def test_mapmri_compare_fitted_pdf_with_multi_tensor(radial_order=6):
gtab = get_gtab_taiwan_dsi()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S, _ = generate_signal_crossing(gtab, l1, l2, l3)
radius_max = 0.02 # 40 microns
gridsize = 10
r_points = mapmri.create_rspace(gridsize, radius_max)
# test MAPMRI fitting
mapm = MapmriModel(gtab,
radial_order=radial_order,
laplacian_weighting=0.0001)
mapfit = mapm.fit(S)
# compare the mapmri pdf with the ground truth multi_tensor pdf
mevals = np.array(([l1, l2, l3], [l1, l2, l3]))
angl = [(0, 0), (60, 0)]
pdf_mt = multi_tensor_pdf(r_points,
mevals=mevals,
angles=angl,
fractions=[50, 50])
pdf_map = mapfit.pdf(r_points)
nmse_pdf = np.sqrt(np.sum((pdf_mt - pdf_map)**2)) / (pdf_mt.sum())
assert_almost_equal(nmse_pdf, 0.0, 2)
def test_mapmri_compare_fitted_pdf_with_multi_tensor(radial_order=6):
gtab = get_gtab_taiwan_dsi()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S, _ = generate_signal_crossing(gtab, l1, l2, l3)
radius_max = 0.02 # 40 microns
gridsize = 10
r_points = mapmri.create_rspace(gridsize, radius_max)
# test MAPMRI fitting
mapm = MapmriModel(gtab, radial_order=radial_order,
laplacian_weighting=0.0001)
mapfit = mapm.fit(S)
# compare the mapmri pdf with the ground truth multi_tensor pdf
mevals = np.array(([l1, l2, l3],
[l1, l2, l3]))
angl = [(0, 0), (60, 0)]
pdf_mt = multi_tensor_pdf(r_points, mevals=mevals,
angles=angl, fractions=[50, 50])
pdf_map = mapfit.pdf(r_points)
nmse_pdf = np.sqrt(np.sum((pdf_mt - pdf_map) ** 2)) / (pdf_mt.sum())
assert_almost_equal(nmse_pdf, 0.0, 2)
def test_positivity_constraint(radial_order=6):
gtab = get_gtab_taiwan_dsi()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S, _ = generate_signal_crossing(gtab, l1, l2, l3, angle2=60)
S_noise = add_noise(S, snr=20, S0=100.)
gridsize = 20
max_radius = 15e-3 # 20 microns maximum radius
r_grad = mapmri.create_rspace(gridsize, max_radius)
# The positivity constraint does not make the pdf completely positive
# but greatly decreases the amount of negativity in the constrained points.
# We test if the amount of negative pdf has decreased more than 90%
mapmod_no_constraint = MapmriModel(gtab,
radial_order=radial_order,
laplacian_regularization=False,
positivity_constraint=False)
mapfit_no_constraint = mapmod_no_constraint.fit(S_noise)
pdf = mapfit_no_constraint.pdf(r_grad)
pdf_negative_no_constraint = pdf[pdf < 0].sum()
mapmod_constraint = MapmriModel(gtab,
radial_order=radial_order,
laplacian_regularization=False,
positivity_constraint=True,
pos_grid=gridsize,
pos_radius='adaptive')
mapfit_constraint = mapmod_constraint.fit(S_noise)
pdf = mapfit_constraint.pdf(r_grad)
pdf_negative_constraint = pdf[pdf < 0].sum()
assert_equal((pdf_negative_constraint / pdf_negative_no_constraint) < 0.1,
True)
# the same for isotropic scaling
mapmod_no_constraint = MapmriModel(gtab,
radial_order=radial_order,
laplacian_regularization=False,
positivity_constraint=False,
anisotropic_scaling=False)
mapfit_no_constraint = mapmod_no_constraint.fit(S_noise)
pdf = mapfit_no_constraint.pdf(r_grad)
pdf_negative_no_constraint = pdf[pdf < 0].sum()
mapmod_constraint = MapmriModel(gtab,
radial_order=radial_order,
laplacian_regularization=False,
positivity_constraint=True,
anisotropic_scaling=False,
pos_grid=gridsize,
pos_radius='adaptive')
mapfit_constraint = mapmod_constraint.fit(S_noise)
pdf = mapfit_constraint.pdf(r_grad)
