def multi_tissue_basis(gtab, sh_order, iso_comp):
"""
Builds a basis for multi-shell multi-tissue CSD model.
Parameters
----------
gtab : GradientTable
sh_order : int
iso_comp: int
Number of tissue compartments for running the MSMT-CSD. Minimum
number of compartments required is 2.
Returns
-------
B : ndarray
Matrix of the spherical harmonics model used to fit the data
m : int ``|m| <= n``
The order of the harmonic.
n : int ``>= 0``
The degree of the harmonic.
"""
if iso_comp < 2:
msg = ("Multi-tissue CSD requires at least 2 tissue compartments")
raise ValueError(msg)
r, theta, phi = geo.cart2sphere(*gtab.gradients.T)
m, n = shm.sph_harm_ind_list(sh_order)
B = shm.real_sh_descoteaux_from_index(m, n, theta[:, None], phi[:, None])
B[np.ix_(gtab.b0s_mask, n > 0)] = 0.
iso = np.empty([B.shape[0], iso_comp])
iso[:] = SH_CONST
B = np.concatenate([iso, B], axis=1)
return B, m, n
def test_hat_and_lcr():
hemi = hemi_icosahedron.subdivide(3)
m, n = sph_harm_ind_list(8)
with warnings.catch_warnings():
warnings.filterwarnings("ignore",
message=descoteaux07_legacy_msg,
category=PendingDeprecationWarning)
B = real_sh_descoteaux_from_index(m, n, hemi.theta[:, None],
hemi.phi[:, None])
H = hat(B)
B_hat = np.dot(H, B)
assert_array_almost_equal(B, B_hat)
R = lcr_matrix(H)
d = np.arange(len(hemi.theta))
r = d - np.dot(H, d)
lev = np.sqrt(1 - H.diagonal())
r /= lev
r -= r.mean()
r2 = np.dot(R, d)
assert_array_almost_equal(r, r2)
r3 = np.dot(d, R.T)
assert_array_almost_equal(r, r3)
def test_mcsd_model_delta():
sh_order = 8
gtab = get_3shell_gtab()
response = multi_shell_fiber_response(sh_order, [0, 1000, 2000, 3500],
wm_response,
gm_response,
csf_response)
model = MultiShellDeconvModel(gtab, response)
iso = response.iso
theta, phi = default_sphere.theta, default_sphere.phi
B = shm.real_sh_descoteaux_from_index(
response.m, response.n, theta[:, None], phi[:, None])
wm_delta = model.delta.copy()
# set isotropic components to zero
wm_delta[:iso] = 0.
wm_delta = _expand(model.m, iso, wm_delta)
for i, s in enumerate([0, 1000, 2000, 3500]):
g = GradientTable(default_sphere.vertices * s)
signal = model.predict(wm_delta, g)
expected = np.dot(response.response[i, iso:], B.T)
npt.assert_array_almost_equal(signal, expected)
signal = model.predict(wm_delta, gtab)
fit = model.fit(signal)
m = model.m
npt.assert_array_almost_equal(fit.shm_coeff[m != 0], 0., 2)
def test_smooth_pinv():
hemi = hemi_icosahedron.subdivide(2)
m, n = sph_harm_ind_list(4)
with warnings.catch_warnings():
warnings.filterwarnings("ignore",
message=descoteaux07_legacy_msg,
category=PendingDeprecationWarning)
B = real_sh_descoteaux_from_index(m, n, hemi.theta[:, None],
hemi.phi[:, None])
L = np.zeros(len(m))
C = smooth_pinv(B, L)
D = np.dot(npl.inv(np.dot(B.T, B)), B.T)
assert_array_almost_equal(C, D)
L = n * (n + 1) * .05
C = smooth_pinv(B, L)
L = np.diag(L)
D = np.dot(npl.inv(np.dot(B.T, B) + L * L), B.T)
assert_array_almost_equal(C, D)
L = np.arange(len(n)) * .05
C = smooth_pinv(B, L)
L = np.diag(L)
D = np.dot(npl.inv(np.dot(B.T, B) + L * L), B.T)
