# -*- coding: utf-8 -*-
"""
===============================================================================
Suppress Gibbs oscillations
===============================================================================

Magnetic Resonance (MR) images are reconstructed from the Fourier coefficients
of acquired k-space images. Since only a finite number of Fourier coefficients
can be acquired in practice, reconstructed MR images can be corrupted by Gibbs
artefacts, which is manifested by intensity oscillations adjacent to edges of
different tissues types [1]_. Although this artefact affects MR images in
general, in the context of diffusion-weighted imaging, Gibbs oscillations
can be magnified in derived diffusion-based estimates [1]_, [2]_.

In the following example, we show how to suppress Gibbs artefacts of MR images.
This algorithm is based on an adapted version of a sub-voxel Gibbs suppression
procedure [3]_. Full details of the implemented algorithm can be found in
chapter 3 of [4]_  (please cite [3]_, [4]_ if you are using this code).

The algorithm to suppress Gibbs oscillations can be imported from the denoise
module of dipy:
"""

from dipy.denoise.gibbs import gibbs_removal

"""
We first apply this algorithm to T1-weighted dataset which can be fetched
using the following code:
"""

from dipy.data import get_fnames
from dipy.io.image import load_nifti_data


t1_fname, t1_denoised_fname, ap_fname = get_fnames('tissue_data')
t1 = load_nifti_data(t1_denoised_fname)

"""
Let's plot a slice of this dataset.
"""

import matplotlib.pyplot as plt
import numpy as np

axial_slice = 88
t1_slice = t1[..., axial_slice]

fig = plt.figure(figsize=(15, 4))
fig.subplots_adjust(wspace=0.2)

t1_slice = np.rot90(t1_slice)

plt.subplot(1, 2, 1)
plt.imshow(t1_slice, cmap='gray', vmin=100, vmax=400)
plt.colorbar()
fig.savefig('structural.png')

"""
.. figure:: structural.png
   :align: center

   Representative slice of a T1-weighted structural image.

Due to the high quality of the data, Gibbs artefacts are not visually
evident in this dataset. Therefore, to analyse the benefits of the Gibbs
suppression algorithm, Gibbs artefacts are artificially introduced by
removing high frequencies of the image's Fourier transform.
"""

c = np.fft.fft2(t1_slice)
c = np.fft.fftshift(c)
N = c.shape[0]
c_crop = c[64: 192, 64: 192]
N = c_crop.shape[0]
t1_gibbs = abs(np.fft.ifft2(c_crop)/4)

"""
Gibbs oscillation suppression of this single data slice can be performed by
running the following command:
"""

t1_unring = gibbs_removal(t1_gibbs, inplace=False)

"""
Let’s plot the results:
"""

fig1, ax = plt.subplots(1, 3, figsize=(12, 6),
                        subplot_kw={'xticks': [], 'yticks': []})

ax.flat[0].imshow(t1_gibbs, cmap="gray", vmin=100, vmax=400)
ax.flat[0].annotate('Rings', fontsize=10, xy=(81, 70),
                    color='red',
                    xycoords='data', xytext=(30, 0),
                    textcoords='offset points',
                    arrowprops=dict(arrowstyle="->",
                                    color='red'))
ax.flat[0].annotate('Rings', fontsize=10, xy=(75, 50),
                    color='red',
                    xycoords='data', xytext=(30, 0),
                    textcoords='offset points',
                    arrowprops=dict(arrowstyle="->",
                                    color='red'))

ax.flat[1].imshow(t1_unring, cmap="gray", vmin=100, vmax=400)
ax.flat[1].annotate('WM/GM', fontsize=10, xy=(75, 50),
                    color='green',
                    xycoords='data', xytext=(30, 0),
                    textcoords='offset points',
                    arrowprops=dict(arrowstyle="->",
                                    color='green'))

