def test_l1_increases_sparsity(radial_order=4, time_order=2):
gtab_4d = generate_gtab4D()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S = generate_signal_crossing(gtab_4d, l1, l2, l3)
qtdmri_mod_no_l1 = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
l1_regularization=True,
l1_weighting=0.)
qtdmri_mod_l1 = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
l1_regularization=True,
l1_weighting=.1)
qtdmri_fit_no_l1 = qtdmri_mod_no_l1.fit(S)
qtdmri_fit_l1 = qtdmri_mod_l1.fit(S)
sparsity_abs_no_reg = qtdmri_fit_no_l1.sparsity_abs()
sparsity_abs_reg = qtdmri_fit_l1.sparsity_abs()
assert_(sparsity_abs_no_reg > sparsity_abs_reg)
sparsity_density_no_reg = qtdmri_fit_no_l1.sparsity_density()
sparsity_density_reg = qtdmri_fit_l1.sparsity_density()
assert_(sparsity_density_no_reg > sparsity_density_reg)
def test_spherical_l1_increases_sparsity(radial_order=4, time_order=2):
gtab_4d = generate_gtab4D()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S = generate_signal_crossing(gtab_4d, l1, l2, l3)
qtdmri_mod_no_l1 = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
l1_regularization=True,
cartesian=False,
normalization=True,
l1_weighting=0.)
qtdmri_mod_l1 = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
l1_regularization=True,
cartesian=False,
normalization=True,
l1_weighting=.1)
with warnings.catch_warnings():
warnings.filterwarnings("ignore",
message=descoteaux07_legacy_msg,
category=PendingDeprecationWarning)
qtdmri_fit_no_l1 = qtdmri_mod_no_l1.fit(S)
qtdmri_fit_l1 = qtdmri_mod_l1.fit(S)
sparsity_abs_no_reg = qtdmri_fit_no_l1.sparsity_abs()
sparsity_abs_reg = qtdmri_fit_l1.sparsity_abs()
assert_equal(sparsity_abs_no_reg > sparsity_abs_reg, True)
sparsity_density_no_reg = qtdmri_fit_no_l1.sparsity_density()
sparsity_density_reg = qtdmri_fit_l1.sparsity_density()
assert_(sparsity_density_no_reg > sparsity_density_reg)
def test_spherical_laplacian_reduces_laplacian_norm(radial_order=4,
time_order=2):
gtab_4d = generate_gtab4D()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S = generate_signal_crossing(gtab_4d, l1, l2, l3)
qtdmri_mod_no_laplacian = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
cartesian=False,
laplacian_regularization=True,
laplacian_weighting=0.)
qtdmri_mod_laplacian = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
cartesian=False,
laplacian_regularization=True,
laplacian_weighting=1e-4)
qtdmri_fit_no_laplacian = qtdmri_mod_no_laplacian.fit(S)
qtdmri_fit_laplacian = qtdmri_mod_laplacian.fit(S)
laplacian_norm_no_reg = qtdmri_fit_no_laplacian.norm_of_laplacian_signal()
laplacian_norm_reg = qtdmri_fit_laplacian.norm_of_laplacian_signal()
assert_(laplacian_norm_no_reg > laplacian_norm_reg)
def test_spherical_laplacian_reduces_laplacian_norm(radial_order=4,
time_order=2):
gtab_4d = generate_gtab4D()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S = generate_signal_crossing(gtab_4d, l1, l2, l3)
qtdmri_mod_no_laplacian = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
cartesian=False,
laplacian_regularization=True,
laplacian_weighting=0.)