pdf_negative_constraint = pdf[pdf < 0].sum()
assert_equal((pdf_negative_constraint / pdf_negative_no_constraint) < 0.1,
True)
def test_mapmri_pdf_integral_unity(radial_order=6):
gtab = get_gtab_taiwan_dsi()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S, _ = generate_signal_crossing(gtab, l1, l2, l3)
sphere = default_sphere
# test MAPMRI fitting
mapm = MapmriModel(gtab,
radial_order=radial_order,
laplacian_weighting=0.02)
mapfit = mapm.fit(S)
c_map = mapfit.mapmri_coeff
# test if the analytical integral of the pdf is equal to one
indices = mapmri_index_matrix(radial_order)
integral = 0
for i in range(indices.shape[0]):
n1, n2, n3 = indices[i]
integral += c_map[i] * int_func(n1) * int_func(n2) * int_func(n3)
assert_almost_equal(integral, 1.0, 3)
# test if numerical integral of odf is equal to one
odf = mapfit.odf(sphere, s=0)
odf_sum = odf.sum() / sphere.vertices.shape[0] * (4 * np.pi)
assert_almost_equal(odf_sum, 1.0, 2)
# do the same for isotropic implementation
radius_max = 0.04 # 40 microns
gridsize = 17
r_points = mapmri.create_rspace(gridsize, radius_max)
with warnings.catch_warnings():
warnings.filterwarnings("ignore",
message=descoteaux07_legacy_msg,
category=PendingDeprecationWarning)
mapm = MapmriModel(gtab,
radial_order=radial_order,
laplacian_weighting=0.02,
anisotropic_scaling=False)
mapfit = mapm.fit(S)
with warnings.catch_warnings():
warnings.filterwarnings("ignore",
message=descoteaux07_legacy_msg,
category=PendingDeprecationWarning)
pdf = mapfit.pdf(r_points)
pdf[r_points[:, 2] == 0.] /= 2 # for antipodal symmetry on z-plane
point_volume = (radius_max / (gridsize // 2))**3
integral = pdf.sum() * point_volume * 2
assert_almost_equal(integral, 1.0, 3)
with warnings.catch_warnings():
warnings.filterwarnings("ignore",
message=descoteaux07_legacy_msg,
category=PendingDeprecationWarning)
odf = mapfit.odf(sphere, s=0)
odf_sum = odf.sum() / sphere.vertices.shape[0] * (4 * np.pi)
assert_almost_equal(odf_sum, 1.0, 2)
def test_positivity_constraint(radial_order=6):
gtab = get_gtab_taiwan_dsi()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S, _ = generate_signal_crossing(gtab, l1, l2, l3, angle2=60)
S_noise = add_noise(S, snr=20, S0=100.)
gridsize = 20
max_radius = 15e-3 # 20 microns maximum radius
r_grad = mapmri.create_rspace(gridsize, max_radius)
# the posivitivity constraint does not make the pdf completely positive
# but greatly decreases the amount of negativity in the constrained points.
# we test if the amount of negative pdf has decreased more than 90%
mapmod_no_constraint = MapmriModel(gtab, radial_order=radial_order,
laplacian_regularization=False,
positivity_constraint=False)
mapfit_no_constraint = mapmod_no_constraint.fit(S_noise)
pdf = mapfit_no_constraint.pdf(r_grad)
pdf_negative_no_constraint = pdf[pdf < 0].sum()
mapmod_constraint = MapmriModel(gtab, radial_order=radial_order,
laplacian_regularization=False,
positivity_constraint=True,
pos_grid=gridsize,
pos_radius='adaptive')
mapfit_constraint = mapmod_constraint.fit(S_noise)
pdf = mapfit_constraint.pdf(r_grad)
pdf_negative_constraint = pdf[pdf < 0].sum()
assert_equal((pdf_negative_constraint / pdf_negative_no_constraint) < 0.1,
True)
# the same for isotropic scaling
mapmod_no_constraint = MapmriModel(gtab, radial_order=radial_order,
laplacian_regularization=False,
positivity_constraint=False,
