NuMRI/codes/CS.py

598 lines
19 KiB
Python

import numpy as np
from numpy import linalg as LA
import sys
from mpi4py import MPI
comm = MPI.COMM_WORLD
size = comm.Get_size()
rank = comm.Get_rank()
# COMPRESSED SENSING: LINEAR BREGMAN METHOD
# Translated and adapted into python from tinycs
#
# *tinycs* is a minimal compressed sensing (CS) toolkit designed
# to allow MR imaging scientists to design undersampled
# acquisitions and reconstruct the resulting data with CS without
# needing to be a CS expert.
#
# The Cartesian reconstruction is based on the split Bregman
# code written by Tom Goldstein, originally available here:
# <http://tag7.web.rice.edu/Split_Bregman.html>
def pdf(k, kw, klo, q):
p = (np.abs(k)/kw)**(-q)
p[np.where(k == 0)] = 0
p[np.where(np.abs(k) <= kw)] = 1
p[np.where(k < klo)] = 0
return p
def mask_pdf_1d(n, norm, q, pf):
ks = np.arange(0, n) - np.ceil(n/2) - 1
kmax = np.floor(n/2)
npf = np.round(pf*n)
klo = ks[n-npf]
for k in range(int(kmax)):
P = pdf(ks, k+1, klo, q)
if np.sum(P) >= norm:
break
P = np.fft.fftshift(P)
return P
def mask_pdf_2d(dims, norm, q, pf):
nz = dims[1]
ny = dims[0]
yc = round(ny/2)
zc = round(nz/2)
rmax = np.sqrt((ny-yc)**2 + (nz-zc)**2)
[Z, Y] = np.meshgrid(np.arange(0, nz), np.arange(0, ny))
RR = np.sqrt((Y-yc)**2 + (Z-zc)**2)
Z = np.abs(Z - nz/2 - 0.5)
Y = np.abs(Y - ny/2 - 0.5)
for rw in range(1, int(rmax)+1):
P = np.ones([ny, nz])/pf
C = np.logical_and(Z <= rw, Y <= rw)
W = np.logical_or(Z > rw, Y > rw)
P[W] = (RR[W]/rw)**(-q)
if np.sum(P) >= norm:
break
return [P, C]
def GeneratePattern(dim, R):
# 3D CASE
if np.size(dim) == 3:
nro = dim[0]
npe = dim[1]
nacq = round(npe/R)
q = 1
pf = 1
P = mask_pdf_1d(npe, nacq, q, pf)
while True:
M = np.random.rand(npe)
M = 1*(M <= P)
if np.sum(M) == nacq:
break
# remove partial Fourier plane and compensate sampling density
M = M != 0
M = np.tile(M, [nro, 1])
#M = M.T
# 4D CASE
if np.size(dim) == 4:
nro = dim[0]
npe1 = dim[1]
npe2 = dim[2]
nacq = round(npe1*npe2/R)
q = 1
pf = 1
[P, C] = mask_pdf_2d([npe1, npe2], nacq, q, pf)
RR = np.random.rand(npe1, npe2)
M = (RR <= P)
nchosen = np.sum(M)
if nchosen > nacq: # Correct for inexact number chosen
#outerOn = np.logical_and( M , P!=1 )
outerOn = np.where((M)*(P != 1))
numToFlip = nchosen-nacq
idxs = np.random.permutation(outerOn[0].size)
idxx = outerOn[0][idxs[0:numToFlip]]
idxy = outerOn[1][idxs[0:numToFlip]]
M[idxx, idxy] = False
elif nchosen < nacq:
outerOff = np.where(~M)
idxs = np.random.permutation(outerOff[0].size)
numToFlip = nacq - nchosen
idxx = outerOff[0][idxs[0:numToFlip]]
idxy = outerOff[1][idxs[0:numToFlip]]
M[idxx, idxy] = True
M = np.rollaxis(np.tile(np.rollaxis(M, 1), [nro, 1, 1]), 2)
M = np.fft.ifftshift(M)
M = M.transpose((1, 0, 2))
return M
def get_norm_factor(MASK, uu):
UM = MASK == 1
return UM.shape[0]/LA.norm(uu)
def Dxyzt(X):
if np.ndim(X) == 3:
dd0 = X[:, :, 0]
dd1 = X[:, :, 1]
DA = dd0 - np.vstack((dd0[1::, :], dd0[0, :]))
DB = dd1 - np.hstack((dd1[:, 1::], dd1[:, 0:1]))
return DA + DB
if np.ndim(X) == 4:
dd0 = X[:, :, :, 0]
dd1 = X[:, :, :, 1]
dd2 = X[:, :, :, 2]
DA = dd0 - np.vstack((dd0[1::, :, :], dd0[0, :, :][np.newaxis, :, :]))
DB = dd1 - np.hstack((dd1[:, 1::, :], dd1[:, 0, :][:, np.newaxis, :]))
