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projective_subtraction.py
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import numpy as np
from dipy.viz import fvtk
from prepare_phantoms import get_data,codebook,simulations_dipy,draw_needles
from dipy.core.triangle_subdivide import create_unit_sphere,create_half_unit_sphere
from sphere_tools import random_uniform_on_sphere
CNT=0
def show_different_ds(bvals,bvecs):
global CNT
r=fvtk.ren()
r.SetBackground(1.,1.,1.)
Signals=[]
for d in [0.0005,0.0010,0.0015,0.0020,0.0025,0.0030,0.0035,0.0040]:
S1,sticks1=simulations_dipy(bvals,bvecs,d=d,S0=100,angles=[(0,0),(45,0),(90,90)],fractions=[100,0,0],snr=None)
Signals.append(S1[1:]/S1[0])
show_signals(r,Signals,bvecs)
CNT=0
draw_needles(r,sticks1,100,2,off=np.array([0,0,0]))
Signals=[]
for d in [0.0005,0.0010,0.0015,0.0020,0.0025,0.0030,0.0035,0.0040]:
S1,sticks1=simulations_dipy(bvals,bvecs,d=d,S0=100,angles=[(0,0),(45,0),(90,90)],fractions=[50,50,0],snr=None)
Signals.append(S1[1:]/S1[0])
show_signals(r,Signals,bvecs,-200)
CNT=0
Signals=[]
for d in [0.0005,0.0010,0.0015,0.0020,0.0025,0.0030,0.0035,0.0040]:
S1,sticks1=simulations_dipy(bvals,bvecs,d=d,S0=100,angles=[(0,0),(45,0),(90,90)],fractions=[33,33,33],snr=None)
Signals.append(S1[1:]/S1[0])
show_signals(r,Signals,bvecs,-400)
"""
Signals=[]
for d in [0.0005,0.0010,0.0015,0.0025,0.0030,0.0035,0.0040]:
S1,sticks1=simulations_dipy(bvals,bvecs,d=d,S0=100,angles=[(0,0),(90,0),(90,90)],fractions=[20,50,0],snr=None)
Signals.append(S1[1:]/S1[0])
show_signals(r,Signals,bvecs,-600)
Signals=[]
for d in [0.0005,0.0010,0.0015,0.0025,0.0030,0.0035,0.0040]:
S1,sticks1=simulations_dipy(bvals,bvecs,d=d,S0=100,angles=[(0,0),(90,0),(90,90)],fractions=[10,50,0],snr=None)
Signals.append(S1[1:]/S1[0])
show_signals(r,Signals,bvecs,-800)
Signals=[]
for d in [0.0005,0.0010,0.0015,0.0025,0.0030,0.0035,0.0040]:
S1,sticks1=simulations_dipy(bvals,bvecs,d=d,S0=100,angles=[(0,0),(90,0),(90,90)],fractions=[0,50,0],snr=None)
Signals.append(S1[1:]/S1[0])
show_signals(r,Signals,bvecs,-1000)
"""
fvtk.show(r)
def needlebook(bvals,bvecs,d=0.0015,steps=21,subdiv=3,fractions=[1.]):
""" Single needles book
"""
sticks,e,t=create_half_unit_sphere(subdiv)
CBK=[]; STK=[]; FRA=[]; REG=[]
def single_needles(CBK,STK,FRA,bvals,bvecs,sticks,fraction):
for s in sticks:
S=np.zeros(len(bvecs)-1)
for (i,g) in enumerate(bvecs[1:]):
S[i]=(1-fraction)*np.exp(-bvals[i+1]*d)+fraction*np.exp(-bvals[i+1]*d*np.dot(s,g)**2)
CBK.append(S)
STK.append(s)
FRA.append(fraction)
#fractions=np.linspace(0,1,steps)
for f in fractions:
single_needles(CBK,STK,FRA,bvals,bvecs,sticks,fraction=f)
CBK=np.array(CBK)
STK=np.array(STK)
FRA=np.array(FRA)
return CBK,STK,FRA
def psi(S,CBK,STK,FRA):
""" Projective Subtraction Diffusion MRI
Parameters
-----------
S: normalized signal
CBK: signal codebook
STK: codebook needles
Returns
--------
A: approximated orientation
"""
#N=S/np.float(S[0])
values=[]
for i in range(len(CBK)):
D=S-CBK[i]
X=np.dot(np.diag(np.concatenate([D,D])),Bvecs)
mX=np.mean(np.sqrt(X[:,0]**2+X[:,1]**2+X[:,2]**2))
#values.append(np.var(D))
