def test_simulated_2d(self):
# # Kind of neat - seeing how phase changes with coil sensitivity...
# view(np.angle(coil_ims0))
# Do GS solution to ESM then take SOS
recon_gs = np.zeros(self.coil_ims0.shape,dtype='complex')
for ii in range(self.num_coils):
recon_gs[ii,...] = gs_recon(self.coil_ims0[ii,...],self.coil_ims1[ii,...],self.coil_ims2[ii,...],self.coil_ims3[ii,...])
# view(np.angle(recon_gs)) # realize this is actually a movie - they all just look the same...
recon_gs_sos = sos(recon_gs,axes=(0))
view(recon_gs_sos)
# Do PCA
n_components = 4
pca0 = coil_pca(self.coil_ims0,coil_dim=0,n_components=n_components)
pca1 = coil_pca(self.coil_ims1,coil_dim=0,n_components=n_components)
pca2 = coil_pca(self.coil_ims2,coil_dim=0,n_components=n_components)
pca3,expl_var = coil_pca(self.coil_ims3,coil_dim=0,n_components=n_components,give_explained_var=True)
# view(expl_var.real)
# view(np.angle(pca3))
# Do GS solution to ESM then take SOS, this time using PCA'd data
recon_pca_gs = np.zeros(pca0.shape,dtype='complex')
for ii in range(n_components):
# view(np.concatenate((pca0[ii,...],pca1[ii,...],pca2[ii,...],pca3[ii,...])))
recon_pca_gs[ii,...] = gs_recon(pca0[ii,...],pca1[ii,...],pca2[ii,...],pca3[ii,...])
# view(np.angle(recon_pca_gs))
recon_pca_gs_sos = sos(recon_pca_gs,axes=(0))
def test_multiphase(self):
# Check out what we got:
# view(self.kspace,fft=True,movie_axis=0,montage_axis=3)
# Under sample even, odd lines
kspace = self.kspace.copy()
Rx = 2
kspace[0,0::Rx,:,:] = 0
kspace[1,1::Rx,:,:] = 0
# view(kspace[0,...],fft=False)
# Make an autocalibration region by combining center lines from each
# Right now still struggling to get GRAPPA to work...
num_acl_lines = 24
acl_idx = range(int(kspace.shape[2]/2-num_acl_lines/2),int(kspace.shape[2]/2+num_acl_lines/2))
acl = self.kspace[0,:,acl_idx,:].transpose((2,0,1))
view(acl,log=True)
# We also need to get some coil sensitivity maps, let's try a crude one
# first from original data. Later we'll do espirit...
imspace = np.fft.fftshift(np.fft.fft2(self.kspace,axes=(1,2)),axes=(1,2))
comb_sos = sos(imspace[0,...],axes=-1)[...,None]
sens = (np.abs(imspace[0,...])/np.tile(comb_sos,(1,1,4))).transpose((2,0,1))
view(sens)
# Get coils in the image domain with dims in order grappa2d expects
coil_ims_pc_0 = np.fft.fftshift(np.fft.ifft2(kspace[0,...],axes=(0,1)),axes=(0,1)).transpose((2,0,1))
view(coil_ims_pc_0)
recon = grappa2d(coil_ims_pc_0,sens,acs=acl,Rx=2,Ry=1)
recon = sos(recon,axes=0)
view(recon)
def test_grappa2d(self):
from mr_utils.recon.grappa import grappa2d
from mr_utils.test_data import GRAPPA
# Get everything set up with downsampling and such
im = GRAPPA.phantom_shl()
sens = GRAPPA.csm()
# view(sens)
coils = sens * im
kspace = np.fft.fftshift(
np.fft.fft2(np.fft.ifftshift(coils), axes=(1, 2)))
Rx = 2
kspace_d = np.zeros(kspace.shape, dtype='complex')
kspace_d[:, ::Rx, :] = kspace[:, ::Rx, :]
# Get the undersampled image space coil images
coil_ims = np.fft.fftshift(
np.fft.ifft2(np.fft.ifftshift(kspace_d), axes=(1, 2)))
# Get the autocalibration signal
center_row, pad = int(sens.shape[1] / 2), 8
mask = np.zeros(kspace_d.shape, dtype=bool)
