def test_nufft_adjoint(self):
# Check deltas
oshape = [3]
input = np.array([1.0, 1.0, 1.0], dtype=np.complex) / 3**0.5
coord = np.array([[-1], [0], [1]], np.float)
npt.assert_allclose(fourier.nufft_adjoint(input, coord, oshape),
np.array([0, 1, 0]),
atol=0.01,
rtol=0.01)
oshape = [4]
input = np.array([1.0, 1.0, 1.0, 1.0], dtype=np.complex) / 4**0.5
coord = np.array([[-2], [-1], [0], [1]], np.float)
npt.assert_allclose(fourier.nufft_adjoint(input, coord, oshape),
np.array([0, 0, 1, 0], np.complex),
atol=0.01,
rtol=0.01)
oshape = [5]
input = np.ones(5, dtype=np.complex) / 5**0.5
coord = np.array([[-2], [-1], [0], [1], [2]], np.float)
npt.assert_allclose(fourier.nufft_adjoint(input, coord, oshape),
np.array([0, 0, 1, 0, 0], np.complex),
atol=0.01,
rtol=0.01)
# Check shifted delta
oshape = [3]
w = np.exp(-1j * 2.0 * np.pi / 3.0)
input = np.array([w.conjugate(), 1.0, w]) / 3**0.5
coord = np.array([[-1], [0], [1]], np.float)
npt.assert_allclose(fourier.nufft_adjoint(input, coord, oshape),
np.array([0, 0, 1], np.complex),
atol=0.01,
rtol=0.01)
oshape = [4]
w = np.exp(-1j * 2.0 * np.pi / 4.0)
input = np.array([w.conjugate()**2, w.conjugate(), 1.0, w]) / 4**0.5
coord = np.array([[-2], [-1], [0], [1]], np.float)
npt.assert_allclose(fourier.nufft_adjoint(input, coord, oshape),
np.array([0, 0, 0, 1], np.complex),
atol=0.01,
rtol=0.01)
def _apply(self, input):
return fourier.nufft_adjoint(input,
self.coord,
self.oshape,
oversamp=self.oversamp,
width=self.width,
n=self.n)
def _apply(self, input):
device = backend.get_device(input)
with device:
coord = backend.to_device(self.coord, device)
return fourier.nufft_adjoint(
input, coord, self.oshape,
oversamp=self.oversamp, width=self.width)
def test_nufft_adjoint_nd(self):
oshape = [3, 1]
input = np.array([1.0, 1.0, 1.0], dtype=np.complex) / 3**0.5
coord = np.array([[-1, 0], [0, 0], [1, 0]], np.float)
npt.assert_allclose(fourier.nufft_adjoint(input, coord, oshape),
np.array([[0], [1], [0]], np.complex),
atol=0.01,
rtol=0.01)
def test_nufft_normal(self):
# Check delta
oshape = [3]
input = np.array([0.0, 1.0, 0.0], dtype=np.complex)
coord = np.array([[-1], [0], [1]], np.float)
npt.assert_allclose(fourier.nufft_adjoint(fourier.nufft(input, coord),
coord, oshape),
np.array([0, 1, 0]),
atol=0.01,
rtol=0.01)
# Check delta scale
oshape = [3]
input = np.array([0.0, 1.0, 0.0], dtype=np.complex)
coord = np.array([[-1], [-0.5], [0], [0.5], [1]], np.float)
npt.assert_allclose(fourier.nufft_adjoint(fourier.nufft(input,
coord), coord,
oshape)[len(input) // 2],
5 / 3,
atol=0.01,
rtol=0.01)
elif trajectory == 'spiral':
traj = Spiral(FOV=FOV,
res=res,
oversampling=2,
lines_per_shot=2,
interleaves=10)
# traj.plot_trajectory()
# Non-cartesian kspace
K = TrajToImage(traj.points, 1000.0 * traj.times, Mxy, r, 50.0)
# Non-uniform fft
x0 = traj.points[0].flatten().reshape((-1, 1))
x1 = traj.points[1].flatten().reshape((-1, 1))
x0 *= res[0] // 2 / x0.max()
x1 *= res[1] // 2 / x1.max()
dcf = (x0**2 + x1**2)**0.5 # density compensation function
kxky = np.concatenate((x0, x1), axis=1) # flattened kspace coordinates
y = K.flatten().reshape((-1, 1)) # flattened kspace measures
image = nufft_adjoint(y * dcf, kxky, res) # inverse nufft
# Show results
fig, axs = plt.subplots(2, 3, figsize=(10, 10))
axs[0, 0].imshow(np.abs(K_c[::2, :]))
axs[0, 1].imshow(np.abs(ktoi(K_c[::2, :])))
axs[0, 2].imshow(np.angle(ktoi(K_c[::2, :])))
axs[1, 0].imshow(np.abs(itok(image)))
axs[1, 1].imshow(np.abs(image))
axs[1, 2].imshow(np.angle(image))
plt.show()