anisotropic_scaling=False)
mapfit_no_constraint = mapmod_no_constraint.fit(S_noise)
pdf = mapfit_no_constraint.pdf(r_grad)
pdf_negative_no_constraint = pdf[pdf < 0].sum()
mapmod_constraint = MapmriModel(gtab, radial_order=radial_order,
laplacian_regularization=False,
positivity_constraint=True,
anisotropic_scaling=False,
pos_grid=gridsize,
pos_radius='adaptive')
mapfit_constraint = mapmod_constraint.fit(S_noise)
pdf = mapfit_constraint.pdf(r_grad)
pdf_negative_constraint = pdf[pdf < 0].sum()
assert_equal((pdf_negative_constraint / pdf_negative_no_constraint) < 0.1,
True)
def test_mapmri_pdf_integral_unity(radial_order=6):
gtab = get_gtab_taiwan_dsi()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S, _ = generate_signal_crossing(gtab, l1, l2, l3)
sphere = get_sphere('symmetric724')
# test MAPMRI fitting
mapm = MapmriModel(gtab, radial_order=radial_order,
laplacian_weighting=0.02)
mapfit = mapm.fit(S)
c_map = mapfit.mapmri_coeff
# test if the analytical integral of the pdf is equal to one
indices = mapmri_index_matrix(radial_order)
integral = 0
for i in range(indices.shape[0]):
n1, n2, n3 = indices[i]
integral += c_map[i] * int_func(n1) * int_func(n2) * int_func(n3)
assert_almost_equal(integral, 1.0, 3)
# test if numerical integral of odf is equal to one
odf = mapfit.odf(sphere, s=0)
odf_sum = odf.sum() / sphere.vertices.shape[0] * (4 * np.pi)
assert_almost_equal(odf_sum, 1.0, 2)
# do the same for isotropic implementation
radius_max = 0.04 # 40 microns
gridsize = 17
r_points = mapmri.create_rspace(gridsize, radius_max)
mapm = MapmriModel(gtab, radial_order=radial_order,
laplacian_weighting=0.02,
anisotropic_scaling=False)
mapfit = mapm.fit(S)
pdf = mapfit.pdf(r_points)
pdf[r_points[:, 2] == 0.] /= 2 # for antipodal symmetry on z-plane
point_volume = (radius_max / (gridsize // 2)) ** 3
integral = pdf.sum() * point_volume * 2
assert_almost_equal(integral, 1.0, 3)
odf = mapfit.odf(sphere, s=0)
odf_sum = odf.sum() / sphere.vertices.shape[0] * (4 * np.pi)
assert_almost_equal(odf_sum, 1.0, 2)
def test_signal_fitting_equality_anisotropic_isotropic(radial_order=6):
gtab = get_gtab_taiwan_dsi()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S, _ = generate_signal_crossing(gtab, l1, l2, l3, angle2=60)
gridsize = 17
radius_max = 0.02
r_points = mapmri.create_rspace(gridsize, radius_max)
tenmodel = dti.TensorModel(gtab)
evals = tenmodel.fit(S).evals
tau = 1 / (4 * np.pi**2)
# estimate isotropic scale factor
u0 = mapmri.isotropic_scale_factor(evals * 2 * tau)
mu = np.array([u0, u0, u0])
qvals = np.sqrt(gtab.bvals / tau) / (2 * np.pi)
q = gtab.bvecs * qvals[:, None]
M_aniso = mapmri.mapmri_phi_matrix(radial_order, mu, q)
K_aniso = mapmri.mapmri_psi_matrix(radial_order, mu, r_points)
M_iso = mapmri.mapmri_isotropic_phi_matrix(radial_order, u0, q)
K_iso = mapmri.mapmri_isotropic_psi_matrix(radial_order, u0, r_points)
coef_aniso = np.dot(np.linalg.pinv(M_aniso), S)
coef_iso = np.dot(np.linalg.pinv(M_iso), S)
# test if anisotropic and isotropic implementation produce equal results
# if the same isotropic scale factors are used
s_fitted_aniso = np.dot(M_aniso, coef_aniso)
s_fitted_iso = np.dot(M_iso, coef_iso)
assert_array_almost_equal(s_fitted_aniso, s_fitted_iso)
# the same test for the PDF
pdf_fitted_aniso = np.dot(K_aniso, coef_aniso)
pdf_fitted_iso = np.dot(K_iso, coef_iso)
assert_array_almost_equal(pdf_fitted_aniso / pdf_fitted_iso,
