def test_mapmri_laplacian_isotropic(radial_order=6):
gtab = get_gtab_taiwan_dsi()
l1, l2, l3 = [0.0003, 0.0003, 0.0003] # isotropic diffusivities
S = single_tensor(gtab, evals=np.r_[l1, l2, l3])
mapm = MapmriModel(gtab,
radial_order=radial_order,
laplacian_regularization=False,
anisotropic_scaling=False)
mapfit = mapm.fit(S)
tau = 1 / (4 * np.pi**2)
# ground truth norm of laplacian of tensor
norm_of_laplacian_gt = ((3 *
(l1**2 + l2**2 + l3**2) + 2 * l2 * l3 + 2 * l1 *
(l2 + l3)) * (np.pi**(5 / 2.) * tau) /
(np.sqrt(2 * l1 * l2 * l3 * tau)))
# check if estimated laplacian corresponds with ground truth
laplacian_matrix = mapmri.mapmri_isotropic_laplacian_reg_matrix(
radial_order, mapfit.mu[0])
coef = mapfit._mapmri_coef
norm_of_laplacian = np.dot(np.dot(coef, laplacian_matrix), coef)
assert_almost_equal(norm_of_laplacian, norm_of_laplacian_gt)
def test_mapmri_laplacian_isotropic(radial_order=6):
gtab = get_gtab_taiwan_dsi()
l1, l2, l3 = [0.0003, 0.0003, 0.0003] # isotropic diffusivities
S = single_tensor(gtab, evals=np.r_[l1, l2, l3])
mapm = MapmriModel(gtab, radial_order=radial_order,
laplacian_regularization=False,
anisotropic_scaling=False)
mapfit = mapm.fit(S)
tau = 1 / (4 * np.pi ** 2)
# ground truth norm of laplacian of tensor
norm_of_laplacian_gt = (
(3 * (l1 ** 2 + l2 ** 2 + l3 ** 2) +
2 * l2 * l3 + 2 * l1 * (l2 + l3)) * (np.pi ** (5 / 2.) * tau) /
(np.sqrt(2 * l1 * l2 * l3 * tau))
)
# check if estimated laplacian corresponds with ground truth
laplacian_matrix = mapmri.mapmri_isotropic_laplacian_reg_matrix(
radial_order, mapfit.mu[0])
coef = mapfit._mapmri_coef
norm_of_laplacian = np.dot(np.dot(coef, laplacian_matrix), coef)
assert_almost_equal(norm_of_laplacian, norm_of_laplacian_gt)
def test_laplacian_regularization(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.)
weight_array = np.linspace(0, .3, 301)
mapmod_unreg = MapmriModel(gtab,
radial_order=radial_order,
laplacian_regularization=False,
laplacian_weighting=weight_array)
mapmod_laplacian_array = MapmriModel(gtab,
radial_order=radial_order,
laplacian_regularization=True,
laplacian_weighting=weight_array)
mapmod_laplacian_gcv = MapmriModel(gtab,
radial_order=radial_order,
laplacian_regularization=True,
laplacian_weighting="GCV")
# test the Generalized Cross Validation
# test if GCV gives very low if there is no noise
mapfit_laplacian_array = mapmod_laplacian_array.fit(S)
assert_equal(mapfit_laplacian_array.lopt < 0.01, True)
# test if GCV gives higher values if there is noise
mapfit_laplacian_array = mapmod_laplacian_array.fit(S_noise)
lopt_array = mapfit_laplacian_array.lopt
assert_equal(lopt_array > 0.01, True)
# test if continuous GCV gives the same the one based on an array
mapfit_laplacian_gcv = mapmod_laplacian_gcv.fit(S_noise)
lopt_gcv = mapfit_laplacian_gcv.lopt
assert_almost_equal(lopt_array, lopt_gcv, 2)
# test if laplacian reduced the norm of the laplacian in the reconstruction
mu = mapfit_laplacian_gcv.mu
laplacian_matrix = mapmri.mapmri_laplacian_reg_matrix(
mapmod_laplacian_gcv.ind_mat, mu, mapmod_laplacian_gcv.S_mat,
mapmod_laplacian_gcv.T_mat, mapmod_laplacian_gcv.U_mat)
coef_unreg = mapmod_unreg.fit(S_noise)._mapmri_coef
coef_laplacian = mapfit_laplacian_gcv._mapmri_coef
laplacian_norm_unreg = np.dot(coef_unreg,
np.dot(coef_unreg, laplacian_matrix))
laplacian_norm_laplacian = np.dot(coef_laplacian,
np.dot(coef_laplacian, laplacian_matrix))
assert_equal(laplacian_norm_laplacian < laplacian_norm_unreg, True)
# the same for isotropic scaling
mapmod_unreg = MapmriModel(gtab,
radial_order=radial_order,
laplacian_regularization=False,
laplacian_weighting=weight_array,
anisotropic_scaling=False)
mapmod_laplacian_array = MapmriModel(gtab,
radial_order=radial_order,
laplacian_regularization=True,
laplacian_weighting=weight_array,
anisotropic_scaling=False)
mapmod_laplacian_gcv = MapmriModel(gtab,
radial_order=radial_order,
laplacian_regularization=True,
laplacian_weighting="GCV",
anisotropic_scaling=False)
# test the Generalized Cross Validation
# test if GCV gives zero if there is no noise
mapfit_laplacian_array = mapmod_laplacian_array.fit(S)
assert_equal(mapfit_laplacian_array.lopt < 0.01, True)
# test if GCV gives higher values if there is noise
mapfit_laplacian_array = mapmod_laplacian_array.fit(S_noise)
lopt_array = mapfit_laplacian_array.lopt
assert_equal(lopt_array > 0.01, True)
# test if continuous GCV gives the same the one based on an array
mapfit_laplacian_gcv = mapmod_laplacian_gcv.fit(S_noise)
lopt_gcv = mapfit_laplacian_gcv.lopt
assert_almost_equal(lopt_array, lopt_gcv, 2)
# test if laplacian reduced the norm of the laplacian in the reconstruction
mu = mapfit_laplacian_gcv.mu
laplacian_matrix = mapmri.mapmri_isotropic_laplacian_reg_matrix(
radial_order, mu[0])
coef_unreg = mapmod_unreg.fit(S_noise)._mapmri_coef
coef_laplacian = mapfit_laplacian_gcv._mapmri_coef
laplacian_norm_unreg = np.dot(coef_unreg,
np.dot(coef_unreg, laplacian_matrix))
laplacian_norm_laplacian = np.dot(coef_laplacian,
np.dot(coef_laplacian, laplacian_matrix))
assert_equal(laplacian_norm_laplacian < laplacian_norm_unreg, True)
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_laplacian_regularization(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.)