assert_array_almost_equal(C, D)
def rho_matrix(sh_order, vecs):
r"""Compute the SH matrix $\rho$
"""
r, theta, phi = cart2sphere(vecs[:, 0], vecs[:, 1], vecs[:, 2])
theta[np.isnan(theta)] = 0
n_c = int((sh_order + 1) * (sh_order + 2) / 2)
rho = np.zeros((vecs.shape[0], n_c))
counter = 0
for l in range(0, sh_order + 1, 2):
for m in range(-l, l + 1):
rho[:, counter] = real_sh_descoteaux_from_index(m, l, theta, phi)
counter += 1
return rho
def test_hat_and_lcr():
hemi = hemi_icosahedron.subdivide(3)
m, n = sph_harm_ind_list(8)
B = real_sh_descoteaux_from_index(m, n, hemi.theta[:, None],
hemi.phi[:, None])
H = hat(B)
B_hat = np.dot(H, B)
assert_array_almost_equal(B, B_hat)
R = lcr_matrix(H)
d = np.arange(len(hemi.theta))
r = d - np.dot(H, d)
lev = np.sqrt(1 - H.diagonal())
r /= lev
r -= r.mean()
r2 = np.dot(R, d)
assert_array_almost_equal(r, r2)
r3 = np.dot(d, R.T)
assert_array_almost_equal(r, r3)
def shore_matrix_pdf(radial_order, zeta, rtab):
r"""Compute the SHORE propagator matrix [1]_"
Parameters
----------
radial_order : unsigned int,
an even integer that represent the order of the basis
zeta : unsigned int,
scale factor
rtab : array, shape (N,3)
real space points in which calculates the pdf
References
----------
.. [1] Merlet S. et al., "Continuous diffusion signal, EAP and
ODF estimation via Compressive Sensing in diffusion MRI", Medical
Image Analysis, 2013.
"""
r, theta, phi = cart2sphere(rtab[:, 0], rtab[:, 1], rtab[:, 2])
theta[np.isnan(theta)] = 0
F = radial_order / 2
n_c = int(np.round(1 / 6.0 * (F + 1) * (F + 2) * (4 * F + 3)))
psi = np.zeros((r.shape[0], n_c))
counter = 0
for l in range(0, radial_order + 1, 2):
for n in range(l, int((radial_order + l) / 2) + 1):
for m in range(-l, l + 1):
psi[:, counter] = real_sh_descoteaux_from_index(
m, l, theta, phi) * \
genlaguerre(n - l, l + 0.5)(4 * np.pi ** 2 *
zeta * r ** 2) *\
np.exp(-2 * np.pi ** 2 * zeta * r ** 2) *\
_kappa_pdf(zeta, n, l) *\
(4 * np.pi ** 2 * zeta * r ** 2) ** (l / 2) * \
(-1) ** (n - l / 2)
counter += 1
return psi
def test_smooth_pinv():
hemi = hemi_icosahedron.subdivide(2)
m, n = sph_harm_ind_list(4)
B = real_sh_descoteaux_from_index(m, n, hemi.theta[:, None],
hemi.phi[:, None])
L = np.zeros(len(m))
C = smooth_pinv(B, L)
D = np.dot(npl.inv(np.dot(B.T, B)), B.T)
assert_array_almost_equal(C, D)
L = n * (n + 1) * .05
C = smooth_pinv(B, L)
L = np.diag(L)
D = np.dot(npl.inv(np.dot(B.T, B) + L * L), B.T)
assert_array_almost_equal(C, D)
L = np.arange(len(n)) * .05
C = smooth_pinv(B, L)
L = np.diag(L)
D = np.dot(npl.inv(np.dot(B.T, B) + L * L), B.T)
assert_array_almost_equal(C, D)
def shore_matrix_odf(radial_order, zeta, sphere_vertices):
r"""Compute the SHORE ODF matrix [1]_"
Parameters
----------
radial_order : unsigned int,
an even integer that represent the order of the basis
zeta : unsigned int,
scale factor
sphere_vertices : array, shape (N,3)
vertices of the odf sphere
References
----------
.. [1] Merlet S. et al., "Continuous diffusion signal, EAP and
ODF estimation via Compressive Sensing in diffusion MRI", Medical
Image Analysis, 2013.