mask[:, center_row - pad:center_row + pad, :] = True
acs = kspace[mask].reshape((sens.shape[0], -1, mask.shape[-1]))
# view(acs)
# Run the recon
recon = grappa2d(coil_ims, sens, acs, Rx, Ry=1, kernel_size=(3, 3))
# Check to see if the answers match
recon = sos(recon, axes=0)
recon_mat = GRAPPA.Im_Recon()
self.assertTrue(np.allclose(recon, recon_mat))
def test_simulated_2d_kspace(self):
# Do PCA on kspace
n_components = 4
pca0 = coil_pca(self.kspace_coil_ims0,coil_dim=0,n_components=n_components)
pca1 = coil_pca(self.kspace_coil_ims1,coil_dim=0,n_components=n_components)
pca2 = coil_pca(self.kspace_coil_ims2,coil_dim=0,n_components=n_components)
pca3,expl_var = coil_pca(self.kspace_coil_ims3,coil_dim=0,n_components=n_components,give_explained_var=True)
# view(expl_var.imag)
# Put it back in image space
pca0 = np.fft.ifftshift(np.fft.ifft2(np.fft.ifftshift(pca0,axes=(1,2)),axes=(1,2)),axes=(1,2))
pca1 = np.fft.ifftshift(np.fft.ifft2(np.fft.ifftshift(pca1,axes=(1,2)),axes=(1,2)),axes=(1,2))
pca2 = np.fft.ifftshift(np.fft.ifft2(np.fft.ifftshift(pca2,axes=(1,2)),axes=(1,2)),axes=(1,2))
pca3 = np.fft.ifftshift(np.fft.ifft2(np.fft.ifftshift(pca3,axes=(1,2)),axes=(1,2)),axes=(1,2))
# Do GS solution to ESM then take SOS, this time using PCA'd data
recon_pca_gs = np.zeros(pca0.shape,dtype='complex')
for ii in range(n_components):
# view(np.concatenate((pca0[ii,...],pca1[ii,...],pca2[ii,...],pca3[ii,...])))
recon_pca_gs[ii,...] = gs_recon(pca0[ii,...],pca1[ii,...],pca2[ii,...],pca3[ii,...])
# view(np.angle(recon_pca_gs))
recon_pca_gs_sos = sos(recon_pca_gs,axes=(0))
def M0fun(x, y, T1, T2, theta, TR, alpha):
'''Residual for M0 estimation.'''
y00 = ssfp(T1, T2, TR, alpha, field_map=theta, phase_cyc=0, M0=x[3])
y01 = ssfp(T1, T2, TR, alpha, field_map=theta, phase_cyc=np.pi, M0=x[3])
y0 = sos((y00, y01))
return y0 - y
T2 = np.random.random(1)[0] * (bnds[1][1] - bnds[0][1]) + bnds[0][1]
df = np.random.random(1)[0] * (bnds[1][2] - bnds[0][2]) + bnds[0][2]
M0 = np.random.random(1)[0] * (bnds[1][3] - bnds[0][3]) + bnds[0][3]
# Simulate acquisiton of two phase cycles
y_train0 = ssfp(T1, T2, TR, alpha, field_map=df, phase_cyc=0, M0=M0)
y_train1 = ssfp(T1,
T2,
TR,
alpha,
field_map=df,
phase_cyc=np.pi,
M0=M0)
y_train = np.array(
(y_train0.real, y_train1.real, y_train0.imag, y_train1.imag))
M0_train = sos((y_train0, y_train1))
# Initialize
x0 = np.zeros(4) # x0 = (T1, T2, theta, M0)
loss = ['linear', 'soft_l1', 'huber', 'cauchy', 'arctan']
weights = [1, 2]
x0[0] = (bnds[1][0] + bnds[0][0]) / 2
x0[1] = (bnds[1][1] + bnds[0][1]) / 2
x0[2] = (bnds[1][2] + bnds[0][2]) / 2
x0[3] = M0_train # Guess M0 is SOS
# Do a 2 step update for a fixed number of steps:
for ii in range(10):
# Solve for M0, only to modify x[3]
x = least_squares(M0fun,
x0,
axes=(1, 2)),
axes=(1, 2))
kspace_coil_ims3 = np.fft.fftshift(np.fft.fft2(np.fft.fftshift(coil_ims3,
axes=(1,
2)),
axes=(1, 2)),
axes=(1, 2))
view(np.angle(coil_ims0))
# Do GS solution to ESM then take SOS
recon_gs = np.zeros(coil_ims0.shape, dtype='complex')
for ii in range(num_coils):
recon_gs[ii, ...] = gs_recon(coil_ims0[ii, ...], coil_ims1[ii, ...],
coil_ims2[ii, ...], coil_ims3[ii, ...])
