def __init__(self,
ksp,
calib_width=24,
thresh=0.01,
kernel_width=6,
crop=0.8,
max_iter=100,
device=sp.cpu_device,
output_eigenvalue=False,
show_pbar=True):
self.device = sp.Device(device)
self.output_eigenvalue = output_eigenvalue
self.crop = crop
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)
xp = self.device.xp
with self.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)
self.mps = xp.ones(ksp.shape[::-1] + (1, ), dtype=ksp.dtype)
alg = sp.alg.PowerMethod(
lambda x: AHA @ x,
self.mps,
norm_func=lambda x: xp.sum(
xp.abs(x)**2, axis=-2, keepdims=True)**0.5,
max_iter=max_iter)
super().__init__(alg, show_pbar=show_pbar)
def image_undersampled_recon(image,
accel_factor=1.5,
eps=1e-6,
recon_type='l1-wavelet',
trajectory=poisson_trajectory,
*args):
"""
This function undersamples the input image in k-space and performs a reconstruction with the undersampled data.
Inputs:
:param image: the image to be undersampled and reconstruced (numpy array complex128)
:param accel_factor: the acceleration factor (float)
:param eps: precision parameter for constrained reconstruction (float)
:param recon_type: specify the reconstruction type. Accepts: 'l1-wavelet' for L1-wavelet constrained reconstruction
(default), 'zero-fill' for a zero-filled image reconstruction
:param trajectory: the trajectory function to use for generating the kspace mask (function)
:param args: extraneous arguments to pass to the trajectory function call (extraneous arguments)
:return: reconstructed_image: (numpy array complex128)
"""
# Convert image to k-space
kspace = sigpy.fft(image, center=True, norm='ortho')
# Generate trajectory mask from kspace size and accel_factor, as well as extraneous arguments.
trajectory_mask = trajectory(kspace.shape, accel_factor, *args)
# Generate undersampled k-space data
undersampled_kspace = kspace * trajectory_mask
if recon_type.lower() == 'zero-fill'.lower():
# Reconstruct zero-filled image
zero_filled_img = sigpy.ifft(undersampled_kspace,
center=True,
norm='ortho')
return zero_filled_img
if recon_type.lower() == 'l1-wavelet'.lower():
# Convert poisson mask into boolean array for indexing
mask = np.bool8(trajectory_mask)
# Build coordinates matrix using poisson mask
x = np.linspace(-image.shape[0] / 2, image.shape[0] / 2 - 1,
image.shape[0])
y = np.linspace(-image.shape[1] / 2, image.shape[1] / 2 - 1,
image.shape[1])
X, Y = np.meshgrid(x, y)
x_idx = Y[
mask] # Dimensions needs to be swapped because of row-major indexing
y_idx = X[mask]
coords = np.concatenate([x_idx[:, np.newaxis], y_idx[:, np.newaxis]],
axis=1)
mask = np.bool8(trajectory_mask)
L1ConstrainedWaveletApp = sigpy.mri.app.L1WaveletConstrainedRecon(
y=kspace[mask],
mps=np.ones((1, image.shape[0], image.shape[1])),
coord=coords,
eps=eps)
L1out = L1ConstrainedWaveletApp.run()
return L1out
def b2rf(b, cancel_alpha_phs=False):
a = b2a(b)
if cancel_alpha_phs:
b_a_phase = sp.fft(b, center=False, norm=None) * \
np.exp(-1j * np.angle(sp.fft(a[np.size(a)::-1],
center=False, norm=None)))
b = sp.ifft(b_a_phase, center=False, norm=None)
rf = ab2rf(a, b)
return rf
def fmp(h):
l = np.size(h)
lp = 128 * np.exp(np.ceil(np.log(l) / np.log(2)) * np.log(2))
padwidths = np.array([np.ceil((lp - l) / 2), np.floor((lp - l) / 2)])
hp = np.pad(h, padwidths.astype(int), 'constant')
hpf = sp.fft(hp, norm=None)
hpfs = hpf - np.min(np.real(hpf)) * 1.000001
hpfmp = mag2mp(np.sqrt(np.abs(hpfs)))
hpmp = sp.ifft(np.fft.ifftshift(np.conj(hpfmp)), center=False, norm=None)
hmp = hpmp[:int((l + 1) / 2)]
return hmp
def mag2mp(x):
n = np.size(x)
xl = np.log(np.abs(x)) # Log of mag spectrum
xlf = sp.fft(xl, center=False, norm=None)
xlfp = xlf
xlfp[0] = xlf[0] # Keep DC the same
xlfp[1:(n // 2):1] = 2 * xlf[1:(n // 2):1] # Double positive frequencies
