def test_masker():
am = masker(arr, mask, order="F", squeeze_output=True)
testing.assert_array_almost_equal(am, [0, 8, 1, 7])
assert am.shape == (nmask, )
expected_embed = arr * mask
testing.assert_array_equal(expected_embed, embed(am, mask, order="F"))
# am = masker(arr, mask, order="C", squeeze_output=True)
# testing.assert_array_almost_equal(am, [0, 1, 7, 8])
# assert am.shape == (nmask,)
# testing.assert_array_equal(expected_embed, embed(am, mask, order="C"))
am = masker(arr, mask, order="F", squeeze_output=False)
testing.assert_array_almost_equal(am[:, 0], [0, 8, 1, 7])
assert am.shape == (nmask, 1)
testing.assert_array_equal(expected_embed, embed(am, mask, order="F"))
def _norm_single_rep(self, x):
# chain forward and adjoint together for a single repetition
y = self._forward_single_rep(x)
if self.sample_mask is not None:
y = embed(y, mask=self.sample_mask, order=self.order, xp=self.xp)
y = y.reshape(self.shape_in, order=self.order)
x = self._adjoint_single_rep(y)
return x
def test_masker_multidim():
nreps = 8
arr3 = np.tile(arr[..., np.newaxis], (1, 1, nreps))
am3 = masker(arr3, mask, order="F")
assert am3.shape == (nmask, nreps)
testing.assert_array_almost_equal(am3[:, 0], [0, 8, 1, 7])
expected_embed = arr3 * mask[..., np.newaxis]
testing.assert_array_almost_equal(expected_embed,
embed(am3, mask, order="F"))
def _norm_single_rep(self, x):
# chain forward and adjoint together for a single repetition
y = self._forward_single_rep(x)
if self.sample_mask is not None:
y = embed(y, mask=self.sample_mask, order=self.order)
if self.order == "C":
y_shape = (self.Ncoils, ) + self.shape_in1
else:
y_shape = self.shape_in1 + (self.Ncoils, )
y = y.reshape(y_shape, order=self.order)
x = self._adjoint_single_rep(y)
return x
def test_embed_demo(show_figure=False):
shape = (512, 500)
mask = np.ones(shape, dtype=np.bool)
mask[:8, :8] = 0
x = np.arange(mask.sum())
y1 = embed(x, mask)
y2 = embed(np.column_stack((x, x, x, x)), mask)
np.testing.assert_allclose(y1, y2[:, :, 1])
if show_figure:
import matplotlib.pyplot as plt
plt.figure(), plt.imshow(y1.T), plt.show()
x3 = np.tile(x[:, None, None], (1, 2, 3))
y3 = embed(x3, mask)
assert y3.ndim == mask.ndim + x3.ndim - 1
np.testing.assert_allclose(y1, y3[:, :, -1, -1])
def adjoint(self, y):
# TODO: add test for this case and the coils + sample_mask case
# if y.ndim == 1 or y.shape[-1] == 1:
xp = self.xp
nreps = int(y.size / self.shape[0])
if self.sample_mask is not None:
if y.ndim == 1 and self.ndim > 1:
y = y[:, np.newaxis]
nmask = self.sample_mask.sum()
if y.shape[0] != nmask:
if self.order == "C":
y = y.reshape((-1, nmask), order=self.order)
else:
y = y.reshape((nmask, -1), order=self.order)
y = embed(y, mask=self.sample_mask, order=self.order)
if nreps == 1:
# 1D or single repetition or single coil nD
y = y.reshape(self.shape_in, order=self.order)
x = self._adjoint_single_rep(y)
else:
if self.order == "C":
shape_tmp = (nreps, ) + self.shape_in
else:
shape_tmp = self.shape_in + (nreps, )
y = y.reshape(shape_tmp, order=self.order)
x = xp.zeros(shape_tmp, dtype=xp.result_type(y, np.complex64))
if self.order == "C":
for rep in range(nreps):
x[rep, ...] = self._adjoint_single_rep(y[rep, ...])