np.ones_like(pdf_fitted_aniso), 3)
# test if the implemented version also produces the same result
mapm = MapmriModel(gtab,
radial_order=radial_order,
laplacian_regularization=False,
anisotropic_scaling=False)
s_fitted_implemented_isotropic = mapm.fit(S).fitted_signal()
# normalize non-implemented fitted signal with b0 value
s_fitted_aniso_norm = s_fitted_aniso / s_fitted_aniso.max()
assert_array_almost_equal(s_fitted_aniso_norm,
s_fitted_implemented_isotropic)
# test if norm of signal laplacians are the same
laplacian_matrix_iso = mapmri.mapmri_isotropic_laplacian_reg_matrix(
radial_order, mu[0])
ind_mat = mapmri.mapmri_index_matrix(radial_order)
S_mat, T_mat, U_mat = mapmri.mapmri_STU_reg_matrices(radial_order)
laplacian_matrix_aniso = mapmri.mapmri_laplacian_reg_matrix(
ind_mat, mu, S_mat, T_mat, U_mat)
norm_aniso = np.dot(coef_aniso, np.dot(coef_aniso, laplacian_matrix_aniso))
norm_iso = np.dot(coef_iso, np.dot(coef_iso, laplacian_matrix_iso))
assert_almost_equal(norm_iso, norm_aniso)
def test_signal_fitting_equality_anisotropic_isotropic(radial_order=6):
gtab = get_gtab_taiwan_dsi()
l1, l2, l3 = [0.0015, 0.0003, 0.0003]
S, _ = generate_signal_crossing(gtab, l1, l2, l3, angle2=60)
gridsize = 17
radius_max = 0.02
r_points = mapmri.create_rspace(gridsize, radius_max)
tenmodel = dti.TensorModel(gtab)
evals = tenmodel.fit(S).evals
tau = 1 / (4 * np.pi ** 2)
# estimate isotropic scale factor
u0 = mapmri.isotropic_scale_factor(evals * 2 * tau)
mu = np.array([u0, u0, u0])
qvals = np.sqrt(gtab.bvals / tau) / (2 * np.pi)
q = gtab.bvecs * qvals[:, None]
M_aniso = mapmri.mapmri_phi_matrix(radial_order, mu, q)
K_aniso = mapmri.mapmri_psi_matrix(radial_order, mu, r_points)
M_iso = mapmri.mapmri_isotropic_phi_matrix(radial_order, u0, q)
K_iso = mapmri.mapmri_isotropic_psi_matrix(radial_order, u0, r_points)
coef_aniso = np.dot(np.linalg.pinv(M_aniso), S)
coef_iso = np.dot(np.linalg.pinv(M_iso), S)
# test if anisotropic and isotropic implementation produce equal results
# if the same isotropic scale factors are used
s_fitted_aniso = np.dot(M_aniso, coef_aniso)
s_fitted_iso = np.dot(M_iso, coef_iso)
assert_array_almost_equal(s_fitted_aniso, s_fitted_iso)
# the same test for the PDF
pdf_fitted_aniso = np.dot(K_aniso, coef_aniso)
pdf_fitted_iso = np.dot(K_iso, coef_iso)
assert_array_almost_equal(pdf_fitted_aniso / pdf_fitted_iso,
np.ones_like(pdf_fitted_aniso), 3)
# test if the implemented version also produces the same result
mapm = MapmriModel(gtab, radial_order=radial_order,
laplacian_regularization=False,
anisotropic_scaling=False)
s_fitted_implemented_isotropic = mapm.fit(S).fitted_signal()
# normalize non-implemented fitted signal with b0 value
s_fitted_aniso_norm = s_fitted_aniso / s_fitted_aniso.max()
assert_array_almost_equal(s_fitted_aniso_norm,
s_fitted_implemented_isotropic)
# test if norm of signal laplacians are the same
laplacian_matrix_iso = mapmri.mapmri_isotropic_laplacian_reg_matrix(
radial_order, mu[0])
ind_mat = mapmri.mapmri_index_matrix(radial_order)
S_mat, T_mat, U_mat = mapmri.mapmri_STU_reg_matrices(radial_order)
laplacian_matrix_aniso = mapmri.mapmri_laplacian_reg_matrix(
ind_mat, mu, S_mat, T_mat, U_mat)
norm_aniso = np.dot(coef_aniso, np.dot(coef_aniso, laplacian_matrix_aniso))
norm_iso = np.dot(coef_iso, np.dot(coef_iso, laplacian_matrix_iso))
assert_almost_equal(norm_iso, norm_aniso)