DC = dd2 - np.dstack((dd2[:, :, 1::], dd2[:, :, 0][:, :, np.newaxis]))
return DA + DB + DC
def Dxyz(u):
if np.ndim(u) == 2:
dx = u[:, :] - np.vstack((u[-1, :], u[0:-1, :]))
dy = u[:, :] - np.hstack((u[:, -1:], u[:, 0:-1]))
D = np.zeros([dx.shape[0], dx.shape[1], 2], dtype=complex)
D[:, :, 0] = dx
D[:, :, 1] = dy
return D
if np.ndim(u) == 3:
dx = u[:, :, :] - \
np.vstack((u[-1, :, :][np.newaxis, :, :], u[0:-1, :, :]))
dy = u[:, :, :] - \
np.hstack((u[:, -1, :][:, np.newaxis, :], u[:, 0:-1, :]))
dz = u[:, :, :] - \
np.dstack((u[:, :, -1][:, :, np.newaxis], u[:, :, 0:-1]))
D = np.zeros([dx.shape[0], dx.shape[1], dx.shape[2], 3], dtype=complex)
D[:, :, :, 0] = dx
D[:, :, :, 1] = dy
D[:, :, :, 2] = dz
return D
def shrink(X, pgam):
p = 1
s = np.abs(X)
tt = pgam/(s)**(1-p)
# t = pgam/np.sqrt(s)
ss = s-tt
ss = ss*(ss > 0)
s = s + 1*(s < tt)
ss = ss/s
return ss*X
def CSMETHOD(ITOT, R):
''' Compressed Sensing Function.
Args:
ITOT: a numpy matrix with the full sampled (3D or 4D) dynamical data
R: the acceleration factor
'''
# Method parameters
ninner = 5
nbreg = 10
lmbda = 4
mu = 20
gam = 1
if np.ndim(ITOT) == 3:
[row, col, numt2] = ITOT.shape
elif np.ndim(ITOT) == 4:
[row, col, dep, numt2] = ITOT.shape
else:
raise Exception('Dynamical data is requested')
MASK = GeneratePattern(ITOT.shape, R)
CS1 = np.zeros(ITOT.shape, dtype=complex)
nit = 0
nit_tot = (numt2-1)/20
if np.ndim(ITOT) == 3:
for t in range(numt2):
if rank == 0:
print('{3D COMPRESSED SENSING} t = ', t)
Kdata = np.fft.fft2(ITOT[:, :, t])*MASK
data_ndims = Kdata.ndim
mask = Kdata != 0 # not perfect, but good enough
# normalize the data so that standard parameter values work
norm_factor = get_norm_factor(mask, Kdata)
Kdata = Kdata*norm_factor
# Reserve memory for the auxillary variables
Kdata0 = Kdata
img = np.zeros([row, col], dtype=complex)
X = np.zeros([row, col, data_ndims])
B = np.zeros([row, col, data_ndims])
# Build Kernels
scale = np.sqrt(row*col)
murf = np.fft.ifft2(mu*mask*Kdata)*scale
uker = np.zeros([row, col])
uker[0, 0] = 4
uker[0, 1] = -1
uker[1, 0] = -1
uker[-1, 0] = -1
uker[0, -1] = -1
uker = 1/(mu*mask + lmbda*np.fft.fftn(uker) + gam)
# Do the reconstruction
for outer in range(nbreg):
for inner in range(ninner):
# update u
rhs = murf + lmbda*Dxyzt(X-B) + gam*img
img = np.fft.ifft2(np.fft.fft2(rhs)*uker)
# update x and y
A = Dxyz(img) + B
X = shrink(A, 1/lmbda)
# update bregman parameters
B = A - X
Kdata = Kdata + Kdata0 - mask*np.fft.fftn(img)/scale
murf = np.fft.ifftn(mu*mask*Kdata)*scale
# undo the normalization so that results are scaled properly
img = img / norm_factor / scale
CS1[:, :, t] = img
if np.ndim(ITOT) == 4:
for t in range(numt2):
if rank == 0:
print(
'[4D CS] R = {re} t = {te}/{tef}'.format(re=R, te=t, tef=numt2))
Kdata_0 = np.fft.fftn(ITOT[:, :, :, t])
Kdata = Kdata_0*MASK
data_ndims = Kdata.ndim
mask = Kdata != 0 # not perfect, but good enough
# normalize the data so that standard parameter values work
norm_factor = get_norm_factor(mask, Kdata)
Kdata = Kdata*norm_factor
# Reserve memory for the auxillary variables
Kdata0 = Kdata
img = np.zeros([row, col, dep], dtype=complex)
X = np.zeros([row, col, dep, data_ndims])
B = np.zeros([row, col, dep, data_ndims])
# Build Kernels
scale = np.sqrt(row*col*dep)