xlfp[n // 2] = xlf[n // 2] # keep half Nyquist the same
xlfp[n // 2 + 1:n:1] = 0 # zero negative frequencies
xlaf = sp.ifft(xlfp, center=False, norm=None)
a = np.exp(xlaf) # complex exponentiation
return a
def test_sense_model_with_comm(self):
img_shape = [16, 16]
mps_shape = [8, 16, 16]
comm = sp.Communicator()
img = sp.randn(img_shape, dtype=np.complex)
mps = sp.randn(mps_shape, dtype=np.complex)
comm.allreduce(img)
comm.allreduce(mps)
ksp = sp.fft(img * mps, axes=[-1, -2])
A = linop.Sense(mps[comm.rank::comm.size], comm=comm)
npt.assert_allclose(A.H(ksp[comm.rank::comm.size]), np.sum(
sp.ifft(ksp, axes=[-1, -2]) * mps.conjugate(), 0))
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 dzls(n=64, tb=4, d1=0.01, d2=0.01):
di = dinf(d1, d2)
w = di / tb
f = np.asarray([0, (1 - w) * (tb / 2), (1 + w) * (tb / 2), (n / 2)])
f = f / (n / 2)
m = [1, 1, 0, 0]
w = [1, d1 / d2]
h = signal.firls(n + 1, f, m, w)
# shift the filter half a sample to make it symmetric, like in MATLAB
c = np.exp(
1j * 2 * np.pi / (2 * (n + 1)) *
np.concatenate([np.arange(0, n / 2 + 1, 1),
np.arange(-n / 2, 0, 1)]))
h = np.real(sp.ifft(np.multiply(sp.fft(h, center=False), c), center=False))
# lop off extra sample
h = h[:n]
return h
def time_ifft(self):
y = sp.ifft(self.x)
def prepare_knee_data(ismrmrd_path):
"""Convert ISMRMRD file to slices along readout.
Args:
ismrmrd_path (pathlib.Path): file path to ISMRMRD file.
"""
logging.info('Processing {}'.format(ismrmrd_path.stem))
dset = ismrmrd.Dataset(str(ismrmrd_path))
hdr = ismrmrd.xsd.CreateFromDocument(dset.read_xml_header())
matrix_size_x = hdr.encoding[0].encodedSpace.matrixSize.x
matrix_size_y = hdr.encoding[0].encodedSpace.matrixSize.y
number_of_slices = hdr.encoding[0].encodingLimits.slice.maximum + 1
number_of_channels = hdr.acquisitionSystemInformation.receiverChannels
ksp = np.zeros(
[number_of_channels, number_of_slices, matrix_size_y, matrix_size_x],
dtype=np.complex64)
for acqnum in range(dset.number_of_acquisitions()):
acq = dset.read_acquisition(acqnum)
y = acq.idx.kspace_encode_step_1
ksp[:, acq.idx.slice, y, :] = acq.data
ksp = np.fft.fft(np.fft.ifftshift(ksp, axes=-3), axis=-3)
ksp_lr_bf = sp.resize(ksp, [
number_of_channels, number_of_slices // 2, matrix_size_y // 2,
matrix_size_x // 2
])
ksp_lr = sp.resize(ksp_lr_bf, ksp.shape)
del ksp
#ksp_lr = sp.resize(sp.resize(ksp, [number_of_channels,
# number_of_slices // 2,
# matrix_size_y // 2,
# matrix_size_x]),
# ksp.shape)
#img = np.sum(np.abs(sp.ifft(ksp, axes=[-1, -2, -3]))**2, axis=0)**0.5
img_lr_bf = np.sum(np.abs(sp.ifft(ksp_lr_bf, axes=[-1, -2, -3]))**2,
axis=0)**0.5
#np.save("./stefan_data/img_lr_bf.npy", img_lr_bf)
#quit()
img_lr = np.sum(np.abs(sp.ifft(ksp_lr, axes=[-1, -2, -3]))**2, axis=0)**0.5
smallMatrixX = matrix_size_x // 2
scale = 1 / img_lr.max()
scale2 = 1 / img_lr_bf.max()
for i in range(matrix_size_x):
logging.info('Processing {}_{:03d}'.format(ismrmrd_path.stem, i))
#img_i_path = ismrmrd_path.parents[1] / 'img' / '{}_{:03d}'.format(ismrmrd_path.stem, i)
#img_lr_i_path = ismrmrd_path.parents[1] / 'img_lr' / '{}_{:03d}'.format(ismrmrd_path.stem, i)
img_lr_i_path = ismrmrd_path.parents[
1] / 'img_lr2' / '{}_{:03d}'.format(ismrmrd_path.stem, i)
if i < smallMatrixX:
img_lr_bf_i_path = ismrmrd_path.parents[
1] / 'img_lr2_bf' / '{}_{:03d}'.format(ismrmrd_path.stem, i)
#img_i = img[..., i]
img_lr_i = img_lr[..., i]
if i < smallMatrixX:
img_lr_bf_i = img_lr_bf[..., i]
#np.save(str(img_i_path), img_i * scale)
np.save(str(img_lr_i_path), img_lr_i * scale)
if i < smallMatrixX:
np.save(str(img_lr_bf_i_path), img_lr_bf_i * scale2)
def dz_hadamard_b(n=128, g=5, gind=1, tb=4, d1=0.01, d2=0.01, shift=32):
r"""Design a pulse with hadamard encoding
Args:
n (int): number of time points.