"""
r, theta, phi = cart2sphere(sphere_vertices[:, 0], sphere_vertices[:, 1],
sphere_vertices[:, 2])
theta[np.isnan(theta)] = 0
F = radial_order / 2
n_c = int(np.round(1 / 6.0 * (F + 1) * (F + 2) * (4 * F + 3)))
upsilon = np.zeros((len(sphere_vertices), n_c))
counter = 0
for l in range(0, radial_order + 1, 2):
for n in range(l, int((radial_order + l) / 2) + 1):
for m in range(-l, l + 1):
upsilon[:, counter] = (-1) ** (n - l / 2.0) * \
_kappa_odf(zeta, n, l) * \
hyp2f1(l - n, l / 2.0 + 1.5, l + 1.5, 2.0) * \
real_sh_descoteaux_from_index(m, l, theta, phi)
counter += 1
return upsilon
def shore_matrix(radial_order, zeta, gtab, tau=1 / (4 * np.pi ** 2)):
r"""Compute the SHORE matrix for modified Merlet's 3D-SHORE [1]_
..math::
:nowrap:
\begin{equation}
\textbf{E}(q\textbf{u})=\sum_{l=0, even}^{N_{max}}
\sum_{n=l}^{(N_{max}+l)/2}
\sum_{m=-l}^l c_{nlm}
\phi_{nlm}(q\textbf{u})
\end{equation}
where $\phi_{nlm}$ is
..math::
:nowrap:
\begin{equation}
\phi_{nlm}^{SHORE}(q\textbf{u})=\Biggl[\dfrac{2(n-l)!}
{\zeta^{3/2} \Gamma(n+3/2)} \Biggr]^{1/2}
\Biggl(\dfrac{q^2}{\zeta}\Biggr)^{l/2}
exp\Biggl(\dfrac{-q^2}{2\zeta}\Biggr)
L^{l+1/2}_{n-l} \Biggl(\dfrac{q^2}{\zeta}\Biggr)
Y_l^m(\textbf{u}).
\end{equation}
Parameters
----------
radial_order : unsigned int,
an even integer that represent the order of the basis
zeta : unsigned int,
scale factor
gtab : GradientTable,
gradient directions and bvalues container class
tau : float,
diffusion time. By default the value that makes q=sqrt(b).
References
----------
.. [1] Merlet S. et al., "Continuous diffusion signal, EAP and
ODF estimation via Compressive Sensing in diffusion MRI", Medical
Image Analysis, 2013.
"""
qvals = np.sqrt(gtab.bvals / (4 * np.pi ** 2 * tau))
qvals[gtab.b0s_mask] = 0
bvecs = gtab.bvecs
qgradients = qvals[:, None] * bvecs
r, theta, phi = cart2sphere(qgradients[:, 0], qgradients[:, 1],
qgradients[:, 2])
theta[np.isnan(theta)] = 0
F = radial_order / 2
n_c = int(np.round(1 / 6.0 * (F + 1) * (F + 2) * (4 * F + 3)))
M = np.zeros((r.shape[0], n_c))
counter = 0
for l in range(0, radial_order + 1, 2):
for n in range(l, int((radial_order + l) / 2) + 1):
for m in range(-l, l + 1):
M[:, counter] = real_sh_descoteaux_from_index(
m, l, theta, phi) * \
genlaguerre(n - l, l + 0.5)(r ** 2 / zeta) * \
np.exp(- r ** 2 / (2.0 * zeta)) * \
_kappa(zeta, n, l) * \
(r ** 2 / zeta) ** (l / 2)
counter += 1
return M
def multi_shell_fiber_response(sh_order,
bvals,
wm_rf,
gm_rf,
csf_rf,
sphere=None,
tol=20):
"""Fiber response function estimation for multi-shell data.