values.append(mX)
values=np.array(values)
return values
def less90(angle):
if angle > 90:
return 180-angle
else:
return angle
def angular_distances(STK,sticks):
A=np.zeros((len(STK),6))
for i in range(len(STK)):
A[i,:3]=STK[i,:]
A[i,3]=less90(np.rad2deg(np.arccos(np.dot(STK[i],sticks[0]))))
A[i,4]=less90(np.rad2deg(np.arccos(np.dot(STK[i],sticks[1]))))
A[i,5]=less90(np.rad2deg(np.arccos(np.dot(STK[i],sticks[2]))))
return A
def random_simulations(no,bvals,gradients,d=0.0015,fractions=[100,0,0],snr=None):
sticks=random_uniform_on_sphere(n=no,coords='xyz')
fractions=[f/100. for f in fractions]
f0=1-np.sum(fractions)
S=np.zeros(len(gradients)-1)
for (i,g) in enumerate(gradients[1:]):
S[i]=f0*np.exp(-bvals[i+1]*d)+ np.sum([fractions[j]*np.exp(-bvals[i+1]*d*np.dot(s,g)**2) for (j,s) in enumerate(sticks)])
if snr!=None:
std=S/snr
S=S+np.random.randn(len(S))*std
return S,sticks
def single_stick_simulations(no,bvals,bvecs,d,fractions,snr):
Bvecs=np.concatenate([bvecs[1:],-bvecs[1:]])
res=[]
for i in range(no):
S0,sticks0=random_simulations(3,bvals,bvecs,d,fractions=fractions,snr=snr)
X0=np.dot(np.diag(np.concatenate([S0,S0])),Bvecs)
values=psi(S0,CBK,STK,FRA)
A=angular_distances(STK[values.argsort()],sticks0)
res.append(A[0,3])
return res
def show_signals(r,Signals,bvecs,offset=0):
#r=fvtk.ren()
global CNT
Bvecs=np.concatenate([bvecs[1:],-bvecs[1:]])
for (i,S) in enumerate(Signals):
X=np.dot(np.diag(np.concatenate([50*S,50*S])),Bvecs)
mX=np.mean(np.sqrt(X[:,0]**2+X[:,1]**2+X[:,2]**2))
print CNT,mX,np.var(S)
CNT=CNT+1
fvtk.add(r,fvtk.point(X+np.array([(i+1)*200,offset,0]),fvtk.green,1,2,6,6))
#fvtk.show(r)
if __name__=='__main__':
np.set_printoptions(4,suppress=True)
data,bvals,bvecs=get_data(name='118_32',par=0)
Bvecs=np.concatenate([bvecs[1:],-bvecs[1:]])
S0,sticks0=simulations_dipy(bvals,bvecs,d=0.0015,S0=100,angles=[(0,0),(90,0),(90,90)],fractions=[100,0,0],snr=None)
X0=np.dot(np.diag(np.concatenate([S0[1:],S0[1:]])),Bvecs)
#CBK,STK,FRA=needlebook(bvals,bvecs,d=0.0015,subdiv=4,fractions=[.8])
#res0=single_stick_simulations(200,bvals,bvecs,d=0.0015,fractions=[80,0,0],snr=None)
#CBK,STK,FRA=needlebook(bvals,bvecs,d=0.0015,subdiv=3,fractions=[.2])
#res1=single_stick_simulations(200,bvals,bvecs,d=0.0015,fractions=[80,0,0],snr=None)
#res0=single_stick_simulations(1000,bvals,bvecs,d=0.0015,fractions=[100,0,0],snr=None)
#res1=single_stick_simulations(1000,bvals,bvecs,d=0.0015,fractions=[80,0,0],snr=None)
#res2=single_stick_simulations(1000,bvals,bvecs,d=0.0015,fractions=[60,0,0],snr=None)
#res3=single_stick_simulations(1000,bvals,bvecs,d=0.0015,fractions=[40,0,0],snr=None)
#res4=single_stick_simulations(1000,bvals,bvecs,d=0.0015,fractions=[20,0,0],snr=None)
# values=psi(S0[1:]/S0[0],CBK,STK,FRA)
# r=fvtk.ren()
# fvtk.add(r,fvtk.point(X0,fvtk.yellow,1,2,8,8))
# draw_needles(r,sticks0,100,2)
# for (i,S) in enumerate((CBK[values.argsort()])):
# NS=S0[1:]-S0[0]*S
# X=np.dot(np.diag(np.concatenate([NS,NS])),Bvecs)
# fvtk.add(r,fvtk.point(X+np.array([(i+1)*200,0,0]),fvtk.green,1,2,8,8))
# #draw_needles(r,sticks0,100,2,off=np.array([(i+1-14)*200,0,0]))
# fvtk.show(r)