g (int): order of the Hadamard matrix.
gind (int): index of vector to use from Hadamard matrix for encoding.
tb (int): time bandwidth product.
d1 (float): passband ripple level in :math:'M_0^{-1}'.
d2 (float): stopband ripple level in :math:'M_0^{-1}'.
shift (int): n time points shift of pulse.
Returns:
b (array): SLR beta parameter.
References:
Souza, S.P., Szumowski, J., Dumoulin, C.L., Plewes, D.P. &
Glover, G. 'Sima: Simultaneous multislice acquisition of MR images
by hadamard - encoded excitation. J.Comput.Assist.Tomogr. 12,
1026–1030(1988).
"""
H = linalg.hadamard(g)
encode = H[gind - 1, :]
ftw = dinf(d1, d2) / tb # fractional transition width of the slab profile
if gind == 1: # no sub-slices
b = dzls(n, tb, d1, d2)
else:
# left stopband
f = np.asarray([0, shift - (1 + ftw) * (tb / 2)])
m = np.asarray([0, 0])
w = np.asarray([d1 / d2])
# first sub-band
ii = 1
gcent = shift + (ii - g / 2 - 1 / 2) * tb / g # first band center
# first band left edge
f = np.append(f, gcent - (tb / g / 2 - ftw * (tb / 2)))
m = np.append(m, encode[ii - 1])
if encode[ii - 1] != encode[ii]:
# add the first band's right edge and its amplitude, and a weight
f = np.append(f, gcent + (tb / g / 2 - ftw * (tb / 2)))
m = np.append(m, encode[ii - 1])
w = np.append(w, 1)
# middle sub-bands
for ii in range(2, g):
gcent = shift + (ii - g / 2 - 1 / 2) * tb / g # center of band
if encode[ii - 1] != encode[ii - 2]:
# add a left edge and amp for this band
f = np.append(f, gcent - (tb / g / 2 - ftw * (tb / 2)))
m = np.append(m, encode[ii - 1])
if encode[ii - 1] != encode[ii]:
# add a right edge and its amp, and a weight for this band
f = np.append(f, gcent + (tb / g / 2 - ftw * (tb / 2)))
m = np.append(m, encode[ii - 1])
w = np.append(w, 1)
# last sub-band
ii = g
gcent = shift + (ii - g / 2 - 1 / 2) * tb / g # center of last band
if encode[ii - 1] != encode[ii - 2]:
# add a left edge and amp for the last band
f = np.append(f, gcent - (tb / g / 2 - ftw * (tb / 2)))
m = np.append(m, encode[ii - 1])
# add a right edge and its amp, and a weight for the last band
f = np.append(f, gcent + (tb / g / 2 - ftw * (tb / 2)))
m = np.append(m, encode[ii - 1])
w = np.append(w, 1)
# right stop-band
f = np.append(f, (shift + (1 + ftw) * (tb / 2), (n / 2))) / (n / 2)
m = np.append(m, [0, 0])
w = np.append(w, d1 / d2)
# separate the positive and negative bands
mp = (m > 0).astype(float)
mn = (m < 0).astype(float)
# design the positive and negative filters
c = np.exp(1j * 2 * np.pi / (2 * (n + 1)) * np.concatenate(
[np.arange(0, n / 2 + 1, 1),
np.arange(-n / 2, 0, 1)]))
bp = signal.firls(n + 1, f, mp, w) # the positive filter
bn = signal.firls(n + 1, f, mn, w) # the negative filter
# combine the filters and demodulate
b = sp.ifft(np.multiply(sp.fft(bp - bn, center=False), c),
center=False)
b = np.real(b[:n])
# hilbert transform to suppress negative passband
b = signal.hilbert(b)
# demodulate to DC
c_shift = np.exp(-1j * 2 * np.pi / n * shift * np.arange(0, n, 1)) / 2
c_shift *= np.exp(-1j * np.pi / n * shift)
b = np.multiply(b, c_shift)
return b
def dz_gslider_b(n=128,
g=5,
gind=1,
tb=4,
d1=0.01,
d2=0.01,
phi=np.pi,
shift=32):
r"""Design a g-slider pulse b
Args:
n (int): number of time points.
g (int): number of sub-slices.
gind (int): subslice index.
tb (int): time bandwidth product.
d1 (float): passband ripple level in :math:'M_0^{-1}'.
d2 (float): stopband ripple level in :math:'M_0^{-1}'.
phi (float): subslice phase.
shift (int): n time points shift of pulse.