weight_array = np.linspace(0, .3, 301)
mapmod_unreg = MapmriModel(gtab, radial_order=radial_order,
laplacian_regularization=False,
laplacian_weighting=weight_array)
mapmod_laplacian_array = MapmriModel(gtab, radial_order=radial_order,
laplacian_regularization=True,
laplacian_weighting=weight_array)
mapmod_laplacian_gcv = MapmriModel(gtab, radial_order=radial_order,
laplacian_regularization=True,
laplacian_weighting="GCV")
# test the Generalized Cross Validation
# test if GCV gives very low if there is no noise
mapfit_laplacian_array = mapmod_laplacian_array.fit(S)
assert_equal(mapfit_laplacian_array.lopt < 0.01, True)
# test if GCV gives higher values if there is noise
mapfit_laplacian_array = mapmod_laplacian_array.fit(S_noise)
lopt_array = mapfit_laplacian_array.lopt
assert_equal(lopt_array > 0.01, True)
# test if continuous GCV gives the same the one based on an array
mapfit_laplacian_gcv = mapmod_laplacian_gcv.fit(S_noise)
lopt_gcv = mapfit_laplacian_gcv.lopt
assert_almost_equal(lopt_array, lopt_gcv, 2)
# test if laplacian reduced the norm of the laplacian in the reconstruction
mu = mapfit_laplacian_gcv.mu
laplacian_matrix = mapmri.mapmri_laplacian_reg_matrix(
mapmod_laplacian_gcv.ind_mat, mu, mapmod_laplacian_gcv.S_mat,
mapmod_laplacian_gcv.T_mat, mapmod_laplacian_gcv.U_mat)
coef_unreg = mapmod_unreg.fit(S_noise)._mapmri_coef
coef_laplacian = mapfit_laplacian_gcv._mapmri_coef
laplacian_norm_unreg = np.dot(
coef_unreg, np.dot(coef_unreg, laplacian_matrix))
laplacian_norm_laplacian = np.dot(
coef_laplacian, np.dot(coef_laplacian, laplacian_matrix))
assert_equal(laplacian_norm_laplacian < laplacian_norm_unreg, True)
# the same for isotropic scaling
mapmod_unreg = MapmriModel(gtab, radial_order=radial_order,
laplacian_regularization=False,
laplacian_weighting=weight_array,
anisotropic_scaling=False)
mapmod_laplacian_array = MapmriModel(gtab, radial_order=radial_order,
laplacian_regularization=True,
laplacian_weighting=weight_array,
anisotropic_scaling=False)
mapmod_laplacian_gcv = MapmriModel(gtab, radial_order=radial_order,
laplacian_regularization=True,
laplacian_weighting="GCV",
anisotropic_scaling=False)
# test the Generalized Cross Validation
# test if GCV gives zero if there is no noise
mapfit_laplacian_array = mapmod_laplacian_array.fit(S)
assert_equal(mapfit_laplacian_array.lopt < 0.01, True)
# test if GCV gives higher values if there is noise
mapfit_laplacian_array = mapmod_laplacian_array.fit(S_noise)
lopt_array = mapfit_laplacian_array.lopt
assert_equal(lopt_array > 0.01, True)
# test if continuous GCV gives the same the one based on an array
mapfit_laplacian_gcv = mapmod_laplacian_gcv.fit(S_noise)
lopt_gcv = mapfit_laplacian_gcv.lopt
assert_almost_equal(lopt_array, lopt_gcv, 2)
# test if laplacian reduced the norm of the laplacian in the reconstruction
mu = mapfit_laplacian_gcv.mu
laplacian_matrix = mapmri.mapmri_isotropic_laplacian_reg_matrix(
radial_order, mu[0])
coef_unreg = mapmod_unreg.fit(S_noise)._mapmri_coef
coef_laplacian = mapfit_laplacian_gcv._mapmri_coef
laplacian_norm_unreg = np.dot(
coef_unreg, np.dot(coef_unreg, laplacian_matrix))
laplacian_norm_laplacian = np.dot(
coef_laplacian, np.dot(coef_laplacian, laplacian_matrix))
assert_equal(laplacian_norm_laplacian < laplacian_norm_unreg, True)
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)
