def tensor2odf(tensors, b, order):
""" Compute a Cartesian Tensor ODF from a given Higher-order diffusion
tensor
Parameters
----------
tensors: list of array [e,] (mandatory)
a list with tensor independent coefficients
b: float (mandatory)
the diffusion b-value
Returns
-------
odfs list of array [e,]
a list of tensor independant coefficients
Reference
Barmpoutnis
"""
# Unit vectors [321,3]
g = numpy.loadtxt(get_sphere("symmetric321"))
# Construct basis
G = construct_matrix_of_monomials(g, order)
C = construct_set_of_polynomials(order).T
BG = construct_matrix_of_integrals(g, order, 100)
B = numpy.dot(BG, C)
# loop over elements
odfs = []
for tensor in tensors:
x = scipy.optimize.nnls(B, numpy.exp(-b * numpy.dot(G, tensor)))[0]
odfs.append(numpy.dot(C, x))
return odfs
def tensor2odf(tensors, b, order):
""" Compute a Cartesian Tensor ODF from a given Higher-order diffusion
tensor
Parameters
----------
tensors: list of array [e,] (mandatory)
a list with tensor independent coefficients
b: float (mandatory)
the diffusion b-value
Returns
-------
odfs list of array [e,]
a list of tensor independant coefficients
Reference
Barmpoutnis
"""
# Unit vectors [321,3]
g = numpy.loadtxt(get_sphere("symmetric321"))
# Construct basis
G = construct_matrix_of_monomials(g, order)
C = construct_set_of_polynomials(order).T
BG = construct_matrix_of_integrals(g, order, 100)
B = numpy.dot(BG, C)
# loop over elements
odfs = []
for tensor in tensors:
x = scipy.optimize.nnls(B, numpy.exp(-b * numpy.dot(G, tensor)))[0]
odfs.append(numpy.dot(C, x))
return odfs
def quartic_tensor_odf_fit(data_flat, mask_flat, reference_flat, bvals, bvecs,
order, delta=100., min_signal=1.,
number_of_workers=1):
""" Compute a Cartesian tensor Odf from a given DW dataset.
Parameters
----------
data_flat: array (mandatory)
flattened diffusion data array.
mask_flat: array (mandatory)
flattened mask data array.
reference_flat: array (mandatory)
flattened reference b0 data array.
bvals: array (mandatory)
the diffusion b-values.
bvecs: array (mandatory)
the diffusion b-vectors.
order: int (mandatory)
the diffusion tensor order.
delta: float (optional, default 100.)
the ODF kernel.
min_signal: float (optional, default 1.)
replace diffusion signal smaller than this threshold.
number_of_workers: int (optional, default 1)
the number of CPUs used during the execution.
Returns
-------
dti_parameters: array [N, e]
the odf tensor independant coefficients:
multiplicity is included in tensor coefficients.
Reference
Barmpoutnis
"""
# Contruct basis
C = construct_set_of_polynomials(order).T
BG = construct_matrix_of_integrals(bvecs, order, delta)
B = numpy.dot(BG, C)
e = C.shape[0]
# Allocate
dti_parameters = numpy.empty((len(data_flat), e))
# NNLS
nb_cpus = None
if number_of_workers > 0:
nb_cpus = number_of_workers
results = multi_processing(
nnls_multi, nb_cpus,
data_flat, reference_flat,
itertools.repeat(B), itertools.repeat(C),
itertools.repeat(min_signal), mask_flat,
itertools.repeat(False))
# Format result
for cnt, item in enumerate(results):
dti_parameters[cnt] = item
return dti_parameters
def quartic_tensor_odf_fit(data_flat,
mask_flat,
reference_flat,
bvals,
bvecs,
order,
delta=100.,
min_signal=1.,
number_of_workers=1):
""" Compute a Cartesian tensor Odf from a given DW dataset.
Parameters
----------
data_flat: array (mandatory)
flattened diffusion data array.
mask_flat: array (mandatory)
flattened mask data array.
reference_flat: array (mandatory)
flattened reference b0 data array.
bvals: array (mandatory)
the diffusion b-values.
bvecs: array (mandatory)
the diffusion b-vectors.
order: int (mandatory)
the diffusion tensor order.
delta: float (optional, default 100.)
the ODF kernel.
min_signal: float (optional, default 1.)
replace diffusion signal smaller than this threshold.
number_of_workers: int (optional, default 1)
the number of CPUs used during the execution.
Returns
-------
dti_parameters: array [N, e]
the odf tensor independant coefficients:
multiplicity is included in tensor coefficients.
