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1767 lines (1316 loc) · 55.4 KB
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# Copyright 2016 Intel Corporation
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""fMRI Simulator
Simulate fMRI data for a single subject.
This code provides a set of functions necessary to produce realistic
simulations of neural data.
Steps:
generate_signal
Specify the volume (or volumes) which represent the signal in the neural data.
generate_stimfunction
Create a function to describe the stimulus onsets/durations
export_stimfunction:
Generate a three column timing file that can be used with software like FSL
double_gamma_hrf
Convolve the stimulus function with the HRF to model when events are expected.
apply_signal
Combine the volume and the HRF
calc_noise
Estimate the noise properties of a given volume
generate_noise
Create the noise for this run. This creates temporal, task and white noise.
Various parameters can be tuned depending on need
mask_brain
Mask the volume to look like a volume. Based on MNI standard space
plot_brain
Show the brain as it unfolds over time with a given opacity.
Authors:
Cameron Ellis (Princeton) 2016-2017
Chris Baldassano (Princeton) 2016-2017
"""
import logging
from itertools import product
import nitime.algorithms.autoregressive as ar
import math
import numpy as np
from pkg_resources import resource_stream
from scipy import stats
import scipy.ndimage as ndimage
__all__ = [
"generate_signal",
"generate_stimfunction",
"export_stimfunction",
"double_gamma_hrf",
"apply_signal",
"calc_noise",
"generate_noise",
"mask_brain",
"plot_brain",
]
logger = logging.getLogger(__name__)
def _generate_feature(feature_type,
feature_size,
signal_magnitude,
thickness=1):
"""Generate features corresponding to signal
Generate signal in specific regions of the brain with for a single
volume. This will then be convolved with the HRF across time
Parameters
----------
feature_type : str
What feature_type of signal is being inserted? Options are cube,
loop, cavity, sphere.
feature_size : int
How big is the signal?
signal_magnitude : float
Set the signal size, a value of 1 means the signal is one standard
deviation of the noise
thickness : int
How thick is the surface of the loop/cavity
Returns
----------
3 dimensional array
The volume representing the signal to be outputed
"""
# If the size is equal to or less than 2 then all features are the same
if feature_size <= 2:
feature_type = 'cube'
# What kind of signal is it?
if feature_type == 'cube':
# Preset the size of the signal
signal = np.ones(np.power(feature_size, 3))
# Reorganize the signal into a 3d matrix
signal = signal.reshape([feature_size,
feature_size,
feature_size])
elif feature_type == 'loop':
# First make a cube of zeros
signal = np.zeros(np.power(feature_size,
3)).reshape([feature_size,
feature_size,
feature_size])
# Make a mesh grid of the space
seq = np.linspace(0, feature_size - 1,
feature_size)
xx, yy = np.meshgrid(seq, seq)
# Make a disk corresponding to the whole mesh grid
xxmesh = (xx - ((feature_size - 1) / 2)) ** 2
yymesh = (yy - ((feature_size - 1) / 2)) ** 2
disk = xxmesh + yymesh
# What are the limits of the rings being made
outer_lim = disk[int((feature_size - 1) / 2), 0]
inner_lim = disk[int((feature_size - 1) / 2), thickness]
# What is the outer disk
outer = disk <= outer_lim
# What is the inner disk
inner = disk <= inner_lim
# Subtract the two disks to get a loop
loop = outer != inner
# If there is complete overlap then make the signal just the
# outer one
if np.all(loop is False):
loop = outer
# store the loop
signal[0:feature_size, 0:feature_size, int(np.round(feature_size /
2))] = loop
elif feature_type == 'sphere' or feature_type == 'cavity':
# Make a mesh grid of the space
seq = np.linspace(0, feature_size - 1,
feature_size)
xx, yy, zz = np.meshgrid(seq, seq, seq)
# Make a disk corresponding to the whole mesh grid
signal = ((xx - ((feature_size - 1) / 2)) ** 2 +
(yy - ((feature_size - 1) / 2)) ** 2 +
(zz - ((feature_size - 1) / 2)) ** 2)
# What are the limits of the rings being made
outer_lim = signal[int((feature_size - 1) / 2), int((feature_size -
1) / 2), 0]
inner_lim = signal[int((feature_size - 1) / 2), int((feature_size -
1) / 2),
thickness]