qtdmri_mod_laplacian = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
cartesian=False,
laplacian_regularization=True,
laplacian_weighting=1e-4)
with warnings.catch_warnings():
warnings.filterwarnings("ignore",
message=descoteaux07_legacy_msg,
category=PendingDeprecationWarning)
qtdmri_fit_no_laplacian = qtdmri_mod_no_laplacian.fit(S)
qtdmri_fit_laplacian = qtdmri_mod_laplacian.fit(S)
laplacian_norm_no_reg = qtdmri_fit_no_laplacian.norm_of_laplacian_signal()
laplacian_norm_reg = qtdmri_fit_laplacian.norm_of_laplacian_signal()
assert_(laplacian_norm_no_reg > laplacian_norm_reg)
def test_cartesian_normalization(radial_order=4, time_order=2):
gtab_4d = generate_gtab4D()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S = generate_signal_crossing(gtab_4d, l1, l2, l3)
qtdmri_mod_aniso = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
cartesian=True,
normalization=False)
qtdmri_mod_aniso_norm = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
cartesian=True,
normalization=True)
qtdmri_fit_aniso = qtdmri_mod_aniso.fit(S)
qtdmri_fit_aniso_norm = qtdmri_mod_aniso_norm.fit(S)
assert_array_almost_equal(qtdmri_fit_aniso.fitted_signal(),
qtdmri_fit_aniso_norm.fitted_signal())
rt_grid = qtdmri.create_rt_space_grid(5, 20e-3, 5, 0.02, .05)
pdf_aniso = qtdmri_fit_aniso.pdf(rt_grid)
pdf_aniso_norm = qtdmri_fit_aniso_norm.pdf(rt_grid)
assert_array_almost_equal(pdf_aniso / pdf_aniso.max(),
pdf_aniso_norm / pdf_aniso.max())
norm_laplacian = qtdmri_fit_aniso.norm_of_laplacian_signal()
norm_laplacian_norm = qtdmri_fit_aniso_norm.norm_of_laplacian_signal()
assert_array_almost_equal(norm_laplacian / norm_laplacian,
norm_laplacian_norm / norm_laplacian)
def test_anisotropic_isotropic_equivalence(radial_order=4, time_order=2):
# generate qt-scheme and arbitary synthetic crossing data.
gtab_4d = generate_gtab4D()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S = generate_signal_crossing(gtab_4d, l1, l2, l3)
# initialize both cartesian and spherical models without any kind of
# regularization
qtdmri_mod_aniso = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
cartesian=True,
anisotropic_scaling=False)
qtdmri_mod_iso = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
cartesian=False,
anisotropic_scaling=False)
# both implementations fit the same signal
qtdmri_fit_cart = qtdmri_mod_aniso.fit(S)
qtdmri_fit_sphere = qtdmri_mod_iso.fit(S)
# same signal fit
assert_array_almost_equal(qtdmri_fit_cart.fitted_signal(),
qtdmri_fit_sphere.fitted_signal())
# same PDF reconstruction
rt_grid = qtdmri.create_rt_space_grid(5, 20e-3, 5, 0.02, .05)
pdf_aniso = qtdmri_fit_cart.pdf(rt_grid)
pdf_iso = qtdmri_fit_sphere.pdf(rt_grid)
assert_array_almost_equal(pdf_aniso / pdf_aniso.max(),
pdf_iso / pdf_aniso.max())
# same norm of the laplacian
norm_laplacian_aniso = qtdmri_fit_cart.norm_of_laplacian_signal()
norm_laplacian_iso = qtdmri_fit_sphere.norm_of_laplacian_signal()
assert_almost_equal(norm_laplacian_aniso / norm_laplacian_aniso,
norm_laplacian_iso / norm_laplacian_aniso)
# all q-space index is the same for arbitrary tau
tau = 0.02
assert_almost_equal(qtdmri_fit_cart.rtop(tau), qtdmri_fit_sphere.rtop(tau))
assert_almost_equal(qtdmri_fit_cart.rtap(tau), qtdmri_fit_sphere.rtap(tau))
assert_almost_equal(qtdmri_fit_cart.rtpp(tau), qtdmri_fit_sphere.rtpp(tau))
assert_almost_equal(qtdmri_fit_cart.msd(tau), qtdmri_fit_sphere.msd(tau))
assert_almost_equal(qtdmri_fit_cart.qiv(tau), qtdmri_fit_sphere.qiv(tau))
# ODF estimation is the same
sphere = get_sphere()
assert_array_almost_equal(qtdmri_fit_cart.odf(sphere, tau, s=0),
qtdmri_fit_sphere.odf(sphere, tau, s=0))
def test_anisotropic_reduced_MSE(radial_order=0, time_order=0):
gtab_4d = generate_gtab4D()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S = generate_signal_crossing(gtab_4d, l1, l2, l3)
qtdmri_mod_aniso = qtdmri.QtdmriModel(gtab_4d, radial_order=radial_order,
