def wls_fit_dki(design_matrix, data):
r""" Computes weighted linear least squares (WLS) fit to calculate
the diffusion tensor and kurtosis tensor using a weighted linear
regression diffusion kurtosis model [1]_.
Parameters
----------
design_matrix : array (g, 22)
Design matrix holding the covariants used to solve for the regression
coefficients.
data : array (N, g)
Data or response variables holding the data. Note that the last
dimension should contain the data. It makes no copies of data.
min_signal : default = 1
All values below min_signal are repalced with min_signal. This is done
in order to avoid taking log(0) durring the tensor fitting.
Returns
-------
dki_params : array (N, 27)
All parameters estimated from the diffusion kurtosis model for all N
voxels.
Parameters are ordered as follow:
1) Three diffusion tensor's eingenvalues
2) Three lines of the eigenvector matrix each containing the first
second and third coordinates of the eigenvector
3) Fifteen elements of the kurtosis tensor
References
----------
[1] Veraart, J., Sijbers, J., Sunaert, S., Leemans, A., Jeurissen, B.,
2013. Weighted linear least squares estimation of diffusion MRI
parameters: Strengths, limitations, and pitfalls. Magn Reson Med 81,
335-346.
"""
tol = 1e-6
# preparing data and initializing parametres
data = np.asarray(data)
data_flat = data.reshape((-1, data.shape[-1]))
dki_params = np.empty((len(data_flat), 27))
# inverting design matrix and defining minimun diffusion aloud
min_diffusivity = tol / -design_matrix.min()
inv_design = np.linalg.pinv(design_matrix)
# lopping WLS solution on all data voxels
for vox in range(len(data_flat)):
dki_params[vox] = _wls_iter(design_matrix, inv_design, data_flat[vox],
min_diffusivity)
# Reshape data according to the input data shape
dki_params = dki_params.reshape((data.shape[:-1]) + (27,))
return dki_params
def wls_fit_dki(design_matrix, data):
r""" Computes weighted linear least squares (WLS) fit to calculate
the diffusion tensor and kurtosis tensor using a weighted linear
regression diffusion kurtosis model [1]_.
Parameters
----------
design_matrix : array (g, 22)
Design matrix holding the covariants used to solve for the regression
coefficients.
data : array (N, g)
Data or response variables holding the data. Note that the last
dimension should contain the data. It makes no copies of data.
min_signal : default = 1
All values below min_signal are repalced with min_signal. This is done
in order to avoid taking log(0) durring the tensor fitting.
Returns
-------
dki_params : array (N, 27)
All parameters estimated from the diffusion kurtosis model for all N
voxels.
Parameters are ordered as follow:
1) Three diffusion tensor's eingenvalues
2) Three lines of the eigenvector matrix each containing the first
second and third coordinates of the eigenvector
3) Fifteen elements of the kurtosis tensor
References
----------
[1] Veraart, J., Sijbers, J., Sunaert, S., Leemans, A., Jeurissen, B.,
2013. Weighted linear least squares estimation of diffusion MRI
parameters: Strengths, limitations, and pitfalls. Magn Reson Med 81,
335-346.
"""
tol = 1e-6
# preparing data and initializing parametres
data = np.asarray(data)
data_flat = data.reshape((-1, data.shape[-1]))
dki_params = np.empty((len(data_flat), 27))
# inverting design matrix and defining minimun diffusion aloud
min_diffusivity = tol / -design_matrix.min()
inv_design = np.linalg.pinv(design_matrix)
# lopping WLS solution on all data voxels
for vox in range(len(data_flat)):
dki_params[vox] = _wls_iter(design_matrix, inv_design, data_flat[vox],
min_diffusivity)
# Reshape data according to the input data shape
dki_params = dki_params.reshape((data.shape[:-1]) + (27, ))
return dki_params
def ols_fit_dki(design_matrix, data):
r""" Computes ordinary least squares (OLS) fit to calculate the diffusion
tensor and kurtosis tensor using a linear regression diffusion kurtosis
model [1]_.
Parameters
----------
design_matrix : array (g, 22)
Design matrix holding the covariants used to solve for the regression
coefficients.
data : array (N, g)
Data or response variables holding the data. Note that the last
dimension should contain the data. It makes no copies of data.
Returns
-------
dki_params : array (N, 27)
All parameters estimated from the diffusion kurtosis model.
Parameters are ordered as follow:
1) Three diffusion tensor's eingenvalues
2) Three lines of the eigenvector matrix each containing the first,
second and third coordinates of the eigenvector
3) Fifteen elements of the kurtosis tensor
See Also
--------
wls_fit_dki
References
----------
[1] Tabesh, A., Jensen, J.H., Ardekani, B.A., Helpern, J.A., 2011.
Estimation of tensors and tensor-derived measures in diffusional
kurtosis imaging. Magn Reson Med. 65(3), 823-836
"""
tol = 1e-6
# preparing data and initializing parameters
data = np.asarray(data)
data_flat = data.reshape((-1, data.shape[-1]))
dki_params = np.empty((len(data_flat), 27))
# inverting design matrix and defining minimun diffusion aloud
min_diffusivity = tol / -design_matrix.min()
inv_design = np.linalg.pinv(design_matrix)
# lopping OLS solution on all data voxels
for vox in range(len(data_flat)):
dki_params[vox] = _ols_iter(inv_design, data_flat[vox],
min_diffusivity)
# Reshape data according to the input data shape
dki_params = dki_params.reshape((data.shape[:-1]) + (27,))
return dki_params
def ols_fit_dki(design_matrix, data):
r""" Computes ordinary least squares (OLS) fit to calculate the diffusion
tensor and kurtosis tensor using a linear regression diffusion kurtosis
model [1]_.
Parameters
----------
design_matrix : array (g, 22)
Design matrix holding the covariants used to solve for the regression
coefficients.
data : array (N, g)
Data or response variables holding the data. Note that the last
dimension should contain the data. It makes no copies of data.
Returns
-------
dki_params : array (N, 27)
All parameters estimated from the diffusion kurtosis model.
Parameters are ordered as follow:
1) Three diffusion tensor's eingenvalues
2) Three lines of the eigenvector matrix each containing the first,
second and third coordinates of the eigenvector
3) Fifteen elements of the kurtosis tensor
See Also
--------
wls_fit_dki
References
----------
[1] Tabesh, A., Jensen, J.H., Ardekani, B.A., Helpern, J.A., 2011.
Estimation of tensors and tensor-derived measures in diffusional
kurtosis imaging. Magn Reson Med. 65(3), 823-836
"""
tol = 1e-6
# preparing data and initializing parameters
data = np.asarray(data)
data_flat = data.reshape((-1, data.shape[-1]))
dki_params = np.empty((len(data_flat), 27))
# inverting design matrix and defining minimun diffusion aloud
min_diffusivity = tol / -design_matrix.min()
inv_design = np.linalg.pinv(design_matrix)
# lopping OLS solution on all data voxels
for vox in range(len(data_flat)):
dki_params[vox] = _ols_iter(inv_design, data_flat[vox],
min_diffusivity)
# Reshape data according to the input data shape
dki_params = dki_params.reshape((data.shape[:-1]) + (27, ))
return dki_params
