def __init__(self, gtab, response, sh_order, lambda_=1, tau=0.1):
super(NumberSmallfODF, self).__init__()
m, n = sph_harm_ind_list(sh_order)
# x, y, z = gtab.gradients[~gtab.b0s_mask].T
# r, theta, phi = cart2sphere(x, y, z)
# self.B_dwi = real_sph_harm(m, n, theta[:, None], phi[:, None])
self.B_dwi = shm.get_B_matrix(gtab, sh_order)
self.sphere = get_sphere('symmetric362')
r, theta, phi = cart2sphere(self.sphere.x, self.sphere.y,
self.sphere.z)
self.B_reg = real_sph_harm(m, n, theta[:, None], phi[:, None])
S_r = shm.estimate_response(gtab, response[0:3], response[3])
r_sh = np.linalg.lstsq(self.B_dwi, S_r[~gtab.b0s_mask], rcond=-1)[0]
n_response = n
m_response = m
r_rh = sh_to_rh(r_sh, m_response, n_response)
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_ * R.shape[0] * r_rh[0] /
(np.sqrt(self.B_reg.shape[0]) * np.sqrt(362.)))
self.B_reg = self.B_reg * lambda_
self.B_reg = nn.Parameter(torch.FloatTensor(self.B_reg),
requires_grad=False)
self.tau = tau
def get_deconv_matrix(gtab, response, sh_order):
""" Compute the deconvolution of the response of a single fiber
Attributes:
gtab (dipy GradientTable): the gradient of the dwi in wich the response
is represented.
response (float[4]): first 3 elements: eigenvalues, 4th: mean b0 value
sh_order (int): the sh_order of the DWI used for the deconvolution
Returns:
R:
r_rh:
B_dwi (np.array(nb_sh_coeff, nb_dwi_directions)): matrix to fit DWi->SH
"""
m, n = sph_harm_ind_list(sh_order)
# x, y, z = gtab.gradients[~gtab.b0s_mask].T
# r, theta, phi = cart2sphere(x, y, z)
# # for the gradient sphere
# B_dwi = real_sph_harm(m, n, theta[:, None], phi[:, None])
B_dwi, _ = get_B_matrix(gtab, sh_order)
S_r = estimate_response(gtab, response[0:3], response[3])
r_sh = np.linalg.lstsq(B_dwi, S_r[~gtab.b0s_mask], rcond=-1)[0]
n_response = n
m_response = m
r_rh = sh_to_rh(r_sh, m_response, n_response)
R = forward_sdeconv_mat(r_rh, n)
# X = R.diagonal() * B_dwi
return R, r_rh, B_dwi
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. 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_sph_harm(m, n, theta[:, None], phi[:, None])
# for the sphere used in the regularization positivity constraint
if reg_sphere is None:
self.sphere = small_sphere
else:
self.sphere = reg_sphere
r, theta, phi = cart2sphere(self.sphere.x, self.sphere.y,
self.sphere.z)
self.B_reg = real_sph_harm(m, n, theta[:, None], phi[:, None])
if response is None:
response = (np.array([0.0015, 0.0003, 0.0003]), 1)
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 __init__(self, gtab, response, reg_sphere=None, sh_order=8, lambda_=1,
tau=0.1):
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. 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
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] C\^ot\'e, 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_sph_harm(m, n, theta[:, None], phi[:, None])
# for the sphere used in the regularization positivity constraint
if reg_sphere is None:
self.sphere = small_sphere
else:
self.sphere = reg_sphere
r, theta, phi = cart2sphere(
self.sphere.x,
self.sphere.y,
self.sphere.z
)
self.B_reg = real_sph_harm(m, n, theta[:, None], phi[:, None])
if response is None:
response = (np.array([0.0015, 0.0003, 0.0003]), 1)
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])[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._X = X = self.R.diagonal() * self.B_dwi
self._P = np.dot(X.T, X)
def csd_predict(sh_coeff, gtab, response=None, S0=1, R=None):
"""
Compute a signal prediction given spherical harmonic coefficients and
(optionally) a response function for the provided GradientTable class
instance
Parameters
----------
sh_coeff : ndarray
Spherical harmonic coefficients
gtab : GradientTable class instance
response : tuple
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.
Default: (np.array([0.0015, 0.0003, 0.0003]), 1)
S0 : ndarray or float
The non diffusion-weighted signal value.
R : ndarray
Optionally, provide an R matrix. If not provided, calculated from the
gtab, response function, etc.
Returns
-------
pred_sig : ndarray
The signal predicted from the provided SH coefficients for a
measurement with the provided GradientTable. The last dimension of the
resulting array is the same as the number of bvals/bvecs in the
GradientTable. The first dimensions have shape: `sh_coeff.shape[:-1]`.
"""
n_coeff = sh_coeff.shape[-1]
sh_order = order_from_ncoef(n_coeff)
x, y, z = gtab.gradients[~gtab.b0s_mask].T
r, theta, phi = cart2sphere(x, y, z)
SH_basis, m, n = real_sym_sh_basis(sh_order, theta, phi)
if R is None:
# for the gradient sphere
B_dwi = real_sph_harm(m, n, theta[:, None], phi[:, None])
if response is None:
response = (np.array([0.0015, 0.0003, 0.0003]), 1)
else:
response = response
S_r = estimate_response(gtab, response[0], response[1])
r_sh = np.linalg.lstsq(B_dwi, S_r[~gtab.b0s_mask])[0]
r_rh = sh_to_rh(r_sh, m, n)
R = forward_sdeconv_mat(r_rh, n)
predict_matrix = np.dot(SH_basis, R)
if np.iterable(S0):
# If it's an array, we need to give it one more dimension:
S0 = S0[..., None]
# This is the key operation: convolve and multiply by S0:
pre_pred_sig = S0 * np.dot(predict_matrix, sh_coeff)
# Now put everything in its right place:
pred_sig = np.zeros(pre_pred_sig.shape[:-1] + (gtab.bvals.shape[0],))
pred_sig[..., ~gtab.b0s_mask] = pre_pred_sig
pred_sig[..., gtab.b0s_mask] = S0
return pred_sig