Returns:
b (array): SLR beta parameter.
References:
Setsompop, K. et al. 'High-resolution in vivo diffusion imaging of the
human brain with generalized slice dithered enhanced resolution:
Simultaneous multislice (gSlider-SMS). Magn. Reson. Med.79, 141–151
(2018).
"""
ftw = dinf(d1, d2) / tb # fractional transition width of the slab profile
if np.fmod(g, 2) and gind == int(np.ceil(g / 2)): # centered sub-slice
if g == 1: # no sub-slices, as a sanity check
b = dzls(n, tb, d1, d2)
else:
# Design 2 filters, to allow arbitrary phases on the subslice the
# first is a wider notch filter with '0's where it the subslice
# appears, and the second is the subslice. Multiply the subslice by
# its phase and add the filters.
f = np.asarray([
0, (1 / g - ftw) * (tb / 2), (1 / g + ftw) * (tb / 2),
(1 - ftw) * (tb / 2), (1 + ftw) * (tb / 2), (n / 2)
])
f = f / (n / 2)
m_notch = [0, 0, 1, 1, 0, 0]
m_sub = [1, 1, 0, 0, 0, 0]
w = [1, 1, d1 / d2]
b_notch = signal.firls(n + 1, f, m_notch, w) # the notched filter
b_sub = signal.firls(n + 1, f, m_sub, w) # the subslice filter
# add them with the subslice phase
b = np.add(b_notch, np.multiply(np.exp(1j * phi), b_sub))
# shift the filter half a sample to make it symmetric,
# like in MATLAB
c = np.exp(1j * 2 * np.pi / (2 * (n + 1)) * np.concatenate(
[np.arange(0, n / 2 + 1, 1),
np.arange(-n / 2, 0, 1)]))
b = sp.ifft(np.multiply(sp.fft(b, center=False), c), center=False)
# lop off extra sample
b = b[:n]
else:
# design filters for the slab and the subslice, hilbert xform them
# to suppress their left bands,
# then demodulate the result back to DC
gcent = shift + (gind - g / 2 - 1 / 2) * tb / g
if gind > 1 and gind < g:
# separate transition bands for slab+slice
f = np.asarray([
0, shift - (1 + ftw) * (tb / 2), shift - (1 - ftw) * (tb / 2),
gcent - (tb / g / 2 + ftw * (tb / 2)),
gcent - (tb / g / 2 - ftw * (tb / 2)),
gcent + (tb / g / 2 - ftw * (tb / 2)),
gcent + (tb / g / 2 + ftw * (tb / 2)),
shift + (1 - ftw) * (tb / 2), shift + (1 + ftw) * (tb / 2),
(n / 2)
])
f = f / (n / 2)
m_notch = [0, 0, 1, 1, 0, 0, 1, 1, 0, 0]
m_sub = [0, 0, 0, 0, 1, 1, 0, 0, 0, 0]
w = [d1 / d2, 1, 1, 1, d1 / d2]
elif gind == 1:
# the slab and slice share a left transition band
f = np.asarray([
0, shift - (1 + ftw) * (tb / 2), shift - (1 - ftw) * (tb / 2),
gcent + (tb / g / 2 - ftw * (tb / 2)),
gcent + (tb / g / 2 + ftw * (tb / 2)),
shift + (1 - ftw) * (tb / 2), shift + (1 + ftw) * (tb / 2),
(n / 2)
])
f = f / (n / 2)
m_notch = [0, 0, 0, 0, 1, 1, 0, 0]
m_sub = [0, 0, 1, 1, 0, 0, 0, 0]
w = [d1 / d2, 1, 1, d1 / d2]
elif gind == g:
# the slab and slice share a right transition band
f = np.asarray([
0, shift - (1 + ftw) * (tb / 2), shift - (1 - ftw) * (tb / 2),
gcent - (tb / g / 2 + ftw * (tb / 2)),
gcent - (tb / g / 2 - ftw * (tb / 2)),
shift + (1 - ftw) * (tb / 2), shift + (1 + ftw) * (tb / 2),
(n / 2)
])
f = f / (n / 2)
m_notch = [0, 0, 1, 1, 0, 0, 0, 0]
m_sub = [0, 0, 0, 0, 1, 1, 0, 0]
w = [d1 / d2, 1, 1, d1 / d2]
c = np.exp(1j * 2 * np.pi / (2 * (n + 1)) * np.concatenate(
[np.arange(0, n / 2 + 1, 1),
np.arange(-n / 2, 0, 1)]))
b_notch = signal.firls(n + 1, f, m_notch, w) # the notched filter
b_notch = sp.ifft(np.multiply(sp.fft(b_notch, center=False), c),
center=False)
b_notch = np.real(b_notch[:n])
# hilbert transform to suppress negative passband
b_notch = signal.hilbert(b_notch)