ax.flat[2].imshow(t1_unring - t1_gibbs, cmap="gray", vmin=0, vmax=10)
ax.flat[2].annotate('Rings', fontsize=10, xy=(81, 70),
                    color='red',
                    xycoords='data', xytext=(30, 0),
                    textcoords='offset points',
                    arrowprops=dict(arrowstyle="->",
                                    color='red'))
ax.flat[2].annotate('Rings', fontsize=10, xy=(75, 50),
                    color='red',
                    xycoords='data', xytext=(30, 0),
                    textcoords='offset points',
                    arrowprops=dict(arrowstyle="->",
                                    color='red'))
plt.show()
fig1.savefig('Gibbs_suppression_structural.png')

"""
.. figure:: Gibbs_suppression_structural.png
   :align: center

   Uncorrected and corrected structural images are shown in the left
   and middle panels, while the difference between these images is shown
   in the right panel.

The image artificially corrupted with Gibb's artefacts is shown in the left
panel. In this panel, the characteristic ringing profile of Gibbs artefacts
can be visually appreciated (see intensity oscillations pointed by the red
arrows). The corrected image is shown in the middle panel. One can appreciate
that artefactual oscillations are visually suppressed without compromising
the contrast between white and grey matter (e.g. details pointed by the green
arrow). The difference between uncorrected and corrected data is plotted in
the right panel which highlights the suppressed Gibbs ringing profile.


Now let's show how to use the Gibbs suppression algorithm in diffusion-weighted
images. We fetch the multi-shell diffusion-weighted dataset which was kindly
supplied by Romain Valabrègue, CENIR, ICM, Paris [5]_.
"""

from dipy.data import read_cenir_multib

bvals = [200, 400, 1000, 2000]

img, gtab = read_cenir_multib(bvals)

data = np.asarray(img.dataobj)

"""
For illustration proposes, we select two slices of this dataset
"""

data_slices = data[:, :, 40:42, :]

"""
Gibbs oscillation suppression of all multi-shell data and all slices
can be performed in the following way:
"""

data_corrected = gibbs_removal(data_slices, slice_axis=2, num_threads=None)

"""
Due to the high dimensionality of diffusion-weighted data, we recommend
that you specify which is the axis of data matrix that corresponds to different
slices in the above step. This is done by using the optional parameter
'slice_axis'.

Below we plot the results for an image acquired with b-value=0:
"""

fig2, ax = plt.subplots(1, 3, figsize=(12, 6),
                        subplot_kw={'xticks': [], 'yticks': []})

ax.flat[0].imshow(data_slices[:, :, 0, 0].T, cmap='gray', origin='lower',
                  vmin=0, vmax=10000)
ax.flat[0].set_title('Uncorrected b0')
ax.flat[1].imshow(data_corrected[:, :, 0, 0].T, cmap='gray',
                  origin='lower', vmin=0, vmax=10000)
ax.flat[1].set_title('Corrected b0')
ax.flat[2].imshow(data_corrected[:, :, 0, 0].T - data_slices[:, :, 0, 0].T,
                  cmap='gray', origin='lower', vmin=-500, vmax=500)
ax.flat[2].set_title('Gibbs residuals')

plt.show()
fig2.savefig('Gibbs_suppression_b0.png')

"""
.. figure:: Gibbs_suppression_b0.png
   :align: center

   Uncorrected (left panel) and corrected (middle panel) b-value=0 images. For
   reference, the difference between uncorrected and corrected images is shown
   in the right panel.

The above figure shows that the benefits of suppressing Gibbs artefacts is hard
to observe on b-value=0 data. Therefore, diffusion derived metrics for both
uncorrected and corrected data are computed using the mean signal diffusion
kurtosis image technique (:ref:`example_reconst_msdki`).