time_order=time_order,
cartesian=True,
anisotropic_scaling=True)
qtdmri_mod_iso = qtdmri.QtdmriModel(gtab_4d, radial_order=radial_order,
time_order=time_order,
cartesian=True,
anisotropic_scaling=False)
qtdmri_fit_aniso = qtdmri_mod_aniso.fit(S)
qtdmri_fit_iso = qtdmri_mod_iso.fit(S)
mse_aniso = np.mean((S - qtdmri_fit_aniso.fitted_signal()) ** 2)
mse_iso = np.mean((S - qtdmri_fit_iso.fitted_signal()) ** 2)
assert_(mse_aniso < mse_iso)
def test_l1_CV(radial_order=4, time_order=2):
gtab_4d = generate_gtab4D()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S = generate_signal_crossing(gtab_4d, l1, l2, l3)
S_noise = add_noise(S, S0=1., snr=10)
qtdmri_mod_l1_cv = qtdmri.QtdmriModel(
gtab_4d, radial_order=radial_order, time_order=time_order,
l1_regularization=True, l1_weighting="CV"
)
qtdmri_fit_noise = qtdmri_mod_l1_cv.fit(S_noise)
assert_(qtdmri_fit_noise.alpha >= 0)
def test_number_of_coefficients(radial_order=4, time_order=2):
gtab_4d = generate_gtab4D()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S = generate_signal_crossing(gtab_4d, l1, l2, l3)
qtdmri_mod = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order)
qtdmri_fit = qtdmri_mod.fit(S)
number_of_coef_model = qtdmri_fit._qtdmri_coef.shape[0]
number_of_coef_analytic = qtdmri.qtdmri_number_of_coefficients(
radial_order, time_order)
assert_equal(number_of_coef_model, number_of_coef_analytic)
def test_spherical_normalization(radial_order=4, time_order=2):
gtab_4d = generate_gtab4D()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S = generate_signal_crossing(gtab_4d, l1, l2, l3)
qtdmri_mod_aniso = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
cartesian=False,
normalization=False)
qtdmri_mod_aniso_norm = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
cartesian=False,
normalization=True)
with warnings.catch_warnings():
warnings.filterwarnings("ignore",
message=descoteaux07_legacy_msg,
category=PendingDeprecationWarning)
qtdmri_fit = qtdmri_mod_aniso.fit(S)
qtdmri_fit_norm = qtdmri_mod_aniso_norm.fit(S)
assert_array_almost_equal(qtdmri_fit.fitted_signal(),
qtdmri_fit_norm.fitted_signal())
rt_grid = qtdmri.create_rt_space_grid(5, 20e-3, 5, 0.02, .05)
with warnings.catch_warnings():
warnings.filterwarnings("ignore",
message=descoteaux07_legacy_msg,
category=PendingDeprecationWarning)
pdf = qtdmri_fit.pdf(rt_grid)
pdf_norm = qtdmri_fit_norm.pdf(rt_grid)
assert_array_almost_equal(pdf / pdf.max(), pdf_norm / pdf.max())
norm_laplacian = qtdmri_fit.norm_of_laplacian_signal()
norm_laplacian_norm = qtdmri_fit_norm.norm_of_laplacian_signal()
assert_array_almost_equal(norm_laplacian / norm_laplacian,
norm_laplacian_norm / norm_laplacian)
def test_laplacian_GCV_higher_weight_with_noise(radial_order=4, time_order=2):
gtab_4d = generate_gtab4D()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S = generate_signal_crossing(gtab_4d, l1, l2, l3)
S_noise = add_noise(S, S0=1., snr=10)
qtdmri_mod_laplacian_GCV = qtdmri.QtdmriModel(
gtab_4d, radial_order=radial_order, time_order=time_order,
laplacian_regularization=True, laplacian_weighting="GCV"
)
qtdmri_fit_no_noise = qtdmri_mod_laplacian_GCV.fit(S)
qtdmri_fit_noise = qtdmri_mod_laplacian_GCV.fit(S_noise)
assert_(qtdmri_fit_noise.lopt > qtdmri_fit_no_noise.lopt)
def test_q0_constraint_and_unity_of_ODFs(radial_order=6, time_order=2):
gtab_4d = generate_gtab4D()
tau = gtab_4d.tau
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S = generate_signal_crossing(gtab_4d, l1, l2, l3)
# first test without regularization
qtdmri_mod_ls = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order)
qtdmri_fit_ls = qtdmri_mod_ls.fit(S)
fitted_signal = qtdmri_fit_ls.fitted_signal()
# only first tau_point is normalized with least squares.
E_q0_first_tau = fitted_signal[np.all([tau == tau.min(), gtab_4d.b0s_mask],
axis=0)]
assert_almost_equal(float(E_q0_first_tau), 1.)