# Is the signal a sphere or a cavity?
if feature_type == 'sphere':
signal = signal <= outer_lim
else:
# Get the inner and outer sphere
outer = signal <= outer_lim
inner = signal <= inner_lim
# Subtract the two disks to get a loop
signal = outer != inner
# If there is complete overlap then make the signal just the
# outer one
if np.all(signal is False):
signal = outer
# Assign the signal magnitude
signal = signal * signal_magnitude
# Return the signal
return signal
def _insert_idxs(feature_centre, feature_size, dimensions):
"""Returns the indexes of where to put the signal into Volume_Static
Parameters
----------
feature_centre : list, int
List of coordinates for the centre location of the signal
feature_size : list, int
How big is the signal.
dimensions : 3 length array, int
What are the dimensions of the volume you wish to create
Returns
----------
x_idxs : tuple
The x coordinates of where the signal is to be inserted
y_idxs : tuple
The y coordinates of where the signal is to be inserted
z_idxs : tuple
The z coordinates of where the signal is to be inserted
"""
# Set up the indexes within which to insert the signal
x_idx = [int(feature_centre[0] - (feature_size / 2)) + 1,
int(feature_centre[0] - (feature_size / 2) +
feature_size) + 1]
y_idx = [int(feature_centre[1] - (feature_size / 2)) + 1,
int(feature_centre[1] - (feature_size / 2) +
feature_size) + 1]
z_idx = [int(feature_centre[2] - (feature_size / 2)) + 1,
int(feature_centre[2] - (feature_size / 2) +
feature_size) + 1]
# Check for out of bounds
# Min Boundary
if 0 > x_idx[0]:
x_idx[0] = 0
if 0 > y_idx[0]:
y_idx[0] = 0
if 0 > z_idx[0]:
z_idx[0] = 0
# Max Boundary
if dimensions[0] < x_idx[1]:
x_idx[1] = dimensions[0]
if dimensions[1] < y_idx[1]:
y_idx[1] = dimensions[1]
if dimensions[2] < z_idx[1]:
z_idx[1] = dimensions[2]
# Return the idxs for data
return x_idx, y_idx, z_idx
def generate_signal(dimensions,
feature_coordinates,
feature_size,
feature_type,
signal_magnitude=[1],
signal_constant=1,
):
"""Generate volume containing signal
Generate signal in specific regions of the brain with for a single
volume. This will then be convolved with the HRF across time
Parameters
----------
dimensions : 1d array, ndarray
What are the dimensions of the volume you wish to create
feature_coordinates : multidimensional array
What are the feature_coordinates of the signal being created.
Be aware of clipping: features far from the centre of the
brain will be clipped. If you wish to have multiple features
then list these as an features x 3 array. To create a signal of
a specific shape then supply all the individual
feature_coordinates and set the feature_size to 1.
feature_size : list, int
How big is the signal. If m=1 then only one value is accepted,
if m>1 then either one value must be supplied or m values
feature_type : list, string
What feature_type of signal is being inserted? Options are cube,
loop, cavity, sphere. If features = 1 then
only one value is accepted, if features > 1 then either one value
must be supplied or m values
signal_magnitude : list, float
What is the (average) magnitude of the signal being generated? A
value of 1 means that the signal is one standard deviation from the
noise
signal_constant : list, bool
Is the signal constant or is it a random pattern (with the same
average magnitude)
Returns
----------
volume_static : 3 dimensional array, float
Creates a single volume containing the signal
"""
# Preset the volume
volume_static = np.zeros(dimensions)
feature_quantity = round(feature_coordinates.shape[0])
# If there is only one feature_size value then make sure to duplicate it
# for all signals
if len(feature_size) == 1:
feature_size = feature_size * feature_quantity
# Do the same for feature_type
if len(feature_type) == 1:
feature_type = feature_type * feature_quantity
if len(signal_magnitude) == 1:
signal_magnitude = signal_magnitude * feature_quantity
# Iterate through the signals and insert in the data
for signal_counter in list(range(0, feature_quantity)):
# What is the centre of this signal
if len(feature_size) > 1:
feature_centre = np.asarray(feature_coordinates[signal_counter, ])
else:
feature_centre = np.asarray(feature_coordinates)[0]
# Generate the feature to be inserted in the volume
signal = _generate_feature(feature_type[signal_counter],
feature_size[signal_counter],
signal_magnitude[signal_counter],
)
# If the signal is a random noise pattern then multiply these ones by
# a noise mask
if signal_constant == 0:
signal = signal * np.random.random([feature_size[signal_counter],
feature_size[signal_counter],
feature_size[signal_counter]])
# Pull out the idxs for where to insert the data
x_idx, y_idx, z_idx = _insert_idxs(feature_centre,
feature_size[signal_counter],
dimensions)
# Insert the signal into the Volume
volume_static[x_idx[0]:x_idx[1], y_idx[0]:y_idx[1], z_idx[0]:z_idx[
1]] = signal
return volume_static
def generate_stimfunction(onsets,
event_durations,
total_time,
weights=[1],
timing_file=None,
temporal_resolution=1000.0,
):
"""Return the function for the onset of events
When do stimuli onset, how long for and to what extent should you
resolve the fMRI time course. There are two ways to create this, either
by supplying onset, duration and weight information or by supplying a
timing file (in the three column format)
Parameters
----------
onsets : list, int
What are the timestamps for when an event you want to generate
onsets?
