def _pre_update(self):
t = self.t_idx.next()
t_start = t * self.batch_size
t_end = (t + 1) * self.batch_size
sp.copyto(self.y_t, self.y[t_start:t_end])
sp.copyto(self.L_old, self.L)
def _pre_update(self):
t = self.t_idx.next()
t_start = t * self.batch_size
t_end = (t + 1) * self.batch_size
sp.copyto(self.input_t, self.input[t_start:t_end])
sp.copyto(self.output_t, self.output[t_start:t_end])
def _output(self):
xp = self.device.xp
# Coil by coil to save memory
with self.device:
mps_rss = 0
mps = np.empty([self.num_coils] + self.img_shape, dtype=self.dtype)
for c in range(self.num_coils):
mps_c = sp.ifft(sp.resize(self.mps_ker[c], self.img_shape))
mps_rss += xp.abs(mps_c)**2
sp.copyto(mps[c], mps_c)
mps_rss = sp.to_device(mps_rss**0.5, sp.cpu_device)
mps /= mps_rss
return mps
def _output(self):
xp = self.device.xp
# Normalize by root-sum-of-squares.
with self.device:
rss = 0
mps = np.empty([self.num_coils] + self.img_shape, dtype=self.dtype)
for c in range(self.num_coils):
mps_c = sp.ifft(sp.resize(self.mps_ker[c], self.img_shape))
rss += xp.abs(mps_c)**2
sp.copyto(mps[c], mps_c)
rss = sp.to_device(rss)
if self.comm is not None:
self.comm.allreduce(rss)
rss = rss**0.5
mps /= rss
return mps
def espirit_maps(ksp,
calib_width=24,
thresh=0.001,
kernel_width=6,
crop=0.8,
max_power_iter=30,
device=sp.cpu_device,
output_eigenvalue=False):
"""Generate ESPIRiT maps from k-space.
Currently only supports outputting one set of maps.
Args:
ksp (array): k-space array of shape [num_coils, n_ndim, ..., n_1]
calib (tuple of ints): length-2 image shape.
thresh (float): threshold for the calibration matrix.
kernel_width (int): kernel width for the calibration matrix.
max_power_iter (int): maximum number of power iterations.
device (Device): computing device.
crop (int): cropping threshold.
Returns:
array: ESPIRiT maps of the same shape as ksp.
References:
Martin Uecker, Peng Lai, Mark J. Murphy, Patrick Virtue, Michael Elad,
John M. Pauly, Shreyas S. Vasanawala, and Michael Lustig
ESPIRIT - An Eigenvalue Approach to Autocalibrating Parallel MRI:
Where SENSE meets GRAPPA.
Magnetic Resonance in Medicine, 71:990-1001 (2014)
"""
img_ndim = ksp.ndim - 1
num_coils = len(ksp)
with sp.get_device(ksp):
# Get calibration region
calib_shape = [num_coils] + [calib_width] * img_ndim
calib = sp.resize(ksp, calib_shape)
calib = sp.to_device(calib, device)
device = sp.Device(device)
xp = device.xp
with device:
# Get calibration matrix
kernel_shape = [num_coils] + [kernel_width] * img_ndim
kernel_strides = [1] * (img_ndim + 1)
mat = sp.array_to_blocks(calib, kernel_shape, kernel_strides)
mat = mat.reshape([-1, sp.prod(kernel_shape)])
# Perform SVD on calibration matrix
_, S, VH = xp.linalg.svd(mat, full_matrices=False)
VH = VH[S > thresh * S.max(), :]
# Get kernels
num_kernels = len(VH)
kernels = VH.reshape([num_kernels] + kernel_shape)
img_shape = ksp.shape[1:]
# Get covariance matrix in image domain
AHA = xp.zeros(img_shape[::-1] + (num_coils, num_coils),
dtype=ksp.dtype)
for kernel in kernels:
img_kernel = sp.ifft(sp.resize(kernel, ksp.shape),
axes=range(-img_ndim, 0))
aH = xp.expand_dims(img_kernel.T, axis=-1)
a = xp.conj(aH.swapaxes(-1, -2))
AHA += aH @ a
AHA *= (sp.prod(img_shape) / kernel_width**img_ndim)
# Power Iteration to compute top eigenvector
mps = xp.ones(ksp.shape[::-1] + (1, ), dtype=ksp.dtype)
for _ in range(max_power_iter):
sp.copyto(mps, AHA @ mps)
eig_value = xp.sum(xp.abs(mps)**2, axis=-2, keepdims=True)**0.5
mps /= eig_value
# Normalize phase with respect to first channel
mps = mps.T[0]
mps *= xp.conj(mps[0] / xp.abs(mps[0]))
# Crop maps by thresholding eigenvalue
eig_value = eig_value.T[0]
mps *= eig_value > crop
if output_eigenvalue:
return mps, eig_value
else:
return mps