recon_gs_sos = sos(recon_gs, axes=(0))
view(recon_gs_sos)
# Do PCA
n_components = 4
pca0 = coil_pca(coil_ims0, coil_dim=0, n_components=n_components)
pca1 = coil_pca(coil_ims1, coil_dim=0, n_components=n_components)
pca2 = coil_pca(coil_ims2, coil_dim=0, n_components=n_components)
pca3, expl_var = coil_pca(coil_ims3,
coil_dim=0,
n_components=n_components,
give_explained_var=True)
view(expl_var.real)
view(np.angle(pca3))
# Do GS solution to ESM then take SOS, this time using PCA'd data
data = np.load(data_fft_filename)
else:
# Else we'll have to do it ourselves
data = np.load(dirname(__file__) + '/data.npy')
# Put 'er in image space
print('Starting fft...')
data = np.fft.fftshift(np.fft.fft2(data, axes=(0, 1)), axes=(0, 1))
np.save(data_fft_filename, data)
print('Finished saving fft!')
# Tell me about it
print('Data shape is:', data.shape)
sx, sy, nc, nt, ns = data.shape[:]
# Take a look at it in all its glory -- notice significant motion
view(sos(data[..., 1::16, :], axes=2).squeeze(),
montage_axis=-1,
movie_axis=-2)
# For each coil for all slices for each possible GS recon in N time points
N = 16 # since we have 16 unique phase-cycles...
print('Starting GS recons...')
sh = np.array(data.shape)
num_gs_recons = int(N / 4) # need 4 coil images for GS recon
sh[3] = num_gs_recons
recons = np.zeros(sh, dtype=data.dtype)
for ii in trange(num_gs_recons, desc='GS recons', leave=False):
for cc in trange(nc, desc='Coils', leave=False):
ims = data[..., cc, ii:N:4, :]
recons[..., cc, ii, :] = gs_recon3d(
*[x.squeeze() for x in np.split(ims, 4, axis=-2)])
path = 'mr_utils/test_data/examples/coils/'
imspace, kspace = load_test_data(path, ['imspace', 'kspace'])
print(imspace.shape)
nx, ny, nc, npcs = imspace.shape[:]
trim = int(nx / 4)
pcs = np.linspace(0, 2 * np.pi, npcs, endpoint=False)
# Get mask
ngs = int(npcs / 4)
tmp = np.zeros((nx, ny, nc, ngs), dtype='complex')
for coil in range(nc):
for ii in range(ngs):
tmp[..., coil, ii] = gs_recon(imspace[..., coil, ii::4],
pc_axis=-1)
im_true = np.mean(tmp, axis=-1)
im_true = sos(im_true, axes=-1)
thresh = threshold_li(im_true)
mask = im_true > thresh
# view(im_true)
# view(mask)
# Define coil combination functions
ccs, cc_list = get_coil_combine_funs(np.min([nx, ny]), v='')
# Do coil combine then ESM
res = np.zeros((len(ccs), nx, ny), dtype='complex')
err_cc_then_gs = np.zeros(len(ccs))
for fun, cc in enumerate(ccs):
tmp = np.zeros((nx, ny, ngs), dtype='complex')
idx = list(range(npcs))[::4]
def comparison_numerical_phantom(SNR=None):
'''Compare coil by coil, Walsh method, and Inati iterative method.'''
