def unwrap_freq( im ):
max_im = ut.scaling(np.absolute(im))
scaled_im = (im)/max_im*np.pi
#ut.plotim1(im)
im = unwrap_phase(scaled_im.astype(np.float))/np.pi*max_im
ut.plotim1(np.real(im),bar=1)
return im
def unwrap_freq(im):
max_im = 0.8 * ut.scaling(np.absolute(im))
scaled_im = (im) / max_im * np.pi
ut.plotim1(im, bar=1, pause_close=5)
im = unwrap_phase(scaled_im) / np.pi * max_im
ut.plotim1(im, bar=1, pause_close=5)
return im
def test():
# simulated image
mat_contents = sio.loadmat(pathdat,
struct_as_record=False,
squeeze_me=True)
xdata = mat_contents["data"]
im = xdata.images
TE = xdata.TE
field = xdata.FieldStrength
fat_freq_arr = 42.58 * field * np.array(
[-3.80, -3.40, -2.60, -1.94, -0.39, 0.60])
fat_rel_amp = np.array([0.087, 0.693, 0.128, 0.004, 0.039, 0.048])
print(TE)
#ut.plotim3(np.angle(im[:,:,:]))
nx, ny, nz, nte = im.shape
scaling = ut.scaling(im)
b = im / scaling
#ut.plotim3(mask)
#ut.plotim3(np.absolute(b)) #undersampled imag
#parameters
xpar = np.zeros((nx, ny, nz, 3), np.complex128)
# IDEAL and FFT jointly
IDEAL = idealc.IDEAL_opt2(TE, fat_freq_arr,
fat_rel_amp) #fat_freq_arr , fat_rel_amp
IDEAL.set_x(xpar) #should update in each gauss newton iteration
residual = IDEAL.residual(b)
#do L2 cs mri recon
Nite = 10 #number of iterations
ostep = 1.0
for i in range(40):
dxpar = pf.prox_l2_Afxnb_CGD2(IDEAL.forward, IDEAL.backward, residual,
Nite)
#if i%1 == 0:
# ut.plotim3(np.absolute(xpar + ostep*dxpar)[...,0:2],bar=1, pause_close = 5)
# ut.plotim3(np.real(xpar + ostep*dxpar)[...,2],bar=1, pause_close = 5)
# ut.plotim3(np.imag(xpar + ostep*dxpar)[...,2],bar=1, pause_close = 5)
xpar = xpar + ostep * dxpar #.astype(np.float64)
#xpar[...,2] = np.real(xpar[...,2])
#xpar[:,:,2] = np.real(xpar[:,:,2])
#if i > 0:
# xpar[:,:,2] = unwrap_freq(np.real(xpar[:,:,2]))\
# +1j*(np.imag(xpar[:,:,2]))
IDEAL.set_x(xpar) #should update in each gauss newton iteration
residual = IDEAL.residual(b)
#ut.plotim3(np.absolute(xpar)[...,0:2],bar=1, pause_close = 5)
sio.savemat(pathdat + 'IDEAL_org_result.mat', {
'xpar': xpar,
'residual': residual
})
def test():
# simulated image
mat_contents = sio.loadmat('data/sim_2dmri.mat')
im = mat_contents["sim_2dmri"]
#plotim2(im)
nx, ny = im.shape
#create undersampling mask
k = int(round(nx * ny * 0.5)) #undersampling
ri = np.random.choice(nx * ny, k, replace=False) #index for undersampling
ma = np.zeros(nx * ny) #initialize an all zero vector
ma[ri] = 1 #set sampled data points to 1
mask = ma.reshape((nx, ny))
# define A and invA fuctions, i.e. A(x) = b, invA(b) = x
def Afunc(image):
ksp = np.fft.fft2(image)
ksp = np.fft.fftshift(ksp, (0, 1))
return np.multiply(ksp, mask)
def invAfunc(ksp):
ksp = np.fft.ifftshift(ksp, (0, 1))
im = np.fft.ifft2(ksp)
return im
cx = np.int(nx / 2)
cy = np.int(ny / 2)
cxr = np.arange(round(cx - 15), round(cx + 15 + 1))
cyr = np.arange(round(cy - 15), round(cy + 15 + 1))
mask[np.ix_(map(int, cxr), map(int, cyr))] = np.ones(
(cxr.shape[0], cyr.shape[0])) #center k-space is fully sampled
plotim1(np.absolute(mask))
b = Afunc(im)
scaling = ut.scaling(invAfunc(b))
b = b / scaling
plotim1(np.absolute(b))
plotim1(np.absolute(invAfunc(b)))