event_durations : list, int
What are the durations of the events you want to generate? If
there is only one value then this will be assigned to all onsets
total_time : int
How long is the experiment in total.
weights : list, float
How large is the box car for each of the onsets. If there is
only one value then this will be assigned to all onsets
timing_file : string
The filename (with path) to a three column timing file (FSL) to
make the events. Still requires tr_duration and total_time
temporal_resolution : float
How many elements per second are you modeling for the stim function
Returns
----------
Iterable[float]
The time course of stimulus related activation
"""
# If the timing file is supplied then use this to acquire the
if timing_file is not None:
# Read in text file line by line
with open(timing_file) as f:
text = f.readlines() # Pull out file as a an array
# Preset
onsets = list()
event_durations = list()
weights = list()
# Pull out the onsets, weights and durations, set as a float
for line in text:
onset, duration, weight = line.strip().split()
onsets.append(float(onset))
event_durations.append(float(duration))
weights.append(float(weight))
# If only one duration is supplied then duplicate it for the length of
# the onset variable
if len(event_durations) == 1:
event_durations = event_durations * len(onsets)
if len(weights) == 1:
weights = weights * len(onsets)
# Generate the time course as empty, each element is a millisecond by
# default
stimfunction = [0] * int(round(total_time * temporal_resolution))
# Cycle through the onsets
for onset_counter in list(range(len(onsets))):
# Adjust for the resolution
onset_idx = int(np.floor(onsets[onset_counter] * temporal_resolution))
# Adjust for the resolution
offset_idx = int(np.floor((onsets[onset_counter] + event_durations[
onset_counter])) * temporal_resolution)
# For the appropriate number of indexes and duration, make this value 1
idx_n = round(event_durations[onset_counter] * temporal_resolution)
stimfunction[onset_idx:offset_idx] = [weights[onset_counter]] * idx_n
# Shorten the data if it's too long
if len(stimfunction) > total_time * temporal_resolution:
stimfunction = stimfunction[0:int(total_time * temporal_resolution)]
return stimfunction
def export_stimfunction(stimfunction,
filename,
temporal_resolution=1000.0
):
""" Output a tab separated timing file
This produces a three column tab separated text file, with the three
columns representing onset time, event duration and weight, respectively
Useful if you want to run the simulated data through FEAT analyses
Parameters
----------
stimfunction : list
The stimulus function describing the time course of events
filename : str
The name of the three column text file to be output
temporal_resolution : float
How many elements per second are you modeling for the stim function
"""
# Iterate through the stim function
stim_counter = 0
event_counter = 0
while stim_counter < len(stimfunction):
# Is it an event?
if stimfunction[stim_counter] != 0:
# When did the event start?
event_onset = str(stim_counter / temporal_resolution)
# The weight of the stimulus
weight = str(stimfunction[stim_counter])
