"""
=====================================================
Using the RESTORE algorithm for robust tensor fitting
=====================================================
The diffusion tensor model takes into account certain kinds of noise (thermal),
but not other kinds, such as "physiological" noise. For example, if a subject
moves during the acquisition of one of the diffusion-weighted samples, this
might have a substantial effect on the parameters of the tensor fit calculated
in all voxels in the brain for that subject. One of the pernicious consequences
of this is that it can lead to wrong interpretation of group differences. For
example, some groups of participants (e.g. young children, patient groups,
etc.) are particularly prone to motion and differences in tensor parameters and
derived statistics (such as FA) due to motion would be confounded with actual
differences in the physical properties of the white matter. An example of this
was shown in a paper by Yendiki et al. [Yendiki2013]_.
One of the strategies to deal with this problem is to apply an automatic method
for detecting outliers in the data, excluding these outliers and refitting the
model without the presence of these outliers. This is often referred to as
"robust model fitting". One of the common algorithms for robust tensor fitting
is called RESTORE, and was first proposed by Chang et al. [Chang2005]_.
In the following example, we will demonstrate how to use RESTORE on a simulated
dataset, which we will corrupt by adding intermittent noise.
We start by importing a few of the libraries we will use.
"""
import numpy as np
import nibabel as nib
"""
The module ``dipy.reconst.dti`` contains the implementation of tensor fitting,
including an implementation of the RESTORE algorithm.
"""
import dipy.reconst.dti as dti
"""
``dipy.data`` is used for small datasets that we use in tests and examples.
"""
import dipy.data as dpd
"""
``dipy.viz`` package is used for 3D visualization and matplotlib for 2D
visualizations:
"""
from dipy.viz import window, actor
import matplotlib.pyplot as plt
# Enables/disables interactive visualization
interactive = False
"""
If needed, the ``fetch_stanford_hardi`` function will download the raw dMRI
dataset of a single subject. The size of this dataset is 87 MBytes. You only
need to fetch once.
"""
dpd.fetch_stanford_hardi()
img, gtab = dpd.read_stanford_hardi()
"""
We initialize a DTI model class instance using the gradient table used in the
measurement. By default, ``dti.TensorModel`` will use a weighted least-squares
algorithm (described in [Chang2005]_) to fit the parameters of the model. We
initialize this model as a baseline for comparison of noise-corrupted models:
"""
dti_wls = dti.TensorModel(gtab)
"""
For the purpose of this example, we will focus on the data from a region of
interest (ROI) surrounding the Corpus Callosum. We define that ROI as the
following indices:
"""
roi_idx = (slice(20, 50), slice(55, 85), slice(38, 39))
"""
And use them to index into the data:
"""
data = img.get_data()[roi_idx]
"""
This dataset is not very noisy, so we will artificially corrupt it to simulate
the effects of "physiological" noise, such as subject motion. But first, let's
establish a baseline, using the data as it is:
"""
fit_wls = dti_wls.fit(data)
fa1 = fit_wls.fa
evals1 = fit_wls.evals
evecs1 = fit_wls.evecs
cfa1 = dti.color_fa(fa1, evecs1)
sphere = dpd.get_sphere('symmetric724')
"""
We visualize the ODFs in the ROI using ``dipy.viz`` module:
"""
ren = window.Renderer()
ren.add(actor.tensor_slicer(evals1, evecs1, scalar_colors=cfa1, sphere=sphere, scale=0.3))
print('Saving illustration as tensor_ellipsoids_wls.png')
window.record(ren, out_path='tensor_ellipsoids_wls.png', size=(600, 600))
if interactive:
window.show(ren)
"""
.. figure:: tensor_ellipsoids_wls.png
:align: center
Tensor Ellipsoids.