#do soft thresholding
Nite = 100 #number of iterations
step = 1 #step size
th = 1.5 # theshold level
xopt = solvers.IST_2(Afunc, invAfunc, b, Nite, step, th)
plotim1(np.absolute(xopt))
def test():
# simulated image
#mat_contents = sio.loadmat('/data/larson/brain_uT2/2016-09-13_3T-volunteer/ute_32echo_random-csreconallec_l2_r0p01.mat', struct_as_record=False, squeeze_me=True)
#datpath = '/data/larson/brain_uT2/2016-12-22_7T-volunteer/' #
datpath = '/data/larson/brain_uT2/2016-09-13_3T-volunteer/'
f = h5py.File(datpath + 'ute_32echo_random-csreconallec_l2_r0p01.mat')
#im3d = f['imallplus'][0:10].transpose([1,2,3,0])
#im = im3d[:,40,:,:].squeeze().view(np.complex128)
Ndiv = 8
im3d = f['imallplus'][0:Ndiv].transpose([1, 3, 2, 0])
im = im3d[35, :, :, :].squeeze().view(np.complex128)
b0_gain = 1000.0
TE = b0_gain * 1e-6 * f['TE'][0][0:Ndiv]
field = 3.0
fat_freq_arr = (1.0 / b0_gain) * 42.58 * field * np.array(
[-3.80, -3.40, -2.60, -1.94, -0.39, 0.60])
fat_rel_amp = np.array([0.087, 0.693, 0.128, 0.004, 0.039, 0.048])
print(1000 / b0_gain * TE)
#ut.plotim3(np.absolute(im[:,:,-10:-1]),[4,-1])
nx, ny, nte = im.shape
#undersampling
#mask = ut.mask3d( nx, ny, nte, [15,15,0], 0.8)
#FTm = opts.FFT2d_kmask(mask)
#FTm = opts.FFTW2d_kmask(mask)
#FTm = opts.FFT2d()
#b = FTm.forward(im)
scaling = ut.scaling(im)
im = im / scaling
ut.plotim3(np.absolute(im[:, :, :]), [4, -1], bar=1, pause_close=2)
#ut.plotim3(mask)
#ut.plotim3(np.absolute(FTm.backward(b))) #undersampled imag
#parameters
xpar = np.zeros((nx, ny, 4), np.complex128)
#xpar[:,:,0] = 10*np.ones((nx,ny))
#ut.plotim3(np.absolute(xpar),[3,-1])
# IDEAL and FFT jointly
IDEAL = idealc.IDEAL_fatmyelin_opt2(
TE, fat_freq_arr, fat_rel_amp) #fat_freq_arr , fat_rel_amp
Aideal_ftm = IDEAL #opts.joint2operators(IDEAL, FTm)#(FTm,IDEAL)#
IDEAL.set_x(xpar) #should update in each gauss newton iteration
residual = IDEAL.residual(im)
#ut.plotim3(np.absolute(FTm.backward(residual)))
# wavelet and x+d_x
addx_water = idealc.x_add_dx()
addx_fat = idealc.x_add_dx()
addx_dfwater = idealc.x_add_dx()
addx_dffat = idealc.x_add_dx()
#addx = idealc.x_add_dx()
#addx.set_x(xpar)
#addx.set_w([1, 1, 0.0001])
addx_water.set_x(xpar[...,
0]) #should update in each gauss newton iteration
addx_fat.set_x(xpar[..., 1])
addx_dfwater.set_x(xpar[..., 2])
addx_dffat.set_x(xpar[..., 3])
dwt = opts.DWT2d(wavelet='haar', level=4)
tvop = tvopc.TV2d_r()
Adwt_addx_w = opts.joint2operators(tvop, addx_water)
Adwt_addx_f = opts.joint2operators(tvop, addx_fat)
Adwt_addx_dwat = opts.joint2operators(tvop, addx_dfwater)
Adwt_addx_dfat = opts.joint2operators(tvop, addx_dffat)
#Adwt_addx = opts.joint2operators(dwt, addx)
#CGD
Nite = 100
l1_r1 = 0.01
l1_r2 = 0.01
l1_r3 = 0.01
l1_r4 = 0.01
def f(xi):
#return np.linalg.norm(Aideal_ftm.forward(xi)-residual)
return alg.obj_fidelity(Aideal_ftm, xi, residual) #\
+ l1_r1 * alg.obj_sparsity(Adwt_addx_w, xi[...,0])\
+ l1_r2 * alg.obj_sparsity(Adwt_addx_f, xi[...,1])\
+ l1_r3 * alg.obj_sparsity(Adwt_addx_dwat, xi[...,2])\
+ l1_r4 * alg.obj_sparsity(Adwt_addx_dfat, xi[...,3])
def df(xi):
#return 2*Aideal_ftm.backward(Aideal_ftm.forward(xi)-residual)