To avoid unnecessary calculations on the background of the image, we also
compute a brain mask.
"""

# Create a brain mask
from dipy.segment.mask import median_otsu

maskdata, mask = median_otsu(data_slices, vol_idx=range(10, 50),
                             median_radius=3, numpass=1, autocrop=False,
                             dilate=1)

# Define mean signal diffusion kurtosis model
import dipy.reconst.msdki as msdki

dki_model = msdki.MeanDiffusionKurtosisModel(gtab)

# Fit the uncorrected data
dki_fit = dki_model.fit(data_slices, mask=mask)
MSKini = dki_fit.msk

# Fit the corrected data
dki_fit = dki_model.fit(data_corrected, mask=mask)
MSKgib = dki_fit.msk

"""
Let's plot the results
"""

fig3, ax = plt.subplots(1, 3, figsize=(12, 12),
                        subplot_kw={'xticks': [], 'yticks': []})

ax.flat[0].imshow(MSKini[:, :, 0].T, cmap='gray', origin='lower',
                  vmin=0, vmax=1.5)
ax.flat[0].set_title('MSK (uncorrected)')
ax.flat[0].annotate('Rings', fontsize=12, xy=(59, 63),
                    color='red',
                    xycoords='data', xytext=(45, 0),
                    textcoords='offset points',
                    arrowprops=dict(arrowstyle="->",
                                    color='red'))

ax.flat[1].imshow(MSKgib[:, :, 0].T, cmap='gray', origin='lower',
                  vmin=0, vmax=1.5)
ax.flat[1].set_title('MSK (corrected)')

ax.flat[2].imshow(MSKgib[:, :, 0].T - MSKini[:, :, 0].T, cmap='gray',
                  origin='lower', vmin=-0.2, vmax=0.2)
ax.flat[2].set_title('MSK (uncorrected - corrected')
ax.flat[2].annotate('Rings', fontsize=12, xy=(59, 63),
                    color='red',
                    xycoords='data', xytext=(45, 0),
                    textcoords='offset points',
                    arrowprops=dict(arrowstyle="->",
                                    color='red'))

plt.show()
fig3.savefig('Gibbs_suppression_msdki.png')

"""
.. figure:: Gibbs_suppression_msdki.png
   :align: center

   Uncorrected and corrected mean signal kurtosis images are shown in the left
   and middle panels. The difference between uncorrected and corrected images
   are show in the right panel.

In the left panel of the figure above, Gibbs artefacts can be appreciated by
the negative values of mean signal kurtosis (black voxels) adjacent to the
brain ventricle (red arrows). These negative values seem to be suppressed
after the `gibbs_removal` function is applied. For a better visualization of
Gibbs oscillations, the difference between corrected and uncorrected images are
shown in the right panel.


References
----------
.. [1] Veraart, J., Fieremans, E., Jelescu, I.O., Knoll, F., Novikov, D.S.,
       2015. Gibbs Ringing in Diffusion MRI. Magn Reson Med 76(1): 301-314.
       https://doi.org/10.1002/mrm.25866
.. [2] Perrone, D., Aelterman, J., Pižurica, A., Jeurissen, B., Philips, W.,
       Leemans A., 2015. The effect of Gibbs ringing artifacts on measures
       derived from diffusion MRI. Neuroimage 120, 441-455.
       https://doi.org/10.1016/j.neuroimage.2015.06.068.
.. [3] Kellner, E., Dhital, B., Kiselev, V.G, Reisert, M., 2016. Gibbs‐ringing
       artifact removal based on local subvoxel‐shifts. Magn Reson Med
       76:1574–1581.
       https://doi.org/10.1002/mrm.26054.
.. [4] Neto Henriques, R., 2018. Advanced Methods for Diffusion MRI Data
       Analysis and their Application to the Healthy Ageing Brain
       (Doctoral thesis). https://doi.org/10.17863/CAM.29356
.. [5] Valabrègue, R. (2015). Diffusion MRI measured at multiple b-values.
       Retrieved from:
       https://digital.lib.washington.edu/researchworks/handle/1773/33311

.. include:: ../links_names.inc
"""
