axes=(0, 1)),
axes=(0, 1))
def sos(x0):
return np.sqrt(np.sum(np.abs(x0)**2, axis=-1))
if __name__ == '__main__':
# Radially sampled Shepp-Logan
N, spokes, nc = 288, 72, 8
kx, ky = radial(N, spokes)
kx = np.reshape(kx, (N, spokes), 'F').flatten().astype(np.float32)
ky = np.reshape(ky, (N, spokes), 'F').flatten().astype(np.float32)
k = kspace_shepp_logan(kx, ky, ncoil=nc).astype(np.complex64)
k = whiten(k) # whitening seems to help conditioning of Gx, Gy
# # Instead of whitening, maybe you prefer to reduce coils:
# nc = 4
# U, S, Vh = np.linalg.svd(k, full_matrices=False)
# k = U[:, :nc] @ np.diag(S[:nc]) @ Vh[:nc, :nc]
# Take a look at the sampling pattern:
plt.scatter(kx, ky, .1)
plt.title('Radial Sampling Pattern')
plt.show()
# Get the GRAPPA operators!
t0 = time()
Gx, Gy = radialgrappaop(kx, ky, k, nspokes=spokes)
from pygrappa import ttgrappa
from utils import gridder
if __name__ == '__main__':
# Simulate a radial trajectory
sx, spokes, nc = 128, 128, 8
kx, ky = radial(sx, spokes)
# We reorder the samples like this for easier undersampling later
kx = np.reshape(kx, (sx, spokes)).flatten('F')
ky = np.reshape(ky, (sx, spokes)).flatten('F')
# Sample Shepp-Logan at points (kx, ky) with nc coils:
kspace = kspace_shepp_logan(kx, ky, ncoil=nc)
k = kspace.copy()
# Get some calibration data -- ideally we would want to simulate
# something other than the image we're going to reconstruct, but
# since this is just proof of concept, we'll go ahead
cx = kx.copy()
cy = ky.copy()
calib = k.copy()
# calib = np.tile(calib[:, None, :], (1, 2, 1))
calib = calib[:, None, :] # middle axis is the through-time dim
# Undersample: R=2
k[::2] = 0
# Reconstruct with Non-Cartesian GRAPPA
import matplotlib.pyplot as plt
from phantominator import radial, kspace_shepp_logan
from skimage.measure import compare_nrmse, compare_ssim
from skimage.morphology import convex_hull_image
from skimage.filters import threshold_li
from pygrappa import radialgrappaop, grog
if __name__ == '__main__':
# 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
# # Instead of whitening, maybe you prefer to reduce coils:
# nc = 4
# U, S, Vh = np.linalg.svd(k, full_matrices=False)
# k = U[:, :nc] @ np.diag(S[:nc]) @ Vh[:nc, :nc]
# 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))
# Take a look at the sampling pattern:
plt.scatter(kx, ky, .1)
plt.title('Radial Sampling Pattern')