else:
for rep in range(nreps):
x[..., rep] = self._adjoint_single_rep(y[..., rep])
# if self.im_mask:
# x = masker(x, self.im_mask, order=self.order)
if self.ortho:
x *= self.scale_ortho
if x.dtype != self.result_dtype:
x = x.astype(self.result_dtype)
if self.force_real_image:
x = x.real.astype(self.result_dtype)
return x
def test_TV_masked(xp):
# generate a random image-domain mask
# im_mask = xp.random.standard_normal(c.shape) > -0.2
# test 1D in/outputs but using masked values for the input array
# r = pywt.data.camera().astype(float)
r = xp.random.randn(16, 16)
x, y = xp.meshgrid(
xp.arange(-r.shape[0] // 2, r.shape[0] // 2),
xp.arange(-r.shape[1] // 2, r.shape[1] // 2),
indexing="ij",
sparse=True,
)
# make a circular mask
im_mask = xp.sqrt(x * x + y * y) < r.shape[0] // 2
# TODO: order='C' case is currently broken
for order, mask_out in product(["F"], [None, im_mask]):
r_masked = masker(r, im_mask, order=order)
Wm = TV_Operator(
r.shape,
order=order,
mask_in=im_mask,
mask_out=mask_out,
nd_input=True,
nd_output=False,
random_shift=True,
**get_loc(xp),
)
out = Wm * r_masked
if mask_out is None:
assert_(out.ndim == 1)
assert_(out.size == r.ndim * r.size)
out = out.reshape(r.shape + (r.ndim, ), order=order)
else:
assert_(out.ndim == 1)
nmask = mask_out.sum()
if xp != np:
nmask = nmask.get()
assert_(out.size == Wm.ndim * nmask)
out = embed(out, mask_out, order=order)
Wm.H * (Wm * r_masked)
def test_FiniteDifference_masked(xp, shape):
# test 1D in/outputs but using masked values for the input array
# r = pywt.data.camera().astype(float)
rstate = xp.random.RandomState(1234)
r = rstate.randn(*shape)
x, y = xp.meshgrid(
xp.arange(-r.shape[0] // 2, r.shape[0] // 2),
xp.arange(-r.shape[1] // 2, r.shape[1] // 2),
indexing="ij",
sparse=True,
)
# make a circular mask
im_mask = xp.sqrt(x ** 2 + y ** 2) < r.shape[0] // 2
# TODO: order='C' case is currently broken
for order, mask_out in product(["F"], [None, im_mask]):
r_masked = masker(r, im_mask, order=order)
Wm = FiniteDifferenceOperator(
r.shape,
order=order,
use_corners=True,
mask_in=im_mask,
mask_out=mask_out,
nd_input=True,
nd_output=mask_out is not None,
random_shift=True,
**get_loc(xp),
)
out = Wm * r_masked
if mask_out is None:
assert_(out.ndim == 1)
assert_(out.size == Wm.num_offsets * r.size)
out = out.reshape(r.shape + (Wm.num_offsets,), order=order)
else:
assert_(out.ndim == 1)
assert_(out.size == Wm.num_offsets * mask_out.sum())
out = embed(out, mask_out, order=order)
Wm.H * (Wm * r_masked)
def forward(self, x):
xp = self.xp
if x.size % self.nargin != 0:
raise ValueError("shape mismatch for forward DWT")
if (self.mask_in is not None) and (not self.nd_input):
x = embed(x, self.mask_in, order=self.order)
nrepetitions = x.size // self.nargin
if nrepetitions > 1:
if self.order == "C":
y = xp.zeros((nrepetitions, ) + self.coeff_arr_shape,
dtype=x.dtype)
for rep in range(nrepetitions):
y[rep, ...] = self._forward1(x[rep, ...])