# Reset
event_duration = 0
# Is the event still ongoing?
while stimfunction[stim_counter] != 0 & stim_counter <= len(
stimfunction):
# Add one millisecond to each duration
event_duration = event_duration + 1
# Increment
stim_counter = stim_counter + 1
# How long was the event in seconds
event_duration = str(event_duration / temporal_resolution)
# Append this row to the data file
with open(filename, "a") as file:
file.write(event_onset + '\t' + event_duration + '\t' +
weight + '\n')
# Increment the number of events
event_counter = event_counter + 1
# Increment
stim_counter = stim_counter + 1
def double_gamma_hrf(stimfunction,
tr_duration,
response_delay=6,
undershoot_delay=12,
response_dispersion=0.9,
undershoot_dispersion=0.9,
response_scale=1,
undershoot_scale=0.035,
scale_function=1,
temporal_resolution=1000.0,
):
"""Return a double gamma HRF
Parameters
----------
stimfunction : list, bool
What is the time course of events to be modelled in this
experiment
tr_duration : float
response_delay : float
How many seconds until the peak of the HRF
undershoot_delay : float
How many seconds until the trough of the HRF
response_dispersion : float
How wide is the rising peak dispersion
undershoot_dispersion : float
How wide is the undershoot dispersion
response_scale : float
How big is the response relative to the peak
undershoot_scale :float
How big is the undershoot relative to the trough
scale_function : bool
Do you want to scale the function to a range of 1
temporal_resolution : float
How many elements per second are you modeling for the stim function
Returns
----------
one dimensional array
The time course of the HRF convolved with the stimulus function
"""
hrf_length = 30 # How long is the HRF being created
# How many seconds of the HRF will you model?
hrf = [0] * int(hrf_length * temporal_resolution)
# When is the peak of the two aspects of the HRF
response_peak = response_delay * response_dispersion
undershoot_peak = undershoot_delay * undershoot_dispersion
for hrf_counter in list(range(len(hrf) - 1)):
# Specify the elements of the HRF for both the response and undershoot
resp_pow = math.pow((hrf_counter / temporal_resolution) /
response_peak, response_delay)
resp_exp = math.exp(-((hrf_counter / temporal_resolution) -
response_peak) /
response_dispersion)
response_model = response_scale * resp_pow * resp_exp
undershoot_pow = math.pow((hrf_counter / temporal_resolution) /
undershoot_peak,
undershoot_delay)
undershoot_exp = math.exp(-((hrf_counter / temporal_resolution) -
undershoot_peak /
undershoot_dispersion))
undershoot_model = undershoot_scale * undershoot_pow * undershoot_exp
# For this time point find the value of the HRF
hrf[hrf_counter] = response_model - undershoot_model
# Convolve the hrf that was created with the boxcar input
signal_function = np.convolve(stimfunction, hrf)
# Decimate the signal function so that it only has one element per TR
decimate_interval = int(tr_duration * temporal_resolution)
signal_function = signal_function[0::decimate_interval]
# Cut off the HRF
signal_function = signal_function[0:int((len(stimfunction) /
tr_duration) /
temporal_resolution)]
# Scale the function so that the peak response is 1
if scale_function == 1:
signal_function = signal_function / np.max(signal_function)
return signal_function
def apply_signal(signal_function,
volume_static,
):
"""Apply the convolution and stimfunction
Apply the convolution of the HRF and stimulus time course to the
volume.
Parameters
----------
signal_function : list, float
The one dimensional timecourse of the signal over time.
Found by convolving the HRF with the stimulus time course.
volume_static : multi dimensional array, float
Returns
----------
multidimensional array, float
Generates the spatial noise volume for these parameters """
# Preset volume
signal = np.ndarray([volume_static.shape[0], volume_static.shape[
1], volume_static.shape[2], len(signal_function)])
# Iterate through the brain, multiplying the volume by the HRF
for tr_counter in list(range(0, len(signal_function))):
signal[0:volume_static.shape[0],
0:volume_static.shape[1],
0:volume_static.shape[2],
tr_counter] = signal_function[tr_counter] * volume_static
return signal
def _calc_fwhm(volume,
mask,
voxel_size=[1.0, 1.0, 1.0],
):
""" Calculate the FWHM of a volume
Takes in a 3d volume and mask and outputs the FWHM (mm) of this
volume for the non-masked voxels
Parameters
----------
volume : 3 dimensional array
Functional data to have the FWHM measured.
mask : 3 dimensional array
A mask of the voxels to have the FWHM measured from
voxel_size : length 3 list, float
Millimeters per voxel for x, y and z.