true_im = get_true_im_numerical_phantom()
csms = get_coil_sensitivity_maps()
params = get_numerical_phantom_params(SNR=SNR)
pc_vals = params['pc_vals']
dim = params['dim']
noise_std = params['noise_std']
coil_nums = params['coil_nums']
# We want to solve gs_recon for each coil we have in the pc set
err = np.zeros((5, len(csms)))
rip = err.copy()
for ii, csm in enumerate(csms):
# I have coil sensitivities, now I need images to apply them to.
# coil_ims: (pc,coil,x,y)
coil_ims = np.zeros((len(pc_vals), csm.shape[0], dim, dim),
dtype='complex')
for jj, pc in enumerate(pc_vals):
im = bssfp_2d_cylinder(dims=(dim, dim), phase_cyc=pc)
im += 1j * im
coil_ims[jj, ...] = im * csm
coil_ims[jj, ...] += np.random.normal(0, noise_std, coil_ims[
jj, ...].shape) / 2 + 1j * np.random.normal(
0, noise_std, coil_ims[jj, ...].shape) / 2
# Solve the gs_recon coil by coil
coil_ims_gs = np.zeros((csm.shape[0], dim, dim), dtype='complex')
for kk in range(csm.shape[0]):
coil_ims_gs[kk, ...] = gs_recon(*[
x.squeeze()
for x in np.split(coil_ims[:, kk, ...], len(pc_vals))
])
coil_ims_gs[np.isnan(coil_ims_gs)] = 0
# Easy way out: combine all the coils using sos
im_est_sos = sos(coil_ims_gs)
# view(im_est_sos)
# Take coil by coil solution and do Walsh on it to collapse coil dim
# walsh
csm_walsh, _ = calculate_csm_walsh(coil_ims_gs)
im_est_recon_then_walsh = np.sum(csm_walsh * np.conj(coil_ims_gs),
axis=0)
im_est_recon_then_walsh[np.isnan(im_est_recon_then_walsh)] = 0
# view(im_est_recon_then_walsh)
# inati
csm_inati, im_est_recon_then_inati = calculate_csm_inati_iter(
coil_ims_gs)
# Collapse the coil dimension of each phase-cycle using Walsh,Inati
pc_est_walsh = np.zeros((len(pc_vals), dim, dim), dtype='complex')
pc_est_inati = np.zeros((len(pc_vals), dim, dim), dtype='complex')
for jj in range(len(pc_vals)):
## Walsh
csm_walsh, _ = calculate_csm_walsh(coil_ims[jj, ...])
pc_est_walsh[jj,
...] = np.sum(csm_walsh * np.conj(coil_ims[jj, ...]),
axis=0)
# view(csm_walsh)
# view(pc_est_walsh)
## Inati
csm_inati, pc_est_inati[jj, ...] = calculate_csm_inati_iter(
coil_ims[jj, ...], smoothing=1)
# pc_est_inati[jj,...] = np.sum(csm_inati*np.conj(coil_ims[jj,...]),axis=0)
# view(csm_inati)
# Now solve the gs_recon using collapsed coils
im_est_walsh = gs_recon(
*[x.squeeze() for x in np.split(pc_est_walsh, len(pc_vals))])
im_est_inati = gs_recon(
*[x.squeeze() for x in np.split(pc_est_inati, len(pc_vals))])
# view(im_est_walsh)
# view(im_est_recon_then_walsh)
# Compute error metrics
err[0, ii] = compare_nrmse(im_est_sos, true_im)
err[1, ii] = compare_nrmse(im_est_recon_then_walsh, true_im)
err[2, ii] = compare_nrmse(im_est_recon_then_inati, true_im)
err[3, ii] = compare_nrmse(im_est_walsh, true_im)
err[4, ii] = compare_nrmse(im_est_inati, true_im)