else:
y = xp.zeros(self.coeff_arr_shape + (nrepetitions, ),
dtype=x.dtype)
for rep in range(nrepetitions):
y[..., rep] = self._forward1(x[..., rep])
else:
y = self._forward1(x)
if (self.mask_out is not None) and (not self.nd_output):
y = masker(y, self.mask_out, order=self.order)
return y
def adjoint(self, coeffs):
xp = self.xp
if coeffs.size % self.nargout != 0:
raise ValueError("shape mismatch for adjoint DWT")
nrepetitions = coeffs.size // self.nargout
if (self.mask_out is not None) and (not self.nd_output):
coeffs = embed(coeffs, self.mask_out, order=self.order)
coeffs = coeffs.ravel(order=self.order)
if nrepetitions > 1:
if self.order == "C":
x = xp.zeros((nrepetitions, ) + self.arr_shape,
dtype=coeffs.dtype)
for rep in range(nrepetitions):
x[rep, ...] = self._adjoint1(coeffs[rep, ...])
else:
x = xp.zeros(self.arr_shape + (nrepetitions, ),
dtype=coeffs.dtype)
for rep in range(nrepetitions):
x[..., rep] = self._adjoint1(coeffs[..., rep])
else:
x = self._adjoint1(coeffs)
if (self.mask_in is not None) and (not self.nd_input):
x = masker(x, self.mask_in, order=self.order)
return x
def norm(self, x):
# if not hasattr(self, 'Q') or self.Q is None:
# warnings.warn("Toeplitz Q did not exist, creating it...")
# self.prep_toeplitz()
x = complexify(x)
if self.masked:
x = embed(x, self.mask, order=self.order)
try:
if x.size % self.nargin != 0:
raise ValueError("wrong size input")
Nrepetitions = x.size // self.nargin
except IndexError:
Nrepetitions = 1
if hasattr(self, "Q"):
slices = [slice(None)] * x.ndim
for d in range(len(self.Nd)):
slices[d] = slice(self.Nd[d])
if Nrepetitions == 1:
y = fftn(x, s=self.Q.shape)
y *= self.Q
y = ifftn(y)[slices]
else:
if self.order == "C":
x_shape = (Nrepetitions,) + tuple(self.Nd)
else:
x_shape = tuple(self.Nd) + (Nrepetitions,)
x = x.reshape(x_shape, order=self.order)
fft_axes = tuple(np.arange(len(self.Nd)))
y = fftn(x, s=self.Q.shape, axes=fft_axes)
y *= self.Q[..., np.newaxis] # add an axis for repetitions
y = ifftn(y, axes=fft_axes)[slices]
else:
y = self.H * (self * x)
return y
def test_partial_FFT_with_im_mask(xp, nd_in, order, shift):
""" masked FFT with missing samples and masked image domain """
c = get_data(xp)
rstate = xp.random.RandomState(1234)
sample_mask = rstate.rand(*(128, 127)) > 0.5
x, y = xp.meshgrid(
xp.arange(-c.shape[0] // 2, c.shape[0] // 2),
xp.arange(-c.shape[1] // 2, c.shape[1] // 2),
indexing="ij",
sparse=True,
)
# make a circular mask
im_mask = xp.sqrt(x * x + y * y) < c.shape[0] // 2
nd_out = False
FTop = FFT_Operator(
c.shape,
order=order,
im_mask=im_mask,
use_fft_shifts=shift,
nd_input=nd_in,
nd_output=nd_out,
sample_mask=sample_mask,
gpu_force_reinit=False,
mask_kspace_on_gpu=(not shift),
**get_loc(xp),
)
# create new linear operator for forward followed by inverse transform
FtF = FTop.H * FTop
assert isinstance(FtF, LinearOperatorMulti)
# test forward only
forw = embed(FTop * masker(c, im_mask, order=order),
sample_mask,
order=order)
if shift:
expected_forw = sample_mask * fftnc(c * im_mask)
else:
expected_forw = sample_mask * fftn(c * im_mask)
xp.testing.assert_allclose(forw, expected_forw, rtol=1e-7, atol=1e-4)