Returns
-------
float, list
Returns the FWHM of each TR in mm"""
# What are the dimensions of the volume
dimensions = volume.shape
# Iterate through the TRs, creating a FWHM for each TR
# Preset
v_count = 0
v_sum = 0
v_sq = 0
d_sum = [0.0, 0.0, 0.0]
d_sq = [0.0, 0.0, 0.0]
d_count = [0, 0, 0]
# Pull out all the voxel coordinates
coordinates = list(product(range(dimensions[0]),
range(dimensions[1]),
range(dimensions[2])))
# Find the sum of squared error for the non-masked voxels in the brain
for i in list(range(len(coordinates))):
# Pull out this coordinate
x, y, z = coordinates[i]
# Is this within the mask?
if mask[x, y, z] > 0:
# Find the the volume sum and squared values
v_count += 1
v_sum += np.abs(volume[x, y, z])
v_sq += volume[x, y, z] ** 2
# Get the volume variance
v_var = (v_sq - ((v_sum ** 2) / v_count)) / (v_count - 1)
for i in list(range(len(coordinates))):
# Pull out this coordinate
x, y, z = coordinates[i]
# Is this within the mask?
if mask[x, y, z] > 0:
# For each xyz dimension calculate the squared
# difference of this voxel and the next
in_range = (x < dimensions[0] - 1)
in_mask = in_range and (mask[x + 1, y, z] > 0)
included = in_mask and (~np.isnan(volume[x + 1, y, z]))
if included:
d_sum[0] += volume[x, y, z] - volume[x + 1, y, z]
d_sq[0] += (volume[x, y, z] - volume[x + 1, y, z]) ** 2
d_count[0] += 1
in_range = (y < dimensions[1] - 1)
in_mask = in_range and (mask[x, y + 1, z] > 0)
included = in_mask and (~np.isnan(volume[x, y + 1, z]))
if included:
d_sum[1] += volume[x, y, z] - volume[x, y + 1, z]
d_sq[1] += (volume[x, y, z] - volume[x, y + 1, z]) ** 2
d_count[1] += 1
in_range = (z < dimensions[2] - 1)
in_mask = in_range and (mask[x, y, z + 1] > 0)
included = in_mask and (~np.isnan(volume[x, y, z + 1]))
if included:
d_sum[2] += volume[x, y, z] - volume[x, y, z + 1]
d_sq[2] += (volume[x, y, z] - volume[x, y, z + 1]) ** 2
d_count[2] += 1
# Find the variance
d_var = np.divide((d_sq - np.divide(np.power(d_sum, 2),
d_count)), (np.add(d_count, -1)))
o_var = np.divide(-1, (4 * np.log(1 - (0.5 * d_var / v_var))))
fwhm3 = np.sqrt(o_var) * 2 * np.sqrt(2 * np.log(2))
fwhm = np.prod(np.multiply(fwhm3, voxel_size)) ** (1 / 3)
return fwhm
def _calc_sfnr(volume,
mask,
):
""" Calculate the SFNR of a volume
This takes the middle of the volume and averages the signal within the
brain and compares to the temporal standard deviation in the voxels
outside the brain.
Parameters
----------
volume : 4d array, float
Take a volume time series to extract the middle slice from the middle TR
mask : 4d array, float
A mask the same size as the volume, specifying the mask (values=0 -> 1)
Returns
-------
float
The sd of the temporal variability of brain voxels.
float
The sfnr of the volume (mean brain activity divided by
temporal
variability in the average non brain voxels)
float
What is the max activity measured here, a point of reference for masking
"""
# What are the midpoints to be extracted
mid_x_idx = int(np.ceil(volume.shape[0] / 2))
mid_tr_idx = int(np.ceil(volume.shape[3] / 2))
# Pull out the slices
slice_volume = volume[mid_x_idx, :, :, mid_tr_idx]
slice_mask = mask[mid_x_idx, :, :, mid_tr_idx]
# Divide by the mask (if the middle slice was low in grey matter mass
# then you would have a lower mean signal by default)
mean_signal = (slice_volume[slice_mask > 0]).mean()
# What are the brain and non-brain voxels
brain_voxels = volume[mask[:, :, :, 0] > 0]
mask_voxels = volume[mask[:, :, :, 0] == 0]
# What is the noise in the masked voxels
mask_noise = np.std(mask_voxels, 1).mean()