im_est_sos[np.isnan(im_est_sos)] = 0
im_est_recon_then_walsh[np.isnan(im_est_recon_then_walsh)] = 0
im_est_recon_then_inati[np.isnan(im_est_recon_then_inati)] = 0
im_est_walsh[np.isnan(im_est_walsh)] = 0
im_est_inati[np.isnan(im_est_inati)] = 0
rip[0, ii] = ripple_normal(im_est_sos)
rip[1, ii] = ripple_normal(im_est_recon_then_walsh)
rip[2, ii] = ripple_normal(im_est_recon_then_inati)
rip[3, ii] = ripple_normal(im_est_walsh)
rip[4, ii] = ripple_normal(im_est_inati)
# view(im_est_inati)
# # SOS of the gs solution on each individual coil gives us low periodic
# # ripple accross the phantom, similar to Walsh method:
# plt.plot(np.abs(true_im[int(dim/2),:]),'--',label='True Im')
# plt.plot(np.abs(im_est_sos[int(dim/2),:]),'-.',label='SOS')
# plt.plot(np.abs(im_est_recon_then_walsh[int(dim/2),:]),label='Recon then Walsh')
# plt.plot(np.abs(im_est_walsh[int(dim/2),:]),label='Walsh then Recon')
# # plt.plot(np.abs(im_est_inati[int(dim/2),:]),label='Inati')
# plt.legend()
# plt.show()
# # Let's show some stuff
# plt.plot(coil_nums,err[0,:],'*-',label='SOS')
# plt.plot(coil_nums,err[1,:],label='Recon then Walsh')
# plt.plot(coil_nums,err[2,:],label='Walsh then Recon')
# # plt.plot(coil_nums,err[3,:],label='Inati')
# plt.legend()
# plt.show()
print('SOS RMSE:', np.mean(err[0, :]))
print('recon then walsh RMSE:', np.mean(err[1, :]))
print('recon then inati RMSE:', np.mean(err[2, :]))
print('walsh then recon RMSE:', np.mean(err[3, :]))
print('inati then recon RMSE:', np.mean(err[4, :]))
print('SOS ripple:', np.mean(err[0, :]))
print('recon then walsh ripple:', np.mean(rip[1, :]))
print('recon then inati ripple:', np.mean(rip[2, :]))
print('walsh then recon ripple:', np.mean(rip[3, :]))
print('inati then recon ripple:', np.mean(rip[4, :]))
view(im_est_recon_then_walsh[int(dim / 2), :])
view(im_est_recon_then_inati[int(dim / 2), :])
view(im_est_walsh[int(dim / 2), :])
view(im_est_inati[int(dim / 2), :])
# view(im_est_inati)
# view(np.stack((im_est_recon_then_walsh,im_est_recon_then_inati,im_est_walsh,im_est_inati)))
return (err)
def comparison_knee():
'''Coil by coil, Walsh method, and Inati iterative method for knee data.'''
# Load the knee data
dir = '/home/nicholas/Documents/rawdata/SSFP_SPECTRA_dphiOffset_08022018/'
files = [
'meas_MID362_TRUFI_STW_TE3_FID29379',
'meas_MID363_TRUFI_STW_TE3_dphi_45_FID29380',
'meas_MID364_TRUFI_STW_TE3_dphi_90_FID29381',
'meas_MID365_TRUFI_STW_TE3_dphi_135_FID29382',
'meas_MID366_TRUFI_STW_TE3_dphi_180_FID29383',
'meas_MID367_TRUFI_STW_TE3_dphi_225_FID29384',
'meas_MID368_TRUFI_STW_TE3_dphi_270_FID29385',
'meas_MID369_TRUFI_STW_TE3_dphi_315_FID29386'
]
pc_vals = [0, 45, 90, 135, 180, 225, 270, 315]
dims = (512, 256)
num_coils = 4
num_avgs = 16