# test roundtrip
roundtrip = FTop.H * (FTop * masker(c, im_mask, order=order))
if shift:
expected_roundtrip = masker(ifftnc(sample_mask * fftnc(c * im_mask)),
im_mask,
order=order)
else:
expected_roundtrip = masker(ifftn(sample_mask * fftn(c * im_mask)),
im_mask,
order=order)
xp.testing.assert_allclose(roundtrip,
expected_roundtrip,
rtol=1e-7,
atol=1e-4)
# test roundtrip with 2 reps
c2 = xp.stack([c] * 2, axis=-1)
roundtrip = FTop.H * (FTop * masker(c2, im_mask, order=order))
if shift:
expected_roundtrip = masker(
ifftnc(
sample_mask[..., xp.newaxis] *
fftnc(c2 * im_mask[..., xp.newaxis], axes=(0, 1)),
axes=(0, 1),
),
im_mask,
order=order,
)
else:
expected_roundtrip = masker(
ifftn(
sample_mask[..., xp.newaxis] *
fftn(c2 * im_mask[..., xp.newaxis], axes=(0, 1)),
axes=(0, 1),
),
im_mask,
order=order,
)
xp.testing.assert_allclose(roundtrip,
expected_roundtrip,
rtol=1e-7,
atol=1e-4)
def adjoint(self, y):
# TODO: add test for this case and the coils + sample_mask case
# if y.ndim == 1 or y.shape[-1] == 1:
xp = self.xp
ncoils = self.Ncoils
nreps = int(y.size / self.shape[0])
if self.sample_mask is not None:
if y.ndim == 1 and self.ndim > 1:
y = y[:, np.newaxis]
nmask = xp.count_nonzero(self.sample_mask)
if self.on_gpu:
nmask = nmask.get()
if y.shape[0] != nmask:
if self.order == "C":
y = y.reshape((-1, nmask), order=self.order)
else:
y = y.reshape((nmask, -1), order=self.order)
y = embed(y, mask=self.sample_mask, order=self.order)
if nreps == 1:
# 1D or single repetition or single coil nD
if self.order == "C":
y = y.reshape((ncoils, ) + self.shape_in1, order=self.order)
else:
y = y.reshape(self.shape_in1 + (ncoils, ), order=self.order)
if self.Nmaps == 1:
x = self._adjoint_single_rep(y, i_map=0)
else:
x = xp.zeros(self.shape_inM,
dtype=xp.result_type(y, xp.complex64))
if self.order == "C":
for i_map in range(self.Nmaps):
x[i_map, ...] = self._adjoint_single_rep(y,
i_map=i_map)
else:
for i_map in range(self.Nmaps):
x[..., i_map] = self._adjoint_single_rep(y,
i_map=i_map)
else:
if self.order == "C":
y = y.reshape((nreps, ncoils) + self.shape_in1,
order=self.order) # or shape_out?
x_shape = (nreps, ) + self.shape_inM
else:
y = y.reshape(self.shape_in1 + (ncoils, nreps),
order=self.order) # or shape_out?
x_shape = self.shape_inM + (nreps, )
x = xp.zeros(x_shape, dtype=xp.result_type(y, xp.complex64))
for i_map in range(self.Nmaps):
if self.order == "C":
for rep in range(nreps):
x[rep, i_map,
...] = self._adjoint_single_rep(y[rep, ...],
i_map=i_map)
else:
for rep in range(nreps):
x[..., i_map,
rep] = self._adjoint_single_rep(y[..., rep],
i_map=i_map)
# if self.im_mask:
# x = masker(x, self.im_mask, order=self.order)
if self.ortho:
x *= self.scale_ortho
if x.dtype != self.result_dtype:
x = x.astype(self.result_dtype)
if self.force_real_image:
# x = x.real.astype(self.result_dtype)
if x.dtype in [np.complex64, np.complex128]:
x.imag[:] = 0
return x
def mri_partial_fourier_nd(
partial_kspace,
pf_mask,
niter=5,
tw_inner=8,
tw_outer=3,
fill_conj=False,
init=None,
verbose=False,
show=False,
return_all_estimates=False,
xp=None,
):
"""Partial Fourier reconstruction.