b_sub = signal.firls(n + 1, f, m_sub, w) # the sub-band filter
b_sub = sp.ifft(np.multiply(sp.fft(b_sub, center=False), c),
center=False)
b_sub = np.real(b_sub[:n])
# hilbert transform to suppress negative passband
b_sub = signal.hilbert(b_sub)
# add them with the subslice phase
b = b_notch + np.exp(1j * phi) * b_sub
# demodulate to DC
c_shift = np.exp(-1j * 2 * np.pi / n * shift * np.arange(0, n, 1)) / 2
c_shift *= np.exp(-1j * np.pi / n * shift)
b = np.multiply(b, c_shift)
return b
def kspace_precond(mps,
weights=None,
coord=None,
lamda=0,
device=sp.cpu_device,
oversamp=1.25):
r"""Compute a diagonal preconditioner in k-space.
Considers the optimization problem:
.. math::
\min_P \| P A A^H - I \|_F^2
where A is the Sense operator.
Args:
mps (array): sensitivity maps of shape [num_coils] + image shape.
weights (array): k-space weights.
coord (array): k-space coordinates of shape [...] + [ndim].
lamda (float): regularization.
Returns:
array: k-space preconditioner of same shape as k-space.
"""
dtype = mps.dtype
if weights is not None:
weights = sp.to_device(weights, device)
device = sp.Device(device)
xp = device.xp
mps_shape = list(mps.shape)
img_shape = mps_shape[1:]
img2_shape = [i * 2 for i in img_shape]
ndim = len(img_shape)
scale = sp.prod(img2_shape)**1.5 / sp.prod(img_shape)
with device:
if coord is None:
idx = (slice(None, None, 2), ) * ndim
ones = xp.zeros(img2_shape, dtype=dtype)
if weights is None:
ones[idx] = 1
else:
ones[idx] = weights**0.5
psf = sp.ifft(ones)
else:
coord2 = coord * 2
ones = xp.ones(coord.shape[:-1], dtype=dtype)
if weights is not None:
ones *= weights**0.5
psf = sp.nufft_adjoint(ones, coord2, img2_shape, oversamp=oversamp)
p_inv = []
for mps_i in mps:
mps_i = sp.to_device(mps_i, device)
mps_i_norm2 = xp.linalg.norm(mps_i)**2
xcorr_fourier = 0
for mps_j in mps:
mps_j = sp.to_device(mps_j, device)
xcorr_fourier += xp.abs(
sp.fft(mps_i * xp.conj(mps_j), img2_shape))**2
xcorr = sp.ifft(xcorr_fourier)
xcorr *= psf
if coord is None:
p_inv_i = sp.fft(xcorr)[idx]
else:
p_inv_i = sp.nufft(xcorr, coord2, oversamp=oversamp)
if weights is not None:
p_inv_i *= weights**0.5
p_inv.append(p_inv_i * scale / mps_i_norm2)
p_inv = (xp.abs(xp.stack(p_inv, axis=0)) + lamda) / (1 + lamda)
p_inv[p_inv == 0] = 1
p = 1 / p_inv
return p.astype(dtype)
plt.imshow(img_lr_bf[:, 100, :], cmap='gray')
plt.show()
#print (img_lr_bf.shape)
quit()
ksp = np.load('./stefan_data/ksp.npy')
ksp_lr = np.load('./stefan_data/ksp_lr.npy')
ksp_lr_bf = np.load('./stefan_data/ksp_lr_bf.npy')
print(ksp_lr_bf.shape)
#quit()
print(ksp.shape)
print(ksp_lr.shape)
print(ksp_lr_bf.shape)
#quit()
import sigpy as sp
img = np.sum(np.abs(sp.ifft(ksp_lr, axes=[-1, -2, -3]))**2, axis=0)**0.5
#img_lr_bf = np.sum(np.abs(sp.ifft(ksp_lr_bf, axes=[-1, -2, -3]))**2, axis=0)**0.5
plt.imshow(img[:, 100, :], cmap='gray')
plt.show()
#plt.imshow(np.real(ksp_lr[0, :, 100, :]))
#plt.show()
#plt.imshow(np.real(lr[0, :, 100, :]))
#plt.imshow(np.real(img_lr_bf[:, 100, :]), cmap='gray')
#plt.show()
quit()
'''
#R = np.load('filter.raisr')
#R = np.load(open(r'./filter.raisr', 'rb'), allow_pickle=True)
#quit()
def dzrf(n=64,
tb=4,
ptype='st',
ftype='ls',
d1=0.01,
d2=0.01,
cancel_alpha_phs=False,
custom_profile=None):
r"""Primary function for design of pulses using the SLR algorithm.