gradall = alg.grad_fidelity(Aideal_ftm, xi, residual)
gradall[..., 0] += l1_r1 * alg.grad_sparsity(Adwt_addx_w, xi[..., 0])
gradall[..., 1] += l1_r2 * alg.grad_sparsity(Adwt_addx_f, xi[..., 1])
gradall[...,
2] += l1_r3 * alg.grad_sparsity(Adwt_addx_dwat, xi[..., 2])
gradall[...,
3] += l1_r4 * alg.grad_sparsity(Adwt_addx_dfat, xi[..., 3])
return gradall
#do soft thresholding
#Nite = 200 #number of iterations
#step = 0.1 #step size
#th = 0.001 # theshold level
#do tv cs mri recon
#Nite = 20 #number of iterations
#step = 1 #step size
#tv_r = 0.01 # regularization term for tv term
#rho = 1.0
#ostep = 0.3
for i in range(40):
#wavelet L1 IST
# dxpar = solvers.IST_3( Aideal_ftm.forward, Aideal_ftm.backward,\
# Adwt_addx.backward, Adwt_addx.forward, residual, Nite, step, th )
#wavelet L1 ADMM
# dxpar = solvers.ADMM_l2Afxnb_l1Tfx( Aideal_ftm.forward, Aideal_ftm.backward, \
# Adwt_addx.backward, Adwt_addx.forward, residual, Nite, step, tv_r, rho,25 )
# TV ADMM
# dxpar = solvers.ADMM_l2Afxnb_tvx( Aideal_ftm.forward, Aideal_ftm.backward, residual\
# , Nite, step, tv_r, rho )
# L2 CGD
# dxpar = pf.prox_l2_Afxnb_CGD2( Aideal_ftm.forward, Aideal_ftm.backward, residual, rho, Nite )
# dxpar = pf.prox_l2_Afxnb_CGD2( Aideal_ftm.forward, Aideal_ftm.backward, residual, Nite )
# L1 CGD
#dxpar = pf.prox_l2_Afxnb_CGD2( IDEAL.forward, IDEAL.backward, residual, Nite )
dxpar = alg.conjugate_gradient(f, df, Aideal_ftm.backward(residual),
Nite)
ostep, j = alg.BacktrackingLineSearch(f, df, xpar, dxpar)
if i % 1 == 0:
nxpar = xpar + ostep * dxpar
nxpar[..., 1] = 10 * nxpar[..., 1]
ut.plotim3(np.absolute(nxpar)[..., 0:2],
colormap='viridis',
bar=1,
vmin=0,
vmax=1,
pause_close=2)
ut.plotim3(b0_gain * np.real(nxpar)[..., 2],
colormap='viridis',
bar=1,
pause_close=2)
ut.plotim3(b0_gain * np.imag(nxpar)[..., 2],
colormap='viridis',
bar=1,
pause_close=2)
ut.plotim3(b0_gain * np.real(nxpar)[..., 3],
colormap='viridis',
bar=1,
pause_close=2)
ut.plotim3(b0_gain * np.imag(nxpar)[..., 3],
colormap='viridis',
bar=1,
pause_close=2)
sio.savemat(datpath + 'cs_ideal_fitting/cs_IDEAL_CGD.mat', {
'xpar': xpar,
'residual': residual
})
xpar = xpar + ostep * dxpar #.astype(np.float64)
#if i > 1: #fix the frequence offset to be equal for two components
# freq_ave = 0.5 * np.real(xpar[:,:,2]) + 0.5 * np.real(xpar[:,:,3])
# xpar[:,:,2] = freq_ave +1j*(np.imag(xpar[:,:,2]))
# xpar[:,:,3] = freq_ave +1j*(np.imag(xpar[:,:,3]))
IDEAL.set_x(xpar) #should update in each gauss newton iteration
residual = IDEAL.residual(im)
ut.plotim3(np.absolute(residual), [4, -1], bar=1, pause_close=2)
sio.savemat('../save_data/myelin/ideal_result_cg.mat', \
{'xpar':xpar, 'residual':residual})
#addx.set_x(xpar) #should update in each gauss newton iteration
addx_water.set_x(
xpar[..., 0]) #should update in each gauss newton iteration
addx_fat.set_x(xpar[..., 1])
addx_dfwater.set_x(xpar[..., 2])
addx_dffat.set_x(xpar[..., 3])
ut.plotim3(np.absolute(xpar)[..., 0:2], bar=1)
ut.plotim3(np.real(xpar + ostep * dxpar)[..., 2], bar=1)
ut.plotim3(np.imag(xpar + ostep * dxpar)[..., 2], bar=1)
ut.plotim3(np.real(xpar + ostep * dxpar)[..., 3], bar=1)
ut.plotim3(np.imag(xpar + ostep * dxpar)[..., 3], bar=1)