# # Load in raw once, then save as npy with collapsed avg dimension
# pcs = np.zeros((len(files),dims[0],dims[1],num_coils),dtype='complex')
# for ii,file in enumerate(files):
# pcs[ii,...] = np.mean(load_raw('%s/%s.dat' % (dir,file),use='s2i'),axis=-1)
# np.save('%s/te3.npy' % dir,pcs)
# pcs looks like (pc,x,y,coil)
pcs = np.load('%s/te3.npy' % dir)
pcs = np.fft.fftshift(np.fft.fft2(pcs, axes=(1, 2)), axes=(1, 2))
# print(pcs.shape)
# view(pcs,fft=True,montage_axis=0,movie_axis=3)
# Do recon then coil combine
coils0 = np.zeros((pcs.shape[-1], pcs.shape[1], pcs.shape[2]),
dtype='complex')
coils1 = coils0.copy()
for ii in range(pcs.shape[-1]):
# We have two sets: 0,90,180,27 and 45,135,225,315
idx0 = [0, 2, 4, 6]
idx1 = [1, 3, 5, 7]
coils0[ii, ...] = gs_recon(*[x.squeeze() for x in pcs[idx0, :, :, ii]])
coils1[ii, ...] = gs_recon(*[x.squeeze() for x in pcs[idx1, :, :, ii]])
# Then do the coil combine
csm_walsh, _ = calculate_csm_walsh(coils0)
im_est_recon_then_walsh0 = np.sum(csm_walsh * np.conj(coils0), axis=0)
# view(im_est_recon_then_walsh0)
csm_walsh, _ = calculate_csm_walsh(coils1)
im_est_recon_then_walsh1 = np.sum(csm_walsh * np.conj(coils1), axis=0)
# view(im_est_recon_then_walsh1)
rip0 = ripple(im_est_recon_then_walsh0)
rip1 = ripple(im_est_recon_then_walsh1)
print('recon then walsh: ', np.mean([rip0, rip1]))
# Now try inati
csm_inati, im_est_recon_then_inati0 = calculate_csm_inati_iter(coils0,
smoothing=5)
csm_inati, im_est_recon_then_inati1 = calculate_csm_inati_iter(coils1,
smoothing=5)
rip0 = ripple(im_est_recon_then_inati0)
rip1 = ripple(im_est_recon_then_inati1)
print('recon then inati: ', np.mean([rip0, rip1]))
# Now try sos
im_est_recon_then_sos0 = sos(coils0, axes=0)
im_est_recon_then_sos1 = sos(coils1, axes=0)
rip0 = ripple(im_est_recon_then_sos0)
rip1 = ripple(im_est_recon_then_sos1)
print('recon then sos: ', np.mean([rip0, rip1]))
# view(im_est_recon_then_sos)
## Now the other way, combine then recon
pcs0 = np.zeros((2, pcs.shape[0], pcs.shape[1], pcs.shape[2]),
dtype='complex')
pcs1 = pcs0.copy()
for ii in range(pcs.shape[0]):
# Walsh it up
csm_walsh, _ = calculate_csm_walsh(pcs[ii, ...].transpose((2, 0, 1)))
pcs0[0, ii, ...] = np.sum(csm_walsh * np.conj(pcs[ii, ...].transpose(
(2, 0, 1))),
axis=0)
# view(pcs0[ii,...])
# Inati it up
csm_inati, pcs0[1, ii,
...] = calculate_csm_inati_iter(pcs[ii, ...].transpose(
(2, 0, 1)),
smoothing=5)
## Now perform gs_recon on each coil combined set
# Walsh
im_est_walsh_then_recon0 = gs_recon(
*[x.squeeze() for x in pcs0[0, idx0, ...]])
im_est_walsh_then_recon1 = gs_recon(
*[x.squeeze() for x in pcs0[0, idx1, ...]])
# Inati
im_est_inati_then_recon0 = gs_recon(
*[x.squeeze() for x in pcs0[1, idx0, ...]])
im_est_inati_then_recon1 = gs_recon(
*[x.squeeze() for x in pcs0[1, idx1, ...]])