# now with cvxpy regularization cartesian
qtdmri_mod_lap = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
laplacian_regularization=True,
laplacian_weighting=1e-4)
qtdmri_fit_lap = qtdmri_mod_lap.fit(S)
fitted_signal = qtdmri_fit_lap.fitted_signal()
E_q0_first_tau = fitted_signal[np.all([tau == tau.min(), gtab_4d.b0s_mask],
axis=0)]
E_q0_last_tau = fitted_signal[np.all([tau == tau.max(), gtab_4d.b0s_mask],
axis=0)]
assert_almost_equal(E_q0_first_tau[0], 1.)
assert_almost_equal(E_q0_last_tau[0], 1.)
# check if odf in spherical harmonics for cartesian raises an error
try:
qtdmri_fit_lap.odf_sh(tau=tau.max())
assert_equal(True, False)
except ValueError:
print('missing spherical harmonics cartesian ODF caught.')
# now with cvxpy regularization spherical
qtdmri_mod_lap = qtdmri.QtdmriModel(gtab_4d,
radial_order=radial_order,
time_order=time_order,
laplacian_regularization=True,
laplacian_weighting=1e-4,
cartesian=False)
with warnings.catch_warnings():
warnings.filterwarnings("ignore",
message=descoteaux07_legacy_msg,
category=PendingDeprecationWarning)
qtdmri_fit_lap = qtdmri_mod_lap.fit(S)
fitted_signal = qtdmri_fit_lap.fitted_signal()
E_q0_first_tau = fitted_signal[np.all([tau == tau.min(), gtab_4d.b0s_mask],
axis=0)]
E_q0_last_tau = fitted_signal[np.all([tau == tau.max(), gtab_4d.b0s_mask],
axis=0)]
assert_almost_equal(float(E_q0_first_tau), 1.)
assert_almost_equal(float(E_q0_last_tau), 1.)
# test if marginal ODF integral in sh is equal to one
# Integral of Y00 spherical harmonic is 1 / (2 * np.sqrt(np.pi))
# division with this results in normalization
odf_sh = qtdmri_fit_lap.odf_sh(s=0, tau=tau.max())
odf_integral = odf_sh[0] * (2 * np.sqrt(np.pi))
assert_almost_equal(odf_integral, 1.)
rtops = []
rtaps = []
rtpps = []
for i, (data_, mask_, gtab_) in enumerate(zip(data, cc_masks, gtabs)):
# select the corpus callsoum voxel for every dataset
cc_voxels = data_[mask_ == 1]
# initialize the qt-dMRI model.
# recommended basis orders are radial_order=6 and time_order=2.
# The combined Laplacian and l1-regularization using Generalized
# Cross-Validation (GCV) and Cross-Validation (CV) settings is most robust,
# but can be used separately and with weightings preset to any positive
# value to optimize for speed.
qtdmri_mod = qtdmri.QtdmriModel(gtab_,
radial_order=6,
time_order=2,
laplacian_regularization=True,
laplacian_weighting='GCV',
l1_regularization=True,
l1_weighting='CV')
# fit the model.
# Here we take every 5th voxel for speed, but of course all voxels can be
# fit for a more robust result later on.
qtdmri_fit = qtdmri_mod.fit(cc_voxels[::5])
qtdmri_fits.append(qtdmri_fit)
# We estimate MSD, RTOP, RTAP and RTPP for the chosen diffusion times.
msds.append(np.array(list(map(qtdmri_fit.msd, taus))))
rtops.append(np.array(list(map(qtdmri_fit.rtop, taus))))
rtaps.append(np.array(list(map(qtdmri_fit.rtap, taus))))
rtpps.append(np.array(list(map(qtdmri_fit.rtpp, taus))))
"""
The estimated :math:`q\tau`-indices, for the chosen diffusion times, are now