Parameters
----------
Returns
-------
Notes
-----
The implementation is based on a multi-dimensional iterative reconstruction
technique as described in [1]_. This is an extension of the 1D iterative
methods described in [2]_ and [3]_. The concept of partial Fourier imaging
was first proposed in [4]_, [5]_.
References
----------
.. [1] Xu, Y. and Haacke, E. M. Partial Fourier imaging in
multi-dimensions: A means to save a full factor of two in time.
J. Magn. Reson. Imaging, 2001; 14:628–635.
doi:10.1002/jmri.1228
.. [2] Haacke, E.; Lindskogj, E. & Lin, W. A fast, iterative,
partial-Fourier technique capable of local phase recovery.
Journal of Magnetic Resonance, 1991; 92:126-145.
.. [3] Liang, Z.-P.; Boada, F.; Constable, R. T.; Haacke, E.; Lauterbur,
P. & Smith, M. Constrained reconstruction methods in MR imaging.
Rev Magn Reson Med, 1992; 4: 67-185
.. [4] Margosian, P.; Schmitt, F. & Purdy, D. Faster MR imaging: imaging
with half the data Health Care Instrum, 1986; 1:195.
.. [5] Feinberg, D. A.; Hale, J. D.; Watts, J. C.; Kaufman, L. & Mark, A.
Halving MR imaging time by conjugation: demonstration at 3.5 kG.
Radiology, 1986, 161, 527-531
"""
xp, on_gpu = get_array_module(partial_kspace, xp)
partial_kspace = xp.asarray(partial_kspace)
# dtype = partial_kspace.dtype
pf_mask = xp.asarray(pf_mask)
if pf_mask.dtype != xp.bool:
pf_mask = pf_mask.astype(xp.bool)
im_shape = pf_mask.shape
ndim = pf_mask.ndim
if not xp.all(xp.asarray(im_shape) % 2 == 0):
raise ValueError(
"This function assumes all k-space dimensions have even length.")
if partial_kspace.size != xp.count_nonzero(pf_mask):
raise ValueError(
"partial kspace should have total size equal to the number of "
"non-zeros in pf_mask")
kspace_init = embed(partial_kspace, pf_mask)
img_est = ifftnc(kspace_init)
lr_kspace = xp.zeros_like(kspace_init)
nz = xp.where(pf_mask)
lr_slices = [slice(None)] * ndim
pf_slices = [slice(None)] * ndim
win2_slices = [slice(None)] * ndim
lr_shape = [0] * ndim
# pf_shape = [0, ]*ndim
win2_shape = [0] * ndim
for d in range(ndim):
nz_min = xp.min(nz[d])
nz_max = xp.max(nz[d])
if hasattr(nz_min, "get"):
# 0-dim GPU array to scalar
nz_min, nz_max = nz_min.get(), nz_max.get()
i_mid = im_shape[d] // 2
if nz_min == 0:
i_end = nz_max
width = i_end - i_mid
else:
i_start = nz_min
width = i_mid - i_start
lr_slices[d] = slice(i_mid - width, i_mid + width + 1)
lr_shape[d] = 2 * width + 1
# pf_slices[d] = slice(nz_min, nz_max + 1)
pf_shape = nz_max - nz_min + 1
pf_slices[d] = slice(nz_min, nz_max + 1)
win2_shape[d] = pf_shape + tw_outer
if nz_min == 0:
# pf_slices[d] = slice(nz_min, nz_max + 1 + tw_outer)
win2_slices[d] = slice(tw_outer, tw_outer + pf_shape)