murf = np.fft.ifftn(mu*mask*Kdata)*scale
uker = np.zeros([row, col, dep])
uker[0, 0, 0] = 8
uker[1, 0, 0] = -1
uker[0, 1, 0] = -1
uker[0, 0, 1] = -1
uker[-1, 0, 0] = -1
uker[0, -1, 0] = -1
uker[0, 0, -1] = -1
uker = 1/(mu*mask + lmbda*np.fft.fftn(uker) + gam)
# Do the reconstruction
for outer in range(nbreg):
for inner in range(ninner):
# update u
rhs = murf + lmbda*Dxyzt(X-B) + gam*img
img = np.fft.ifft2(np.fft.fft2(rhs)*uker)
# update x and y
A = Dxyz(img) + B
X = shrink(A, 1/lmbda)
# update bregman parameters
B = A - X
Kdata = Kdata + Kdata0 - mask*np.fft.fftn(img)/scale
murf = np.fft.ifftn(mu*mask*Kdata)*scale
# undo the normalization so that results are scaled properly
img = img / norm_factor / scale
CS1[:, :, :, t] = img
return CS1
def CSMETHOD_SENSE(ITOT, R, R_SENSE):
''' Compressed sense algorith with SENSE... in contruction!.
Args:
ITOT: a numpy matrix with the full sampled (3D or 4D) dynamical data
R: the acceleration factor
'''
# Method parameters
ninner = 5
nbreg = 10
lmbda = 4
mu = 20
gam = 1
[row, col, dep, numt2] = ITOT.shape
MASK = {}
ITOTCS = {}
MASK[0] = GeneratePattern([row, int(np.ceil(col/2)), dep, numt2], R)
MASK[1] = GeneratePattern([row, int(np.ceil(col/2)), dep, numt2], R)
SenseMAP = {}
[SenseMAP[0], SenseMAP[1]] = Sensitivity_Map([row, col, dep])
col = int(np.ceil(col/2))
ITOTCS[0] = np.zeros([row, col, dep, numt2], dtype=complex)
ITOTCS[1] = np.zeros([row, col, dep, numt2], dtype=complex)
for rs in range(R_SENSE):
for t in range(numt2):
if rank == 0:
print(
'[4D CS] R = {re} t = {te}/{tef}'.format(re=R, te=t, tef=numt2))
Kdata_0 = np.fft.fftn(ITOT[:, :, :, t])
Kdata_0 = Kdata_0*SenseMAP[rs]
Kdata_0 = Kdata_0[:, 0::R_SENSE, :]
Kdata = Kdata_0*MASK[rs]
data_ndims = Kdata.ndim
mask = Kdata != 0 # not perfect, but good enough
# normalize the data so that standard parameter values work
norm_factor = get_norm_factor(mask, Kdata)
Kdata = Kdata*norm_factor
# Reserve memory for the auxillary variables
Kdata0 = Kdata
img = np.zeros([row, col, dep], dtype=complex)
X = np.zeros([row, col, dep, data_ndims])
B = np.zeros([row, col, dep, data_ndims])
# Build Kernels
scale = np.sqrt(row*col*dep)
murf = np.fft.ifftn(mu*mask*Kdata)*scale
uker = np.zeros([row, col, dep])
uker[0, 0, 0] = 8
uker[1, 0, 0] = -1
uker[0, 1, 0] = -1
uker[0, 0, 1] = -1
uker[-1, 0, 0] = -1
uker[0, -1, 0] = -1
uker[0, 0, -1] = -1
uker = 1/(mu*mask + lmbda*np.fft.fftn(uker) + gam)
# Do the reconstruction
for outer in range(nbreg):
for inner in range(ninner):
# update u
rhs = murf + lmbda*Dxyzt(X-B) + gam*img
img = np.fft.ifft2(np.fft.fft2(rhs)*uker)
# update x and y
A = Dxyz(img) + B
X = shrink(A, 1/lmbda)
# update bregman parameters
B = A - X
Kdata = Kdata + Kdata0 - mask*np.fft.fftn(img)/scale
murf = np.fft.ifftn(mu*mask*Kdata)*scale
# undo the normalization so that results are scaled properly
img = img / norm_factor / scale
ITOTCS[rs][:, :, :, t] = img
return [ITOTCS[0], ITOTCS[1]]
def phase_contrast(M1, M0, VENC, scantype='0G'):
param = 1
if scantype == '-G+G':
param = 0.5
return VENC*param*(np.angle(M1) - np.angle(M0))/np.pi
def GenerateMagnetization(Sq, VENC, noise, scantype='0G'):
''' Simulation of a typical magnetization. A x-dependent plane is added into the
reference phase.