# view(im_est_walsh_then_recon0)
# view(im_est_walsh_then_recon1)
view(im_est_inati_then_recon0)
view(im_est_inati_then_recon1)
rip0 = ripple(im_est_walsh_then_recon0)
rip1 = ripple(im_est_walsh_then_recon1)
print('walsh then recon: ', np.mean([rip0, rip1]))
rip0 = ripple(im_est_inati_then_recon0)
rip1 = ripple(im_est_inati_then_recon1)
print('inati then recon: ', np.mean([rip0, rip1]))
def test_recon(self):
from mr_utils.test_data import GRAPPA
# Get the shepp logan phantom
im = GRAPPA.phantom_shl()
dim = im.shape[0]
# Get simple coil sensitivities
N = 6
# csm = simple_csm(N,(dim,dim))
csm = GRAPPA.csm()
# self.assertTrue(np.allclose(csm,csm_mat))
# Apply csm to image to get coil images
coils = csm * im
coils_mat = GRAPPA.phantom_ch()
self.assertTrue(np.allclose(coils, coils_mat))
# Put each channel into kspace
kspace = np.fft.fftshift(
np.fft.fft2(np.fft.ifftshift(coils), axes=(1, 2)))
kspace_mat = GRAPPA.phantom_ch_k()
self.assertTrue(np.allclose(kspace, kspace_mat))
# Undersample by Rx
Rx = 2
kspace_d = np.zeros(kspace.shape, dtype='complex')
kspace_d[:, ::Rx, :] = kspace[:, ::Rx, :]
kspace_d_mat = GRAPPA.phantom_ch_k_u()
self.assertTrue(np.allclose(kspace_d, kspace_d_mat))
# Choose center fully samples lines as autocalibration signal (ACS)
center_row, pad = int(dim / 2), 8
mask = np.zeros(kspace_d.shape, dtype=bool)
mask[:, center_row - pad:center_row + pad, :] = True
autocal = kspace[mask].reshape((N, -1, mask.shape[-1]))
autocal_mat = GRAPPA.phantom_ch_k_acl()
self.assertTrue(
np.allclose(
np.pad(autocal, ((0, 0), (24, 24), (0, 0)), mode='constant'),
autocal_mat))
# Separate the autocalibration region into patches to get source matrix
patch_size = (3, 3)
S0 = np.zeros((N, (autocal.shape[1] - 2) *
(autocal.shape[2] - 2), patch_size[0] * patch_size[1]),
dtype='complex')
for ii in range(N):
S0[ii, :, :] = view_as_windows(autocal[ii, :, :],
patch_size).reshape(
(S0.shape[1], S0.shape[2]))
S0_mat = GRAPPA.S_ch_temp()
self.assertTrue(np.allclose(np.conj(S0), S0_mat))
# Remove the unknown values. The remaiming values form source matrix,
# S, for each coil
S_temp = S0[:, :, [0, 1, 2, 6, 7, 8]]
S_temp_mat = GRAPPA.S_ch()
self.assertTrue(np.allclose(np.conj(S_temp), S_temp_mat))
S = np.hstack(S_temp[:])
S_mat = GRAPPA.S()
self.assertTrue(np.allclose(np.conj(S), S_mat))
# The middle pts form target vector, T, for each coil
T = S0[:, :, 4].T
T_mat = GRAPPA.T()
self.assertTrue(np.allclose(np.conj(T), T_mat))
# Invert S to find weights, W
W = np.linalg.pinv(S).dot(T)
W_mat = GRAPPA.W()
self.assertTrue(np.allclose(np.conj(W), W_mat))
# Now onto the forward problem to fill in the missing lines...
# Make patches out of all acquired data (skip the missing lines)
S0 = np.zeros((N, int((kspace_d.shape[1] - 2) / Rx) *
(kspace_d.shape[2] - 2), patch_size[0] * patch_size[1]),
dtype='complex')
for ii in range(N):
S0[ii, :, :] = view_as_windows(kspace_d[ii, :, :],
patch_size,
step=(Rx, 1)).reshape(
(S0.shape[1], S0.shape[2]))
S0_mat = GRAPPA.S_ch_new_temp()
self.assertTrue(np.allclose(np.conj(S0), S0_mat))
# Remove the unknown values. The remaiming values form source matrix,
# S, for each coil
S_new_temp = S0[:, :, [0, 1, 2, 6, 7, 8]]
S_new_temp_mat = GRAPPA.S_ch_new()
self.assertTrue(np.allclose(np.conj(S_new_temp), S_new_temp_mat))
S_new = np.hstack(S_new_temp[:])
S_new_mat = GRAPPA.S_new()
self.assertTrue(np.allclose(np.conj(S_new), S_new_mat))
T_new = S_new.dot(W)
T_new_mat = GRAPPA.T_new()
self.assertTrue(np.allclose(np.conj(T_new), T_new_mat))
# Back fill in the missing lines to recover the image
lines = np.reshape(T_new.T, (N, -1, dim - 2))
lines_mat = GRAPPA.T_ch_new_M()
self.assertTrue(np.allclose(lines, lines_mat))
kspace_d[:, 1:-1:Rx, 1:-1] = lines
recon = sos(np.fft.fftshift(
np.fft.ifft2(np.fft.ifftshift(kspace_d), axes=(1, 2))),
axes=0)
recon_mat = GRAPPA.Im_Recon()
self.assertTrue(np.allclose(recon, recon_mat))