Reference
Barmpoutnis
"""
# Contruct basis
C = construct_set_of_polynomials(order).T
BG = construct_matrix_of_integrals(bvecs, order, delta)
B = numpy.dot(BG, C)
e = C.shape[0]
# Allocate
dti_parameters = numpy.empty((len(data_flat), e))
# NNLS
nb_cpus = None
if number_of_workers > 0:
nb_cpus = number_of_workers
results = multi_processing(nnls_multi, nb_cpus, data_flat, reference_flat,
itertools.repeat(B), itertools.repeat(C),
itertools.repeat(min_signal), mask_flat,
itertools.repeat(False))
# Format result
for cnt, item in enumerate(results):
dti_parameters[cnt] = item
return dti_parameters
def quartic_tensor_fit(data_flat,
mask_flat,
reference_flat,
bvals,
bvecs,
order,
min_signal=1.,
number_of_workers=1):
""" Fits a diffusion tensor given diffusion-weighted signals and
gradient inforomation using a quartic decomposition and non negative least
square estimation strategy.
This procedure guarentees the positive-definite or at least positive
semi-definite nature of tensors.
Parameters
----------
data_flat: array (mandatory)
flattened diffusion data array.
mask_flat: array (mandatory)
flattened mask data array.
reference_flat: array (mandatory)
flattened reference b0 data array.
bvals: array (mandatory)
the diffusion b-values.
bvecs: array (mandatory)
the diffusion b-vectors.
order: int (mandatory)
the diffusion tensor order.
min_signal: float (optional, default 1.)
replace diffusion signal smaller than this threshold.
number_of_workers: int (optional, default 1)
the number of CPUs used during the execution.
Returns
-------
dti_parameters: array [N, e]
the tensor independant coefficients:
multiplicity is included in tensor coefficients.
Reference
Barmpoutnis
"""
# Construct b diag
b_diag = numpy.diag(bvals)
# construct basis
G = construct_matrix_of_monomials(bvecs, order)
C = construct_set_of_polynomials(order).T
P = numpy.dot(G, C)
P = numpy.dot(-b_diag, P)
e = G.shape[1]
# Allocate
dti_parameters = numpy.empty((len(data_flat), e))
# NNLS
nb_cpus = None
if number_of_workers > 0:
nb_cpus = number_of_workers
results = multi_processing(nnls_multi, nb_cpus, data_flat, reference_flat,
itertools.repeat(P), itertools.repeat(C),
itertools.repeat(min_signal), mask_flat,
itertools.repeat(True))
# Format result
for cnt, item in enumerate(results):
dti_parameters[cnt] = item
return dti_parameters
def quartic_tensor_fit(data_flat, mask_flat, reference_flat, bvals, bvecs,
order, min_signal=1., number_of_workers=1):
""" Fits a diffusion tensor given diffusion-weighted signals and
gradient inforomation using a quartic decomposition and non negative least
square estimation strategy.
This procedure guarentees the positive-definite or at least positive
semi-definite nature of tensors.
Parameters
----------
data_flat: array (mandatory)
flattened diffusion data array.
mask_flat: array (mandatory)
flattened mask data array.
reference_flat: array (mandatory)
flattened reference b0 data array.
bvals: array (mandatory)
the diffusion b-values.
bvecs: array (mandatory)
the diffusion b-vectors.
order: int (mandatory)
the diffusion tensor order.
min_signal: float (optional, default 1.)
replace diffusion signal smaller than this threshold.
number_of_workers: int (optional, default 1)
the number of CPUs used during the execution.
Returns
-------
dti_parameters: array [N, e]
the tensor independant coefficients:
multiplicity is included in tensor coefficients.
Reference
Barmpoutnis
"""
# Construct b diag
b_diag = numpy.diag(bvals)
# construct basis
G = construct_matrix_of_monomials(bvecs, order)
C = construct_set_of_polynomials(order).T
P = numpy.dot(G, C)
P = numpy.dot(- b_diag, P)
e = G.shape[1]
# Allocate
dti_parameters = numpy.empty((len(data_flat), e))
# NNLS
nb_cpus = None
if number_of_workers > 0:
nb_cpus = number_of_workers
results = multi_processing(
nnls_multi, nb_cpus,
data_flat, reference_flat,
itertools.repeat(P), itertools.repeat(C),
itertools.repeat(min_signal), mask_flat,
itertools.repeat(True))
# Format result
for cnt, item in enumerate(results):
dti_parameters[cnt] = item
return dti_parameters