Args:
n (int): number of time points.
tb (int): pulse time bandwidth product.
ptype (string): pulse type, 'st' (small-tip excitation), 'ex' (pi/2
excitation pulse), 'se' (spin-echo pulse), 'inv' (inversion), or
'sat' (pi/2 saturation pulse).
ftype (string): type of filter to use: 'ms' (sinc), 'pm'
(Parks-McClellan equal-ripple), 'min' (minphase using factored pm),
'max' (maxphase using factored pm), 'ls' (least squares), or 'cp'
(custom excitation profile).
d1 (float): passband ripple level in :math:'M_0^{-1}'.
d2 (float): stopband ripple level in :math:'M_0^{-1}'.
cancel_alpha_phs (bool): For 'ex' pulses, absorb the alpha phase
profile from beta's profile, so they cancel for a flatter
total phase
custom_profile (array): if provided, pulse will be designed to excite
an arbitrary profile rather than a rectangular one, following [2].
Returns:
rf (array): designed RF pulse.
References:
[1] Pauly, J., Le Roux, Patrick., Nishimura, D., and Macovski, A.
(1991). Parameter Relations for the Shinnar-LeRoux Selective Excitation
Pulse Design Algorithm.
IEEE Transactions on Medical Imaging, Vol 10, No 1, 53-65.
[2] Barral, J., Pauly, J., and Nishimura, D. (2008). SLR RF Pulse
Design for Arbitrarily-Shaped Excitation Profiles.
Proc. Intl. Soc. Mag. Reson. Med. 16, 1323.
"""
[bsf, d1, d2] = calc_ripples(ptype, d1, d2)
if ftype == 'ms': # sinc
b = msinc(n, tb / 4)
elif ftype == 'pm': # linphase
b = dzlp(n, tb, d1, d2)
elif ftype == 'min': # minphase
b = dzmp(n, tb, d1, d2)
b = b[::-1]
elif ftype == 'max': # maxphase
b = dzmp(n, tb, d1, d2)
elif ftype == 'ls': # least squares
b = dzls(n, tb, d1, d2)
elif ftype == 'cp': # custom profile, [2]
if custom_profile is None:
raise Exception('cp filter selected but custom_profile not passed')
b = np.sin(np.arcsin(custom_profile) / 2)
else:
raise Exception('Filter type ("{}") is not recognized.'.format(ftype))
if ftype == 'cp': # custom profile rf design, following [2]
b_hat = bsf * sp.ifft(b, center=True, norm=None)
rf = b2rf(b_hat, cancel_alpha_phs=True)
else:
if ptype == 'st':
rf = b
elif ptype == 'ex':
b = bsf * b
rf = b2rf(b, cancel_alpha_phs)
else:
b = bsf * b
rf = b2rf(b)
return rf
def dz_recursive_rf(n_seg,
tb,
n,
se_seq=False,
tb_ref=8,
z_pad_fact=4,
win_fact=1.75,
cancel_alpha_phs=True,
t1=np.inf,
tr_seg=60,
use_mz=True,
d1=0.01,
d2=0.01,
d1se=0.01,
d2se=0.01):
r"""Recursive SLR pulse design.
Args:
n_seg (int): number of segments designed by recursion.
tb (int): time bandwidth product.
n (int): pulse length.
se_seq (bool): spin echo sequence.
tb_ref (int): time bandwidth product of refocusing pulse.
z_pad_fact (float): zero padding factor.
win_fact (float): applied window factor.
cancel_alpha_phs (bool): absorb the alpha phase
profile from beta's profile, so they cancel for a flatter
total phase
t1 (float): t1
tr_seg (int): length of tr
use_mz (bool): design the pulses accounting for the actual Mz profile
d1 (float): passband ripple level in :math:'M_0^{-1}'.
d2 (float): stopband ripple level in :math:'M_0^{-1}'.
d1se (float): passband ripple level for se
d2se (float): stopband ripple level for se
Returns:
If se_seq=True, 2-element tuple containing
- **rf** (*array*): rf pulse out.