else:
# pf_slices[d] = slice(nz_min - tw_outer, nz_max + 1)
win2_slices[d] = slice(pf_shape)
lr_slices = tuple(lr_slices)
win2_slices = tuple(win2_slices)
pf_slices = tuple(pf_slices)
# lr_mask = xp.zeros(pf_mask, dtype=xp.zeros)
lr_win = hanning_apodization_window(lr_shape, tw_inner, xp)
lr_kspace[lr_slices] = kspace_init[lr_slices] * lr_win
img_lr = ifftnc(lr_kspace)
phi = xp.angle(img_lr)
pf_win = hanning_apodization_window(win2_shape, tw_outer, xp)[win2_slices]
lr_mask = xp.zeros(pf_mask.shape, dtype=xp.float32)
lr_mask[lr_slices] = lr_win
win2_mask = xp.zeros(pf_mask.shape, dtype=xp.float32)
win2_mask[pf_slices] = pf_win
if show and ndim == 2:
from matplotlib import pyplot as plt
fig, axes = plt.subplots(2, 2)
axes = axes.ravel()
axes[0].imshow(pf_mask)
axes[0].set_title("PF mask")
axes[1].imshow(lr_mask)
axes[1].set_title("LR Filter")
axes[2].imshow(win2_mask)
axes[2].set_title("Filter")
axes[3].imshow(xp.abs(img_est).T)
axes[3].set_title("Initial Estimate")
for ax in axes:
ax.set_xticklabels("")
ax.set_yticklabels("")
if verbose:
norm0 = xp.linalg.norm(img_est)
max0 = xp.max(xp.abs(img_est))
if return_all_estimates:
all_img_est = [img_est]
# POCS iterations
for i in range(niter):
# step 5
rho1 = xp.abs(img_est) * xp.exp(1j * phi)
if verbose:
change2 = xp.linalg.norm(rho1 - img_est) / norm0
change1 = xp.max(xp.abs(rho1 - img_est)) / max0
print("change = {}%% {}%%".format(100 * change2, 100 * change1))
# step 6
s1 = fftnc(rho1)
# steps 7 & 8
full_kspace = win2_mask * kspace_init + (1 - win2_mask) * s1
# step 9
img_est = ifftnc(full_kspace)
if return_all_estimates:
all_img_est.append(img_est)
if return_all_estimates:
return all_img_est
return img_est
def test_DWT_masked(xp, order, decimation):
rstate = xp.random.RandomState(5)
c = rstate.randn(128, 128)
# generate a random image-domain mask
# im_mask = xp.random.standard_normal(c.shape) > -0.2
# test 1D in/outputs but using masked values for the input array
im_mask = xp.ones(c.shape, dtype=xp.bool)
im_mask[16:64, 16:64] = 0 # mask out a region
c_masked = masker(c, im_mask, order=order)
fb = filters.pywt_as_filterbank("db2", xp=xp, decimation=decimation)
Wm = MDWT_Operator(
c.shape,
level=2,
filterbank=fb,
order=order,
mode="periodization",
mask_in=im_mask,
mask_out=None,
nd_input=False,
nd_output=False,
random_shift=True,
**get_loc(xp),
)
coeffs = Wm * c_masked
assert_(coeffs.ndim == 1)
if decimation == 2:
assert_(coeffs.size == c.size)
coeffs = coeffs.reshape(c.shape, order=order)
else:
assert_(coeffs.size > c.size)
c_recon = Wm.H * coeffs
assert_(c_recon.ndim == 1)
if xp is np:
assert_(c_recon.size == im_mask.sum())
else:
assert_(c_recon.size == im_mask.sum().get())
