""" This modules contains signal model based signal modification due to Diffusion """
__all__ = ["GaussianDiffusionTensor"]
import tensorflow as tf
from cmrsim.analytic.contrast.base import BaseSignalModel
# pylint: disable=abstract-method, disable=anomalous-backslash-in-string
[docs]
class GaussianDiffusionTensor(BaseSignalModel):
""" Model based Gaussian diffusion contrast.
Instantiates a module that evaluates the diffusion signal representation:
.. math::
F = \exp(-\mathbf{b}^T\mathbf{D}\mathbf{b})
Assumes the b-vector to be the diffusion direction be scaled
with the square-root of the b-value: :math:`\mathbf{b} = \sqrt{b}\mathbf{d}`
Instead of two dimensions for direction and b-value just uses one dimension of scaled b-vectors.
:param b_vectors: - (#directions * #bvalues, 3) in units sqrt(s/mm*2)
:param expand_repetitions: See BaseSignalModel for explanation
"""
required_quantities = ('diffusion_tensor', )
def __init__(self, b_vectors: tf.Tensor, expand_repetitions: bool, **kwargs):
"""
:param b_vectors: - (#directions * #bvalues, 3) in units sqrt(s/mm*2)
:param expand_repetitions: See BaseSignalModel for explanation
"""
super().__init__(name="dti_gauss", expand_repetitions=expand_repetitions, **kwargs)
with tf.device(self.device):
self.b_vectors = tf.Variable(b_vectors, shape=(None, 3), dtype=tf.float32, name='b_vectors')
self.update()
[docs]
@tf.function(jit_compile=True)
def __call__(self, signal_tensor: tf.Tensor, diffusion_tensor: tf.Tensor, **kwargs)\
-> tf.Tensor:
""" Evaluates the diffusion operator.
:param signal_tensor: (#voxel, #repetitions, #k-space-samples) last two dimensions can be 1
:param diffusion_tensor: diffusion_tensor (#voxels, #repetitions, #k_space_samples, 3, 3)
:return: - if expand_repetitions == True: (#voxel, #repetitions * #self.b_vectors,
#k-space-samples)
- if expand_repetitions == False: (#voxel, #repetitions, #k-space-samples)
"""
with tf.device(self.device):
# All Cases : --> repetitions-axis of argument diffusion_tensor must be either 1 or
# equal to self.expansion_factor
tf.Assert(tf.shape(diffusion_tensor)[1] == 1 or
tf.shape(diffusion_tensor)[1] == self.expansion_factor,
["Shape missmatch for input argument diffusion_tensor"])
input_shape = tf.shape(signal_tensor)
k_space_axis_tiling = tf.cast((tf.floor(input_shape[2]/tf.shape(diffusion_tensor)[2])),
tf.int32)
# Case 1: expand-dimensions
if self.expand_repetitions or self.expansion_factor == 1:
exponent = tf.einsum('ni, vrkij, nj -> vrnk', self.b_vectors, diffusion_tensor,
self.b_vectors)
decay_factor = tf.cast(tf.exp(-exponent), tf.complex64)
decay_factor = tf.tile(decay_factor, [1, 1, 1, k_space_axis_tiling])
temp = tf.einsum('v...k, v...nk -> v...nk', signal_tensor, decay_factor)
result = tf.reshape(temp, (input_shape[0], -1, input_shape[2]))
# Case 2: repetition-axis of signal_tensor must match self.expansion_factor
else:
tf.Assert(input_shape[1] == self.expansion_factor,
["Shape missmatch for input argument signal_tensor for case no-expand"])
exponent = tf.einsum('...i, v...kij, ...j -> v...k',
self.b_vectors, diffusion_tensor, self.b_vectors)
decay_factor = tf.cast(tf.exp(-exponent), tf.complex64)
decay_factor = tf.tile(decay_factor, [1, 1, k_space_axis_tiling])
result = signal_tensor * decay_factor
return result
[docs]
def update(self):
super().update()
self.expansion_factor = self.b_vectors.read_value().shape[0]