"""
window.clear(ren)
"""
Next, we corrupt the data with some noise. To simulate a subject that moves
intermittently, we will replace a few of the images with a very low signal
"""
noisy_data = np.copy(data)
noisy_idx = slice(-10, None) # The last 10 volumes are corrupted
noisy_data[..., noisy_idx] = 1.0
"""
We use the same model to fit this noisy data
"""
fit_wls_noisy = dti_wls.fit(noisy_data)
fa2 = fit_wls_noisy.fa
evals2 = fit_wls_noisy.evals
evecs2 = fit_wls_noisy.evecs
cfa2 = dti.color_fa(fa2, evecs2)
ren = window.Renderer()
ren.add(actor.tensor_slicer(evals2, evecs2, scalar_colors=cfa2, sphere=sphere, scale=0.3))
print('Saving illustration as tensor_ellipsoids_wls_noisy.png')
window.record(ren, out_path='tensor_ellipsoids_wls_noisy.png', size=(600, 600))
if interactive:
window.show(ren)
"""
In places where the tensor model is particularly sensitive to noise, the
resulting tensor field will be distorted
.. figure:: tensor_ellipsoids_wls_noisy.png
:align: center
Tensor Ellipsoids from noisy data.
To estimate the parameters from the noisy data using RESTORE, we need to
estimate what would be a reasonable amount of noise to expect in the
measurement. To do that, we use the ``dipy.denoise.noise_estimate`` module:
"""
import dipy.denoise.noise_estimate as ne
sigma = ne.estimate_sigma(data)
"""
This estimate of the standard deviation will be used by the RESTORE algorithm
to identify the outliers in each voxel and is given as an input when
initializing the TensorModel object:
"""
dti_restore = dti.TensorModel(gtab, fit_method='RESTORE', sigma=sigma)
fit_restore_noisy = dti_restore.fit(noisy_data)
fa3 = fit_restore_noisy.fa
evals3 = fit_restore_noisy.evals
evecs3 = fit_restore_noisy.evecs
cfa3 = dti.color_fa(fa3, evecs3)
ren = window.Renderer()
ren.add(actor.tensor_slicer(evals3, evecs3, scalar_colors=cfa3, sphere=sphere, scale=0.3))
print('Saving illustration as tensor_ellipsoids_restore_noisy.png')
window.record(ren, out_path='tensor_ellipsoids_restore_noisy.png', size=(600, 600))
if interactive:
window.show(ren)
"""
.. figure:: tensor_ellipsoids_restore_noisy.png
:align: center
Tensor Ellipsoids from noisy data recovered with RESTORE.
The tensor field looks rather restored to its noiseless state in this
image, but to convince ourselves further that this did the right thing, we will
compare the distribution of FA in this region relative to the baseline, using
the RESTORE estimate and the WLS estimate [Chung2006]_.
"""
fig_hist, ax = plt.subplots(1)
ax.hist(np.ravel(fa2), color='b', histtype='step', label='WLS')
ax.hist(np.ravel(fa3), color='r', histtype='step', label='RESTORE')
ax.hist(np.ravel(fa1), color='g', histtype='step', label='Original')
ax.set_xlabel('Fractional Anisotropy')
ax.set_ylabel('Count')
plt.legend()
fig_hist.savefig('dti_fa_distributions.png')
"""
.. figure:: dti_fa_distributions.png
:align: center
This demonstrates that RESTORE can recover a distribution of FA that more
closely resembles the baseline distribution of the noiseless signal, and
demonstrates the utility of the method to data with intermittent
noise. Importantly, this method assumes that the tensor is a good
representation of the diffusion signal in the data. If you have reason to
believe this is not the case (for example, you have data with very high b
values and you are particularly interested in locations in the brain in which
fibers cross), you might want to use a different method to fit your data.
References
----------
.. [Yendiki2013] Yendiki, A, Koldewynb, K, Kakunooria, S, Kanwisher, N, and
Fischl, B. (2013). Spurious group differences due to head motion in a
diffusion MRI study. Neuroimage.
.. [Chang2005] Chang, L-C, Jones, DK and Pierpaoli, C (2005). RESTORE: robust
estimation of tensors by outlier rejection. MRM, 53: 1088-95.
.. [Chung2006] Chung, SW, Lu, Y, Henry, R-G, (2006). Comparison of bootstrap
approaches for estimation of uncertainties of DTI parameters. NeuroImage 33,
531-541.
.. include:: ../links_names.inc
"""