# Assume the mask noise is a combination of random + drift. Thus average
# all masked voxels and find the variation over time, this is the
# variance due to drift.
drift_noise = np.mean(mask_voxels, 0).std()
# Subtract the drift variance from total mask noise to find the system
# noise
background_noise = np.sqrt(mask_noise ** 2 - drift_noise ** 2)
# Find the noise to brain voxels
temporal_noise = np.std(brain_voxels, 1).mean()
# Convert temporal noise into percent signal change
temporal_noise = temporal_noise / mean_signal * 100
# Calculate sfnr
sfnr = mean_signal / background_noise
# Convert from memmap
sfnr = float(sfnr)
# What is the max activation of this volume
max_activity = volume.max()
return temporal_noise, sfnr, max_activity
def _calc_temporal_noise(volume,
mask,
auto_reg_order=1,
):
""" Calculate the mix of autoregressive and drift noise.
Parameters
----------
volume : 4d masarray, float
Input data to be calculate the autoregression
mask : 4d array, float
What voxels of the input are within the brain
auto_reg_order : int
What order of the autoregression do you want to pull out
Returns
-------
float
A sigma of the autoregression in the data
float
Sigma of the drift in the data
"""
# Calculate the time course
timecourse = np.mean(volume[mask[:, :, :, 0] > 0], 0)
# Pull out the AR values (depends on order)
auto_reg_sigma = ar.AR_est_YW(timecourse, auto_reg_order)[1]
auto_reg_sigma = np.sqrt(auto_reg_sigma)
# What is the size of the change in the time course
drift_sigma = timecourse.std().tolist()
return auto_reg_sigma, drift_sigma
def calc_noise(volume,
mask=None,
noise_dict=None,
):
""" Calculates the noise properties of the volume supplied.
This estimates what noise properties the volume has. For instance it
determines the spatial smoothness, the autoregressive noise, system
noise etc. Read the doc string for generate_noise to understand how
these different types of noise interact.
Parameters
----------
volume : 4d numpy array, float
Take in a functional volume (either the file name or the numpy
array) to be used to estimate the noise properties of this
mask : 4d numpy array, float
The mask to be used, the same size as the volume
Returns
-------
dict
Return a dictionary of the calculated noise parameters of the provided
dataset
"""
# Preset
# Create the mask
if mask is None:
mask = np.ones(volume.shape)
# Update noise dict
if noise_dict is None:
noise_dict = {'voxel_size': [1.0, 1.0, 1.0]}
elif 'voxel_size' not in noise_dict:
noise_dict['voxel_size'] = [1.0, 1.0, 1.0]
# Since you are deriving the 'true' values then you want your noise to
# be set to that level
# Calculate the temporal_noise noise and SFNR of the volume
noise_dict['temporal_noise'], noise_dict['sfnr'], noise_dict[
'max_activity'] = _calc_sfnr(volume, mask)
# Calculate the fwhm on a subset of volumes
if volume.shape[3] > 100:
# Take only 100 shuffled TRs
trs = np.arange(volume.shape[3])
np.random.shuffle(trs)
trs = trs[0:100]
else:
trs = list(range(0, volume.shape[3]))
# Go through the trs and pull out the fwhm
fwhm = [0] * len(trs)
for tr in list(range(0, len(trs))):
fwhm[tr] = _calc_fwhm(volume[:, :, :, trs[tr]],
mask[:, :, :, trs[tr]],
noise_dict['voxel_size'],
)
# Keep only the mean
noise_dict['fwhm'] = np.mean(fwhm)
# Calculate the autoregressive and drift noise
auto_reg_sigma, drift_sigma = _calc_temporal_noise(volume, mask)
# Calibrate for how sigma is originally calculated
auto_reg_sigma = auto_reg_sigma / noise_dict['temporal_noise']
# Total temporal noise, since these values only make sense relatively
total_temporal_noise = auto_reg_sigma + drift_sigma
# What proportion of noise is accounted for by these variables?
noise_dict['auto_reg_sigma'] = auto_reg_sigma / total_temporal_noise
noise_dict['drift_sigma'] = drift_sigma / total_temporal_noise
# Return the noise dictionary
return noise_dict
def _generate_noise_system(dimensions_tr,
):
"""Generate the scanner noise
Generate the noise that is typical of a scanner. This is comprised
of two types of noise, Rician and Gaussian
Parameters
----------
dimensions_tr : n length array, int
What are the dimensions of the volume you wish to insert