ifft = lambda x0: np.fft.fftshift(np.fft.ifft2(
np.fft.ifftshift(x0, axes=(0, 1)), axes=(0, 1)),
axes=(0, 1))
sos = lambda x0: np.sqrt(np.sum(np.abs(x0)**2, axis=-1))
# Radially sampled Shepp-Logan
N, spokes, nc = 288, 72, 8
kx, ky = radial(N, spokes)
kx = np.reshape(kx, (N, spokes), 'F').flatten()
ky = np.reshape(ky, (N, spokes), 'F').flatten()
k = kspace_shepp_logan(kx, ky, ncoil=nc)
k = whiten(k) # whitening seems to help conditioning of Gx, Gy
# Get the GRAPPA operators
t0 = time()
Gx, Gy = radialgrappaop(kx, ky, k, nspokes=spokes)
print('Gx, Gy computed in %g seconds' % (time() - t0))
# Do forward GROG (with oversampling)
t0 = time()
res_cart = grog(kx, ky, k, 2 * N, 2 * N, Gx, Gy)
print('Gridded in %g seconds' % (time() - t0))
# Now back to radial (inverse GROG)
res_radial = grog(kx,
ky,
np.reshape(res_cart, (-1, nc), order='F'),
2 * N,
2 * N,
Gx,
Gy,
# Radially sampled Shepp-Logan
N, spokes, nc = 288, 72, 8
kx, ky = radial(N, spokes)
kx = np.reshape(kx, (N, spokes), 'F').flatten()
ky = np.reshape(ky, (N, spokes), 'F').flatten()
k = kspace_shepp_logan(kx, ky, ncoil=nc)
k = whiten(k) # whitening seems to help conditioning of Gx, Gy
# Put in correct shape for radialgrappaop
k = np.reshape(k, (N, spokes, nc))
kx = np.reshape(kx, (N, spokes))
ky = np.reshape(ky, (N, spokes))
# Get the GRAPPA operators!
t0 = time()
Gx, Gy = radialgrappaop(kx, ky, k)
print('Gx, Gy computed in %g seconds' % (time() - t0))
# Put in correct order for GROG
kx = kx.flatten()
ky = ky.flatten()
k = np.reshape(k, (-1, nc))
# Do GROG without primefac
t0 = time()
res = grog(kx, ky, k, N, N, Gx, Gy, use_primefac=False)
print('Gridded in %g seconds' % (time() - t0))
# Do GROG with primefac
t0 = time()
res_prime = grog(kx, ky, k, N, N, Gx, Gy, use_primefac=True)
from phantominator import kspace_shepp_logan
from phantominator.traj import radial
if __name__ == '__main__':
# Example usage (requires pygrappa package to be installed!)
sx, spokes, ncoil = 288, 72, 8
kx, ky = radial(sx, spokes)
kx = np.reshape(kx, (sx, spokes), 'F').flatten()
ky = np.reshape(ky, (sx, spokes), 'F').flatten()
k = kspace_shepp_logan(kx, ky, ncoil=ncoil)
k = whiten(k)
# Grid via GROG and check out the results:
Gx, Gy = radialgrappaop(
np.reshape(kx, (sx, spokes)),
np.reshape(ky, (sx, spokes)),
np.reshape(k, (sx, spokes, ncoil)))
coil_ims = np.abs(np.fft.fftshift(np.fft.ifft2(np.fft.ifftshift(
grog(kx, ky, k, sx, sx, Gx, Gy),
axes=(0, 1)), axes=(0, 1)), axes=(0, 1)))
# Some code to look at the animation
fig = plt.figure()
ax = plt.imshow(coil_ims[..., 0], cmap='gray')
def init():
'''Initialize ax data.'''
ax.set_array(coil_ims[..., 0])
return(ax,)
def animate(frame):