Parameters
----------
sh_order : int
Maximum spherical harmonics order.
bvals : ndarray
Array containing the b-values. Must be unique b-values, like outputed
by `dipy.core.gradients.unique_bvals_tolerance`.
wm_rf : (4, len(bvals)) ndarray
Response function of the WM tissue, for each bvals.
gm_rf : (4, len(bvals)) ndarray
Response function of the GM tissue, for each bvals.
csf_rf : (4, len(bvals)) ndarray
Response function of the CSF tissue, for each bvals.
sphere : `dipy.core.Sphere` instance, optional
Sphere where the signal will be evaluated.
Returns
-------
MultiShellResponse
MultiShellResponse object.
"""
NUMPY_1_14_PLUS = LooseVersion(np.__version__) >= LooseVersion('1.14.0')
rcond_value = None if NUMPY_1_14_PLUS else -1
bvals = np.array(bvals, copy=True)
evecs = np.zeros((3, 3))
z = np.array([0, 0, 1.])
evecs[:, 0] = z
evecs[:2, 1:] = np.eye(2)
n = np.arange(0, sh_order + 1, 2)
m = np.zeros_like(n)
if sphere is None:
sphere = default_sphere
big_sphere = sphere.subdivide()
theta, phi = big_sphere.theta, big_sphere.phi
B = shm.real_sh_descoteaux_from_index(m, n, theta[:, None], phi[:, None])
A = shm.real_sh_descoteaux_from_index(0, 0, 0, 0)
response = np.empty([len(bvals), len(n) + 2])
if bvals[0] < tol:
gtab = GradientTable(big_sphere.vertices * 0)
wm_response = single_tensor(gtab,
wm_rf[0, 3],
wm_rf[0, :3],
evecs,
snr=None)
response[0, 2:] = np.linalg.lstsq(B, wm_response, rcond=rcond_value)[0]
response[0, 1] = gm_rf[0, 3] / A
response[0, 0] = csf_rf[0, 3] / A
for i, bvalue in enumerate(bvals[1:]):
gtab = GradientTable(big_sphere.vertices * bvalue)
wm_response = single_tensor(gtab,
wm_rf[i, 3],
wm_rf[i, :3],
evecs,
snr=None)
response[i + 1, 2:] = np.linalg.lstsq(B,
wm_response,
rcond=rcond_value)[0]
response[i + 1,
1] = gm_rf[i, 3] * np.exp(-bvalue * gm_rf[i, 0]) / A
response[i + 1,
0] = csf_rf[i, 3] * np.exp(-bvalue * csf_rf[i, 0]) / A
S0 = [csf_rf[0, 3], gm_rf[0, 3], wm_rf[0, 3]]
else:
warnings.warn("""No b0 given. Proceeding either way.""", UserWarning)
for i, bvalue in enumerate(bvals):
gtab = GradientTable(big_sphere.vertices * bvalue)
wm_response = single_tensor(gtab,
wm_rf[i, 3],
wm_rf[i, :3],
evecs,
snr=None)
response[i, 2:] = np.linalg.lstsq(B,
wm_response,
rcond=rcond_value)[0]
response[i, 1] = gm_rf[i, 3] * np.exp(-bvalue * gm_rf[i, 0]) / A
response[i, 0] = csf_rf[i, 3] * np.exp(-bvalue * csf_rf[i, 0]) / A
S0 = [csf_rf[0, 3], gm_rf[0, 3], wm_rf[0, 3]]
return MultiShellResponse(response, sh_order, bvals, S0=S0)
def __init__(self,
gtab,
ratio,
reg_sphere=None,
sh_order=8,
lambda_=1.,
tau=0.1):
r""" Spherical Deconvolution Transform (SDT) [1]_.