'''
# MRI PARAMETERS
gamma = 267.513e6 # rad/Tesla/sec Gyromagnetic ratio for H nuclei
B0 = 1.5 # Tesla Magnetic Field Strenght
TE = 5e-3 # Echo-time
PHASE0 = np.zeros(Sq.shape)
PHASE1 = np.zeros(Sq.shape)
RHO0 = np.zeros(Sq.shape, dtype=complex)
RHO1 = np.zeros(Sq.shape, dtype=complex)
if np.ndim(Sq) == 3:
[row, col, numt2] = Sq.shape
[X, Y] = np.meshgrid(np.linspace(0, col, col),
np.linspace(0, row, row))
for k in range(numt2):
if noise:
Drho = np.random.normal(0, 0.2, [row, col])
Drho2 = np.random.normal(0, 0.2, [row, col])
else:
Drho = np.zeros([row, col])
Drho2 = np.zeros([row, col])
varPHASE0 = np.random.randint(-10, 11, size=(row, col))*np.pi/180*(
np.abs(Sq[:, :, k]) < 0.001) # Hugo's observation
modulus = 0.5 + 0.5*(np.abs(Sq[:, :, k]) > 0.001)
if scantype == '0G':
PHASE0[:, :, k] = (gamma*B0*TE+0.01*X) * \
(np.abs(Sq[:, :, k]) > 0.001) + 10*varPHASE0
PHASE1[:, :, k] = (gamma*B0*TE+0.01*X)*(np.abs(Sq[:, :, k])
> 0.001) + 10*varPHASE0 + np.pi*Sq[:, :, k]/VENC
if scantype == '-G+G':
PHASE0[:, :, k] = gamma*B0*TE * \
np.ones([row, col]) + 10*varPHASE0 - np.pi*Sq[:, :, k]/VENC
PHASE1[:, :, k] = gamma*B0*TE * \
np.ones([row, col]) + 10*varPHASE0 + np.pi*Sq[:, :, k]/VENC
RHO0[:, :, k] = modulus*np.cos(PHASE0[:, :, k]) + \
Drho + 1j*modulus*np.sin(PHASE0[:, :, k]) + 1j*Drho2
RHO1[:, :, k] = modulus*np.cos(PHASE1[:, :, k]) + \
Drho + 1j*modulus*np.sin(PHASE1[:, :, k]) + 1j*Drho2
if np.ndim(Sq) == 4:
[row, col, dep, numt2] = Sq.shape
[X, Y, Z] = np.meshgrid(np.linspace(0, col, col), np.linspace(
0, row, row), np.linspace(0, dep, dep))
for k in range(numt2):
if noise:
Drho = np.random.normal(0, 0.2, [row, col, dep])
Drho2 = np.random.normal(0, 0.2, [row, col, dep])
else:
Drho = np.zeros([row, col, dep])
Drho2 = np.zeros([row, col, dep])
varPHASE0 = np.random.randint(-10, 11, size=(row, col, dep)) * \
np.pi/180*(np.abs(Sq[:, :, :, k]) < 0.001)
modulus = 0.5 + 0.5*(np.abs(Sq[:, :, :, k]) > 0.001)
if scantype == '0G':
PHASE0[:, :, :, k] = (gamma*B0*TE+0.01*X) * \
(np.abs(Sq[:, :, :, k]) > 0.001) + 10*varPHASE0
PHASE1[:, :, :, k] = (gamma*B0*TE+0.01*X)*(np.abs(Sq[:, :, :, k])
> 0.001) + 10*varPHASE0 + np.pi*Sq[:, :, :, k]/VENC
if scantype == '-G+G':
PHASE0[:, :, :, k] = gamma*B0*TE * \
np.ones([row, col, dep]) + varPHASE0 - \
np.pi*Sq[:, :, :, k]/VENC
PHASE1[:, :, :, k] = gamma*B0*TE * \
np.ones([row, col, dep]) + varPHASE0 + \
np.pi*Sq[:, :, :, k]/VENC
RHO0[:, :, :, k] = modulus*np.cos(PHASE0[:, :, :, k]) + \
Drho + 1j*modulus*np.sin(PHASE0[:, :, :, k]) + 1j*Drho2
RHO1[:, :, :, k] = modulus*np.cos(PHASE1[:, :, :, k]) + \
Drho + 1j*modulus*np.sin(PHASE1[:, :, :, k]) + 1j*Drho2
