return snr

    # Run the 3D sinusoid demo
    demo_3d_sinusoid()


.. image-sg:: /auto_examples/06_denoise/images/sphx_glr_06_03_3d_volume_smoothing_001.png
   :alt: Clean Volume Slice, Noisy Slice (SNR=10.01 dB), Smoothed Slice (SNR=24.98 dB)
   :srcset: /auto_examples/06_denoise/images/sphx_glr_06_03_3d_volume_smoothing_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    3D Sinusoid Volume:
    SNR of noisy volume: 10.01 dB
    SNR after smoothing: 24.98 dB
    SNR improvement: 14.97 dB






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

   **Total running time of the script:** (0 minutes 0.159 seconds)


.. _sphx_glr_download_auto_examples_06_denoise_06_03_3d_volume_smoothing.py:

.. only:: html

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

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/splineops/splineops.github.io/main?urlpath=lab/tree/notebooks_binder/auto_examples/06_denoise/06_03_3d_volume_smoothing.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../lite/lab/index.html?path=auto_examples/06_denoise/06_03_3d_volume_smoothing.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: 06_03_3d_volume_smoothing.ipynb <06_03_3d_volume_smoothing.ipynb>`

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

      :download:`Download Python source code: 06_03_3d_volume_smoothing.py <06_03_3d_volume_smoothing.py>`

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

      :download:`Download zipped: 06_03_3d_volume_smoothing.zip <06_03_3d_volume_smoothing.zip>`


.. only:: html

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

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