The SDT computes a fiber orientation distribution (FOD) as opposed to a
diffusion ODF as the QballModel or the CsaOdfModel. This results in a
sharper angular profile with better angular resolution. The Constrained
SDTModel is similar to the Constrained CSDModel but mathematically it
deconvolves the q-ball ODF as oppposed to the HARDI signal (see [1]_
for a comparison and a through discussion).
A sharp fODF is obtained because a single fiber *response* function is
injected as *a priori* knowledge. In the SDTModel, this response is a
single fiber q-ball ODF as opposed to a single fiber signal function
for the CSDModel. The response function will be used as deconvolution
kernel.
Parameters
----------
gtab : GradientTable
ratio : float
ratio of the smallest vs the largest eigenvalue of the single
prolate tensor response function
reg_sphere : Sphere
sphere used to build the regularization B matrix
sh_order : int
maximal spherical harmonics order
lambda_ : float
weight given to the constrained-positivity regularization part of
the deconvolution equation
tau : float
threshold (tau *mean(fODF)) controlling the amplitude below
which the corresponding fODF is assumed to be zero.
References
----------
.. [1] Descoteaux, M., et al. IEEE TMI 2009. Deterministic and
Probabilistic Tractography Based on Complex Fibre Orientation
Distributions.
"""
SphHarmModel.__init__(self, gtab)
m, n = sph_harm_ind_list(sh_order)
self.m, self.n = m, n
self._where_b0s = lazy_index(gtab.b0s_mask)
self._where_dwi = lazy_index(~gtab.b0s_mask)
no_params = ((sh_order + 1) * (sh_order + 2)) / 2
if no_params > np.sum(~gtab.b0s_mask):
msg = "Number of parameters required for the fit are more "
msg += "than the actual data points"
warnings.warn(msg, UserWarning)
x, y, z = gtab.gradients[self._where_dwi].T
r, theta, phi = cart2sphere(x, y, z)
# for the gradient sphere
self.B_dwi = real_sh_descoteaux_from_index(m, n, theta[:, None],
phi[:, None])
# for the odf sphere
if reg_sphere is None:
self.sphere = get_sphere('symmetric362')
else:
self.sphere = reg_sphere
r, theta, phi = cart2sphere(self.sphere.x, self.sphere.y,
self.sphere.z)
self.B_reg = real_sh_descoteaux_from_index(m, n, theta[:, None],
phi[:, None])
self.R, self.P = forward_sdt_deconv_mat(ratio, n)
# scale lambda_ to account for differences in the number of
# SH coefficients and number of mapped directions
self.lambda_ = (lambda_ * self.R.shape[0] * self.R[0, 0] /
self.B_reg.shape[0])
self.tau = tau
self.sh_order = sh_order
def __init__(self,
gtab,
response,
reg_sphere=None,
sh_order=8,
lambda_=1,
tau=0.1,
convergence=50):
r""" Constrained Spherical Deconvolution (CSD) [1]_.
Spherical deconvolution computes a fiber orientation distribution
(FOD), also called fiber ODF (fODF) [2]_, as opposed to a diffusion ODF
as the QballModel or the CsaOdfModel. This results in a sharper angular
profile with better angular resolution that is the best object to be
used for later deterministic and probabilistic tractography [3]_.
A sharp fODF is obtained because a single fiber *response* function is
injected as *a priori* knowledge. The response function is often
data-driven and is thus provided as input to the
ConstrainedSphericalDeconvModel. It will be used as deconvolution
kernel, as described in [1]_.
