def dki_prediction(dki_params, gtab, S0=150):
""" Predict a signal given diffusion kurtosis imaging parameters.
Parameters
----------
dki_params : ndarray (x, y, z, 27) or (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
gtab : a GradientTable class instance
The gradient table for this prediction
S0 : float or ndarray (optional)
The non diffusion-weighted signal in every voxel, or across all
voxels. Default: 150
Returns
--------
S : (..., N) ndarray
Simulated signal based on the DKI model:
.. math::
S=S_{0}e^{-bD+\frac{1}{6}b^{2}D^{2}K}
"""
evals, evecs, kt = split_dki_param(dki_params)
# Define DKI design matrix according to given gtab
A = design_matrix(gtab)
# Flat parameters and initialize pred_sig
fevals = evals.reshape((-1, evals.shape[-1]))
fevecs = evecs.reshape((-1, ) + evecs.shape[-2:])
fkt = kt.reshape((-1, kt.shape[-1]))
pred_sig = np.zeros((len(fevals), len(gtab.bvals)))
# lopping for all voxels
for v in range(len(pred_sig)):
DT = np.dot(np.dot(fevecs[v], np.diag(fevals[v])), fevecs[v].T)
dt = lower_triangular(DT)
MD = (dt[0] + dt[2] + dt[5]) / 3
X = np.concatenate((dt, fkt[v] * MD * MD, np.array([np.log(S0)])),
axis=0)
pred_sig[v] = np.exp(np.dot(A, X))
# Reshape data according to the shape of dki_params
pred_sig = pred_sig.reshape(dki_params.shape[:-1] + (pred_sig.shape[-1], ))
return pred_sig
def dki_prediction(dki_params, gtab, S0=150):
""" Predict a signal given diffusion kurtosis imaging parameters.
Parameters
----------
dki_params : ndarray (x, y, z, 27) or (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
gtab : a GradientTable class instance
The gradient table for this prediction
S0 : float or ndarray (optional)
The non diffusion-weighted signal in every voxel, or across all
voxels. Default: 150
Returns
--------
S : (..., N) ndarray
Simulated signal based on the DKI model:
.. math::
S=S_{0}e^{-bD+\frac{1}{6}b^{2}D^{2}K}
"""
evals, evecs, kt = split_dki_param(dki_params)
# Define DKI design matrix according to given gtab
A = design_matrix(gtab)
# Flat parameters and initialize pred_sig
fevals = evals.reshape((-1, evals.shape[-1]))
fevecs = evecs.reshape((-1,) + evecs.shape[-2:])
fkt = kt.reshape((-1, kt.shape[-1]))
pred_sig = np.zeros((len(fevals), len(gtab.bvals)))
# lopping for all voxels
for v in range(len(pred_sig)):
DT = np.dot(np.dot(fevecs[v], np.diag(fevals[v])), fevecs[v].T)
dt = lower_triangular(DT)
MD = (dt[0] + dt[2] + dt[5]) / 3
X = np.concatenate((dt, fkt[v]*MD*MD, np.array([np.log(S0)])), axis=0)
pred_sig[v] = np.exp(np.dot(A, X))
# Reshape data according to the shape of dki_params
pred_sig = pred_sig.reshape(dki_params.shape[:-1] + (pred_sig.shape[-1],))
return pred_sig
def __init__(self, gtab, fit_method="OLS", *args, **kwargs):
""" Diffusion Kurtosis Tensor Model [1]
Parameters
----------
gtab : GradientTable class instance
fit_method : str or callable
str can be one of the following:
'OLS' or 'ULLS' for ordinary least squares
dki.ols_fit_dki
'WLS' or 'UWLLS' for weighted ordinary least squares
dki.wls_fit_dki
callable has to have the signature:
fit_method(design_matrix, data, *args, **kwargs)
args, kwargs : arguments and key-word arguments passed to the
fit_method. See dki.ols_fit_dki, dki.wls_fit_dki for details
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
"""
ReconstModel.__init__(self, gtab)
if not callable(fit_method):
try:
self.fit_method = common_fit_methods[fit_method]
except KeyError:
raise ValueError('"' + str(fit_method) + '" is not a known '
'fit method, the fit method should either be '
'a function or one of the common fit methods')
self.design_matrix = design_matrix(self.gtab)
self.args = args
self.kwargs = kwargs
self.min_signal = self.kwargs.pop('min_signal', None)
if self.min_signal is not None and self.min_signal <= 0:
e_s = "The `min_signal` key-word argument needs to be strictly"
e_s += " positive."
raise ValueError(e_s)
def __init__(self, gtab, fit_method="OLS", *args, **kwargs):
""" Diffusion Kurtosis Tensor Model [1]
Parameters
----------
gtab : GradientTable class instance
fit_method : str or callable
str can be one of the following:
'OLS' or 'ULLS' for ordinary least squares
dki.ols_fit_dki
'WLS' or 'UWLLS' for weighted ordinary least squares
dki.wls_fit_dki
callable has to have the signature:
fit_method(design_matrix, data, *args, **kwargs)
args, kwargs : arguments and key-word arguments passed to the
fit_method. See dki.ols_fit_dki, dki.wls_fit_dki for details
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
"""
ReconstModel.__init__(self, gtab)
if not callable(fit_method):
try:
self.fit_method = common_fit_methods[fit_method]
except KeyError:
raise ValueError('"' + str(fit_method) + '" is not a known '
'fit method, the fit method should either be '
'a function or one of the common fit methods')
self.design_matrix = design_matrix(self.gtab)
self.args = args
self.kwargs = kwargs
self.min_signal = self.kwargs.pop('min_signal', None)
if self.min_signal is not None and self.min_signal <= 0:
e_s = "The `min_signal` key-word argument needs to be strictly"
e_s += " positive."
raise ValueError(e_s)