c_recon = embed(c_recon, im_mask, order=order)
xp.testing.assert_allclose(c_recon, c * im_mask, rtol=1e-9, atol=1e-9)
# test 1D in/outputs but using masked values for both input and output
# arrays
coeffs_mask = coeffs != 0 # mask out regions of zero-valued coeffs
Wm2 = MDWT_Operator(
c.shape,
level=2,
filterbank=fb,
order=order,
mode="periodization",
mask_in=im_mask,
mask_out=coeffs_mask,
nd_input=False,
nd_output=False,
random_shift=True,
**get_loc(xp),
)
coeffs = Wm2 * c_masked
assert_(coeffs.ndim == 1)
if decimation == 2:
if xp is np:
assert_(coeffs.size == coeffs_mask.sum())
else:
assert_(coeffs.size == coeffs_mask.sum().get())
c_recon = Wm2.H * coeffs
c_recon = embed(c_recon, im_mask, order=order)
xp.testing.assert_allclose(c_recon, c * im_mask, rtol=1e-9, atol=1e-9)
def _test_mri_multi(
ndim=3,
N0=8,
grid_os_factor=1.5,
J0=4,
Ld=4096,
n_coils=1,
fieldmap_segments=None,
precisions=["single", "double"],
phasings=["real", "complex"],
recon_cases=["CPU,Tab0", "CPU,Tab", "CPU,Sp"],
rtol=1e-3,
compare_to_exact=False,
show_figures=False,
nufft_kwargs={},
navg_time=1,
n_creation=1,
return_errors=False,
gpu_memflags=None,
verbose=False,
return_operator=False,
spectral_offsets=None,
):
"""Run a batch of NUFFT tests."""
all_err_forward = np.zeros(
(len(recon_cases), len(precisions), len(phasings))
)
all_err_adj = np.zeros((len(recon_cases), len(precisions), len(phasings)))
alltimes = {}
if not np.isscalar(navg_time):
navg_time_cpu, navg_time_gpu = navg_time
else:
navg_time_cpu = navg_time_gpu = navg_time
for i, recon_case in enumerate(recon_cases):
if "CPU" in recon_case:
navg_time = navg_time_cpu
else:
navg_time = navg_time_gpu
for j, precision in enumerate(precisions):
for k, phasing in enumerate(phasings):
if verbose:
print(
"phasing={}, precision={}, type={}".format(
phasing, precision, recon_case
)
)
if "Tab" in recon_case:
# may want to create twice when benchmarking GPU case
# because the custom kernels are compiled the first time
ncr_max = n_creation
else:
ncr_max = 1
# on_gpu = ('GPU' in recon_case)
for ncr in range(ncr_max):
(
Gn,
wi_full,
xTrue,
ig,
data_true,
times,
) = generate_sim_data(
recon_case=recon_case,
ndim=ndim,
N0=N0,
J0=J0,
grid_os_factor=grid_os_factor,
fieldmap_segments=fieldmap_segments,
Ld=Ld,
n_coils=n_coils,
precision=precision,
phasing=phasing,
nufft_kwargs=nufft_kwargs,
MRI_object_kwargs=dict(gpu_memflags=gpu_memflags),
spectral_offsets=spectral_offsets,
)
xp = Gn.xp
# time the forward operator
sim_data = Gn * xTrue # dry run
tstart = time.time()
for nt in range(navg_time):
sim_data = Gn * xTrue
sim_data += 0.0
sim_data = xp.squeeze(sim_data) # TODO: should be 1D already?