Parameters
----------
gtab : GradientTable
response : tuple or AxSymShResponse object
A tuple with two elements. The first is the eigen-values as an (3,)
ndarray and the second is the signal value for the response
function without diffusion weighting (i.e. S0). This is to be able
to generate a single fiber synthetic signal. The response function
will be used as deconvolution kernel ([1]_).
reg_sphere : Sphere (optional)
sphere used to build the regularization B matrix.
Default: 'symmetric362'.
sh_order : int (optional)
maximal spherical harmonics order. Default: 8
lambda_ : float (optional)
weight given to the constrained-positivity regularization part of
the deconvolution equation (see [1]_). Default: 1
tau : float (optional)
threshold controlling the amplitude below which the corresponding
fODF is assumed to be zero. Ideally, tau should be set to
zero. However, to improve the stability of the algorithm, tau is
set to tau*100 % of the mean fODF amplitude (here, 10% by default)
(see [1]_). Default: 0.1
convergence : int
Maximum number of iterations to allow the deconvolution to
converge.
References
----------
.. [1] Tournier, J.D., et al. NeuroImage 2007. Robust determination of
the fibre orientation distribution in diffusion MRI:
Non-negativity constrained super-resolved spherical
deconvolution
.. [2] Descoteaux, M., et al. IEEE TMI 2009. Deterministic and
Probabilistic Tractography Based on Complex Fibre Orientation
Distributions
.. [3] Côté, M-A., et al. Medical Image Analysis 2013. Tractometer:
Towards validation of tractography pipelines
.. [4] Tournier, J.D, et al. Imaging Systems and Technology
2012. MRtrix: Diffusion Tractography in Crossing Fiber Regions
"""
# Initialize the parent class:
SphHarmModel.__init__(self, gtab)
m, n = sph_harm_ind_list(sh_order)
self.m, self.n = m, n
self._where_b0s = lazy_index(gtab.b0s_mask)
self._where_dwi = lazy_index(~gtab.b0s_mask)
no_params = ((sh_order + 1) * (sh_order + 2)) / 2
if no_params > np.sum(~gtab.b0s_mask):
msg = "Number of parameters required for the fit are more "
msg += "than the actual data points"
warnings.warn(msg, UserWarning)
x, y, z = gtab.gradients[self._where_dwi].T
r, theta, phi = cart2sphere(x, y, z)
# for the gradient sphere
self.B_dwi = real_sh_descoteaux_from_index(m, n, theta[:, None],
phi[:, None])
# for the sphere used in the regularization positivity constraint
self.sphere = reg_sphere or small_sphere
r, theta, phi = cart2sphere(self.sphere.x, self.sphere.y,
self.sphere.z)
self.B_reg = real_sh_descoteaux_from_index(m, n, theta[:, None],
phi[:, None])
self.response = response
if isinstance(response, AxSymShResponse):
r_sh = response.dwi_response
self.response_scaling = response.S0
n_response = response.n
m_response = response.m
else:
self.S_r = estimate_response(gtab, self.response[0],
self.response[1])
r_sh = np.linalg.lstsq(self.B_dwi,
self.S_r[self._where_dwi],
rcond=-1)[0]
n_response = n
m_response = m
self.response_scaling = response[1]
r_rh = sh_to_rh(r_sh, m_response, n_response)
self.R = forward_sdeconv_mat(r_rh, n)
# scale lambda_ to account for differences in the number of
# SH coefficients and number of mapped directions
# This is exactly what is done in [4]_
lambda_ = (lambda_ * self.R.shape[0] * r_rh[0] /
(np.sqrt(self.B_reg.shape[0]) * np.sqrt(362.)))
self.B_reg *= lambda_
self.sh_order = sh_order
self.tau = tau
self.convergence = convergence
self._X = X = self.R.diagonal() * self.B_dwi
self._P = np.dot(X.T, X)
def basis(self, sphere):
"""A basis that maps the response coefficients onto a sphere."""