- **rf_ref** (*array*): rf refocusing pulse out.
"""
# get refocusing pulse and its rotation parameters
if se_seq is True:
[bsf, d1se, d2se] = calc_ripples('se', d1se, d2se)
b_ref = bsf * dzls(n, tb_ref, d1se, d2se)
b_ref = np.concatenate(
(np.zeros(int(z_pad_fact * n / 2 - n / 2)), b_ref,
np.zeros(int(z_pad_fact * n / 2 - n / 2))))
rf_ref = b2rf(b_ref)
bref = sp.fft(b_ref, norm=None)
bref /= np.max(np.abs(bref))
bref_mag = np.abs(bref)
aref_mag = np.abs(np.sqrt(1 - bref_mag**2))
flip_ref = 2 * np.arcsin(bref_mag[int(z_pad_fact * n / 2)]) \
* 180 / np.pi
# get flip angles
flip = np.zeros(n_seg)
flip[n_seg - 1] = 90
for jj in range(n_seg - 2, -1, -1):
if se_seq is False:
flip[jj] = np.arctan(np.sin(flip[jj + 1] * np.pi / 180))
flip[jj] = flip[jj] * 180 / np.pi # deg
else:
flip[jj] = np.arctan(
np.cos(flip_ref * np.pi / 180) *
np.sin(flip[jj + 1] * np.pi / 180))
flip[jj] = flip[jj] * 180 / np.pi # deg
# design first RF pulse
b = np.zeros((int(z_pad_fact * n), n_seg), dtype=complex)
b[int(z_pad_fact * n / 2 - n / 2):int(z_pad_fact * n / 2 + n / 2), 0] = \
dzls(n, tb, d1, d2)
# b = np.concatenate((np.zeros(int(zPadFact*N/2-N/2)), b,
# np.zeros(int(zPadFact*N/2-N/2))))
B = sp.fft(b[:, 0], norm=None)
c = np.exp(-1j * 2 * np.pi / (n * z_pad_fact) / 2 *
np.arange(-n * z_pad_fact / 2, n * z_pad_fact / 2, 1))
B = np.multiply(B, c)
b[:, 0] = sp.ifft(B / np.max(np.abs(B)), norm=None)
b[:, 0] *= np.sin(flip[0] * (np.pi / 180) / 2)
rf = np.zeros((z_pad_fact * n, n_seg), dtype=complex)
a = b2a(b[:, 0])
if cancel_alpha_phs:
# cancel a phase by absorbing into b
# Note that this is the only time we need to do it
b_a_phase = sp.fft(b[:, 0], center=False, norm=None) * \
np.exp(-1j * np.angle(sp.fft(a[np.size(a)::-1],
center=False, norm=None)))
b[:, 0] = sp.ifft(b_a_phase, center=False, norm=None)
rf[:, 0] = b2rf(b[:, 0])
# get min-phase alpha and its response
# a = b2a(b[:, 0])
A = sp.fft(a)
# calculate beta filter response
B = sp.fft(b[:, 0], norm=None)
if win_fact < z_pad_fact:
win_len = (win_fact - 1) * n
npad = n * z_pad_fact - win_fact * n
# blackman window?
window = signal.blackman(int((win_fact - 1) * n))
# split in half; stick N ones in the middle
window = np.concatenate((window[0:int(win_len / 2)], np.ones(n),
window[int(win_len / 2):]))
window = np.concatenate(
(np.zeros(int(npad / 2)), window, np.zeros(int(npad / 2))))
# apply windowing to first pulse for consistency
b[:, 0] = np.multiply(b[:, 0], window)
rf[:, 0] = b2rf(b[:, 0])
# recalculate B and A
B = sp.fft(b[:, 0], norm=None)
A = sp.fft(b2a(b[:, 0]), norm=None)
# use A and B to get Mxy
# Mxy = np.zeros((zPadFact*N, Nseg), dtype = complex)
if se_seq is False:
mxy0 = 2 * np.conj(A) * B
else:
mxy0 = 2 * A * np.conj(B) * bref**2
# Amplitude of next pulse's Mxy profile will be
# |Mz*2*a*b| = |Mz*2*sqrt(1-abs(B).^2)*B|.
# If we set this = |Mxy_1|, we can solve for |B| via solving quadratic
# equation 4*Mz^2*(1-B^2)*B^2 = |Mxy_1|^2.
# Subsequently solve for |A|, and get phase of A via min-phase, and
# then get phase of B by dividing phase of A from first pulse's Mxy phase.
mz = np.ones((z_pad_fact * n), dtype=complex)
for jj in range(1, n_seg):
# calculate Mz profile after previous pulse
if se_seq is False:
mz = mz * (1 - 2 * np.abs(B) ** 2) * np.exp(-tr_seg / t1) + \
(1 - np.exp(-tr_seg / t1))
else:
mz = mz * (1 - 2 *
(np.abs(A * bref_mag)**2 + np.abs(aref_mag * B)**2))
# (second term is about 1%)
if use_mz is True: # design the pulses accounting for the
# actual Mz profile (the full method)
# set up quadratic equation to get |B|
cq = -np.abs(mxy0)**2
if se_seq is False:
bq = 4 * mz**2
aq = -4 * mz**2
else:
bq = 4 * (bref_mag**4) * mz**2
aq = -4 * (bref_mag**4) * mz**2
bmag = np.sqrt(
(-bq + np.real(np.sqrt(bq**2 - 4 * aq * cq))) / (2 * aq))
bmag[np.isnan(bmag)] = 0
# get A - easier to get complex A than complex B since |A| is
# determined by |B|, and phase is gotten by min-phase relationship
# Phase of B doesn't matter here since only profile mag is used by
# b2a
A = sp.fft(b2a(sp.ifft(bmag, norm=None)), norm=None)
# trick: now we can get complex B from ratio of Mxy and A
B = mxy0 / (2 * np.conj(A) * mz)
else: # design assuming ideal Mz (conventional VFA)
B *= np.sin(np.pi / 180 * flip[jj] / 2) \
/ np.sin(np.pi / 180 * flip[jj - 1] / 2)
A = sp.fft(b2a(sp.ifft(B, norm=None)), norm=None)
# get polynomial
b[:, jj] = sp.ifft(B, norm=None)
if win_fact < z_pad_fact:
b[:, jj] *= window
# recalculate B and A
B = sp.fft(b[:, jj], norm=None)
A = sp.fft(b2a(b[:, jj]), norm=None)
rf[:, jj] = b2rf(b[:, jj])
# truncate the RF
if win_fact < z_pad_fact:
pulse_len = int(win_fact * n)
rf = rf[int(npad / 2):int(npad / 2 + pulse_len), :]
if se_seq is False:
return rf
else:
return rf, rf_ref
def circulant_precond(mps,
weights=None,
coord=None,
lamda=0,
device=sp.cpu_device):
r"""Compute circulant preconditioner.
Considers the optimization problem:
.. math::
\min_P \| A^H A - F P F^H \|_2^2
where A is the Sense operator,
and F is a unitary Fourier transform operator.
Args:
mps (array): sensitivity maps of shape [num_coils] + image shape.
weights (array): k-space weights.
coord (array): k-space coordinates of shape [...] + [ndim].
lamda (float): regularization.
Returns:
array: circulant preconditioner of image shape.
"""
if coord is not None:
coord = sp.to_device(coord, device)
if weights is not None:
weights = sp.to_device(weights, device)
dtype = mps.dtype
device = sp.Device(device)
xp = device.xp
mps_shape = list(mps.shape)
img_shape = mps_shape[1:]
img2_shape = [i * 2 for i in img_shape]
ndim = len(img_shape)
scale = sp.prod(img2_shape)**1.5 / sp.prod(img_shape)**2
with device:
idx = (slice(None, None, 2), ) * ndim
if coord is None:
ones = xp.zeros(img2_shape, dtype=dtype)
if weights is None:
ones[idx] = 1
else:
ones[idx] = weights**0.5
psf = sp.ifft(ones)
else:
coord2 = coord * 2
ones = xp.ones(coord.shape[:-1], dtype=dtype)
if weights is not None:
ones *= weights**0.5
psf = sp.nufft_adjoint(ones, coord2, img2_shape)
p_inv = 0
for mps_i in mps:
mps_i = sp.to_device(mps_i, device)
xcorr_fourier = xp.abs(sp.fft(xp.conj(mps_i), img2_shape))**2
xcorr = sp.ifft(xcorr_fourier)
xcorr *= psf
p_inv_i = sp.fft(xcorr)
p_inv_i = p_inv_i[idx]
p_inv_i *= scale
if weights is not None:
p_inv_i *= weights**0.5
p_inv += p_inv_i
p_inv += lamda
p_inv[p_inv == 0] = 1
p = 1 / p_inv
return p.astype(dtype)
def time_ifft_non_centered(self):
y = sp.ifft(self.x, center=False)
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