return [RHO0, RHO1]
def undersampling(Sqx, Sqy, Sqz, options, savepath):
R = options['cs']['R']
for r in R:
if rank == 0:
print('Using Acceleration Factor R = ' + str(r))
print('Component x of M0')
[M0, M1] = GenerateMagnetization(
Sqx, options['cs']['VENC'], options['cs']['noise'])
print('\n Component x of M0')
M0_cs = CSMETHOD(M0, r)
print('\n Component x of M1')
M1_cs = CSMETHOD(M1, r)
Sqx_cs = phase_contrast(M1_cs, M0_cs, options['cs']['VENC'])
del M0, M1
del M0_cs, M1_cs
[M0, M1] = GenerateMagnetization(
Sqy, options['cs']['VENC'], options['cs']['noise'])
print('\n Component y of M0')
M0_cs = CSMETHOD(M0, r)
print('\n Component y of M1')
M1_cs = CSMETHOD(M1, r)
Sqy_cs = phase_contrast(M1_cs, M0_cs, options['cs']['VENC'])
del M0, M1
del M0_cs, M1_cs
[M0, M1] = GenerateMagnetization(
Sqz, options['cs']['VENC'], options['cs']['noise'])
if rank == 0:
print('\n Component z of M0')
M0_cs = CSMETHOD(M0, r)
if rank == 0:
print('\n Component z of M1')
M1_cs = CSMETHOD(M1, r)
if rank == 0:
print(' ')
Sqz_cs = phase_contrast(M1_cs, M0_cs, options['cs']['VENC'])
if rank == 0:
print('saving the sequences in ' + savepath)
seqname = options['cs']['name'] + '_R' + str(r) + '.npz'
print('sequence name: ' + seqname)
np.savez_compressed(savepath + seqname,
x=Sqx_cs, y=Sqy_cs, z=Sqz_cs)
del Sqx_cs, Sqy_cs, Sqz_cs
def undersampling_short(Mx, My, Mz, options):
R = options['cs']['R']
savepath = options['cs']['savepath']
R_SENSE = 1
if 'R_SENSE' in options['cs']:
R_SENSE = options['cs']['R_SENSE'][0]
for r in R:
if rank == 0:
print('Using Acceleration Factor R = ' + str(r))
if R_SENSE == 2:
[MxS0_cs, MxS1_cs] = CSMETHOD_SENSE(Mx, r, 2)
[MyS0_cs, MyS1_cs] = CSMETHOD_SENSE(My, r, 2)
[MzS0_cs, MzS1_cs] = CSMETHOD_SENSE(Mz, r, 2)
if rank == 0:
print('saving the sequences in ' + savepath)
seqname_s0 = options['cs']['name'] + 'S0_R' + str(r) + '.npz'
seqname_s1 = options['cs']['name'] + 'S1_R' + str(r) + '.npz'
print('sequence name: ' + seqname_s0)
np.savez_compressed(savepath + seqname_s0,
x=MxS0_cs, y=MyS0_cs, z=MzS0_cs)
print('sequence name: ' + seqname_s1)
np.savez_compressed(savepath + seqname_s1,
x=MxS1_cs, y=MyS1_cs, z=MzS1_cs)
del MxS0_cs, MyS0_cs, MzS0_cs
del MxS1_cs, MyS1_cs, MzS1_cs
elif R_SENSE == 1:
Mx_cs = CSMETHOD(Mx, r)
My_cs = CSMETHOD(My, r)
Mz_cs = CSMETHOD(Mz, r)
if rank == 0:
print('saving the sequences in ' + savepath)
seqname = options['cs']['name'] + '_R' + str(r) + '.npz'
print('sequence name: ' + seqname)
np.savez_compressed(savepath + seqname,
x=Mx_cs, y=My_cs, z=Mz_cs)
del Mx_cs, My_cs, Mz_cs
else:
raise Exception('Only implemented for 2-fold SENSE!!')
# THE END