# print("type(xTrue) = {}".format(type(xTrue)))
# print("type(sim_data) = {}".format(type(sim_data)))
t_for = (time.time() - tstart) / navg_time
times["MRI: forward"] = t_for
# time the norm operator
Gn.norm(xTrue) # dry run
tstart = time.time()
for nt in range(navg_time):
Gn.norm(xTrue)
t_norm = (time.time() - tstart) / navg_time
times["MRI: norm"] = t_norm
if precision == "single":
dtype_real = np.float32
dtype_cplx = np.complex64
else:
dtype_real = np.float64
dtype_cplx = np.complex128
if "Tab" in recon_case:
if phasing == "complex":
assert_equal(Gn.Gnufft.h[0].dtype, dtype_cplx)
else:
assert_equal(Gn.Gnufft.h[0].dtype, dtype_real)
else:
if phasing == "complex":
assert_equal(Gn.Gnufft.p.dtype, dtype_cplx)
else:
assert_equal(Gn.Gnufft.p.dtype, dtype_real)
assert_equal(sim_data.dtype, dtype_cplx)
if compare_to_exact:
# compare_to_exact only currently for single-coil,
# no fieldmap case
if spectral_offsets is not None:
raise NotImplementedError(
"compare_to_exact doesn't currently support "
"spectral offsets"
)
nshift_exact = tuple(s / 2 for s in Gn.Nd)
sim_data2 = dtft(
xTrue, Gn.omega, shape=Gn.Nd, n_shift=nshift_exact
)
sd2_norm = xp.linalg.norm(sim_data2)
rel_err = xp.linalg.norm(sim_data - sim_data2) / sd2_norm
if "GPU" in recon_case:
if hasattr(rel_err, "get"):
rel_err = rel_err.get()
all_err_forward[i, j, k] = rel_err
print(
"{},{},{}: forward error = {}".format(
recon_case, precision, phasing, rel_err
)
)
rel_err_mag = (
xp.linalg.norm(np.abs(sim_data) - np.abs(sim_data2))
/ sd2_norm
)
print(
f"{recon_case},{precision},{phasing}: "
f"forward mag diff error = {rel_err_mag}"
)
assert rel_err < rtol
# TODO: update DiagonalOperatorMulti to auto-set loc_in,
# loc_out appropriately
if xp is np:
diag_args = dict(loc_in="cpu", loc_out="cpu")
else:
diag_args = dict(loc_in="gpu", loc_out="gpu")
diag_op = DiagonalOperatorMulti(wi_full, **diag_args)
if n_coils == 1:
data_dcf = diag_op * data_true
else:
data_dcf = diag_op * sim_data
# time the adjoint operation
im_est = Gn.H * data_dcf # dry run
tstart = time.time()
for nt in range(navg_time):
im_est = Gn.H * data_dcf
t_adj = (time.time() - tstart) / navg_time
times["MRI: adjoint"] = t_adj
if hasattr(Gn, "mask") and Gn.mask is not None:
im_est = embed(im_est, Gn.mask)
else:
if spectral_offsets is None:
im_est = im_est.reshape(Gn.Nd, order=Gn.order)
else:
im_est = im_est.reshape(
tuple(Gn.Nd) + (len(spectral_offsets),),
order=Gn.order,
)
if compare_to_exact:
im_est_exact = dtft_adj(
data_dcf, Gn.omega, shape=Gn.Nd, n_shift=nshift_exact
)
ex_norm = xp.linalg.norm(im_est_exact)
rel_err = xp.linalg.norm(im_est - im_est_exact) / ex_norm
all_err_adj[i, j, k] = rel_err
if verbose:
print(
"{},{},{}: adjoint error = {}".format(
recon_case, precision, phasing, rel_err
)
)
rel_err_mag = (
xp.linalg.norm(np.abs(im_est) - np.abs(im_est_exact))
/ ex_norm
)
if verbose:
print(
"{},{},{}: adjoint mag diff error = {}".format(
recon_case, precision, phasing, rel_err
)
)
assert_(rel_err < rtol)
title = ", ".join([recon_case, precision, phasing])
if show_figures:
from matplotlib import pyplot as plt
from pyvolplot import volshow
if compare_to_exact:
volshow(
[
im_est_exact,
im_est,
im_est_exact - im_est,
xp.abs(im_est_exact) - xp.abs(im_est),
]
)
else:
volshow(im_est)
plt.title(title)
alltimes[title] = times
if return_operator:
if return_errors:
return Gn, alltimes, all_err_forward, all_err_adj
return Gn, alltimes
if return_errors:
return alltimes, all_err_forward, all_err_adj
return alltimes