theta = sphere.theta[:, None]
phi = sphere.phi[:, None]
return real_sh_descoteaux_from_index(self.m, self.n, theta, phi)
def recursive_response(gtab,
data,
mask=None,
sh_order=8,
peak_thr=0.01,
init_fa=0.08,
init_trace=0.0021,
iter=8,
convergence=0.001,
parallel=True,
nbr_processes=None,
sphere=default_sphere):
""" Recursive calibration of response function using peak threshold
Parameters
----------
gtab : GradientTable
data : ndarray
diffusion data
mask : ndarray, optional
mask for recursive calibration, for example a white matter mask. It has
shape `data.shape[0:3]` and dtype=bool. Default: use the entire data
array.
sh_order : int, optional
maximal spherical harmonics order. Default: 8
peak_thr : float, optional
peak threshold, how large the second peak can be relative to the first
peak in order to call it a single fiber population [1]. Default: 0.01
init_fa : float, optional
FA of the initial 'fat' response function (tensor). Default: 0.08
init_trace : float, optional
trace of the initial 'fat' response function (tensor). Default: 0.0021
iter : int, optional
maximum number of iterations for calibration. Default: 8.
convergence : float, optional
convergence criterion, maximum relative change of SH
coefficients. Default: 0.001.
parallel : bool, optional
Whether to use parallelization in peak-finding during the calibration
procedure. Default: True
nbr_processes: int
If `parallel` is True, the number of subprocesses to use
(default multiprocessing.cpu_count()).
sphere : Sphere, optional.
The sphere used for peak finding. Default: default_sphere.
Returns
-------
response : ndarray
response function in SH coefficients
Notes
-----
In CSD there is an important pre-processing step: the estimation of the
fiber response function. Using an FA threshold is not a very robust method.
It is dependent on the dataset (non-informed used subjectivity), and still
depends on the diffusion tensor (FA and first eigenvector),
which has low accuracy at high b-value. This function recursively
calibrates the response function, for more information see [1].
References
----------
.. [1] Tax, C.M.W., et al. NeuroImage 2014. Recursive calibration of
the fiber response function for spherical deconvolution of
diffusion MRI data.
"""
S0 = 1.
evals = fa_trace_to_lambdas(init_fa, init_trace)
res_obj = (evals, S0)
if mask is None:
data = data.reshape(-1, data.shape[-1])
else:
data = data[mask]
n = np.arange(0, sh_order + 1, 2)
where_dwi = lazy_index(~gtab.b0s_mask)
response_p = np.ones(len(n))
for _ in range(iter):
r_sh_all = np.zeros(len(n))
csd_model = ConstrainedSphericalDeconvModel(gtab,
res_obj,
sh_order=sh_order)
csd_peaks = peaks_from_model(model=csd_model,
data=data,
sphere=sphere,
relative_peak_threshold=peak_thr,
min_separation_angle=25,
parallel=parallel,
nbr_processes=nbr_processes)
dirs = csd_peaks.peak_dirs
vals = csd_peaks.peak_values
single_peak_mask = (vals[:, 1] / vals[:, 0]) < peak_thr
data = data[single_peak_mask]
dirs = dirs[single_peak_mask]
for num_vox in range(data.shape[0]):
rotmat = vec2vec_rotmat(dirs[num_vox, 0], np.array([0, 0, 1]))
rot_gradients = np.dot(rotmat, gtab.gradients.T).T
x, y, z = rot_gradients[where_dwi].T
r, theta, phi = cart2sphere(x, y, z)
# for the gradient sphere
B_dwi = real_sh_descoteaux_from_index(0, n, theta[:, None],
phi[:, None])
r_sh_all += np.linalg.lstsq(B_dwi,
data[num_vox, where_dwi],
rcond=-1)[0]
response = r_sh_all / data.shape[0]
res_obj = AxSymShResponse(data[:, gtab.b0s_mask].mean(), response)
change = abs((response_p - response) / response_p)
if all(change < convergence):
break
response_p = response
return res_obj
