def test_2d_kbnufft_backward(params_2d, testing_tol, testing_dtype,
device_list):
dtype = testing_dtype
norm_tol = testing_tol
im_size = params_2d["im_size"]
numpoints = params_2d["numpoints"]
x = params_2d["x"]
y = params_2d["y"]
ktraj = params_2d["ktraj"]
for device in device_list:
x = x.detach().to(dtype=dtype, device=device)
y = y.detach().to(dtype=dtype, device=device)
ktraj = ktraj.detach().to(dtype=dtype, device=device)
kbnufft_ob = KbNufft(im_size=im_size,
numpoints=numpoints).to(dtype=dtype,
device=device)
adjkbnufft_ob = AdjKbNufft(im_size=im_size,
numpoints=numpoints).to(dtype=dtype,
device=device)
x.requires_grad = True
y = kbnufft_ob.forward(x, ktraj)
((y**2) / 2).sum().backward()
x_grad = x.grad.clone().detach()
x_hat = adjkbnufft_ob.forward(y.clone().detach(), ktraj)
assert torch.norm(x_grad - x_hat) < norm_tol
def test_2d_kbnufft_backward():
dtype = torch.double
nslice = 2
ncoil = 4
im_size = (33, 24)
klength = 112
x = np.random.normal(size=(nslice, ncoil) + im_size) + \
1j*np.random.normal(size=(nslice, ncoil) + im_size)
x = torch.tensor(np.stack((np.real(x), np.imag(x)), axis=2)).to(dtype)
y = np.random.normal(size=(nslice, ncoil, klength)) + \
1j*np.random.normal(size=(nslice, ncoil, klength))
y = torch.tensor(np.stack((np.real(y), np.imag(y)), axis=2)).to(dtype)
ktraj = torch.randn(*(nslice, 2, klength)).to(dtype)
kbnufft_ob = KbNufft(im_size=im_size, numpoints=(4, 6))
adjkbnufft_ob = AdjKbNufft(im_size=im_size, numpoints=(4, 6))
x.requires_grad = True
y = kbnufft_ob.forward(x, ktraj)
((y**2) / 2).sum().backward()
x_grad = x.grad.clone().detach()
x_hat = adjkbnufft_ob.forward(y.clone().detach(), ktraj)
assert torch.norm(x_grad - x_hat) < norm_tol
def test_3d_kbnufft_adjoint_backward():
dtype = torch.double
nslice = 2
ncoil = 4
im_size = (11, 33, 24)
klength = 112
x = np.random.normal(size=(nslice, ncoil) + im_size) + \
1j*np.random.normal(size=(nslice, ncoil) + im_size)
x = torch.tensor(np.stack((np.real(x), np.imag(x)), axis=2)).to(dtype)
y = np.random.normal(size=(nslice, ncoil, klength)) + \
1j*np.random.normal(size=(nslice, ncoil, klength))
y = torch.tensor(np.stack((np.real(y), np.imag(y)), axis=2)).to(dtype)
ktraj = torch.randn(*(nslice, 3, klength)).to(dtype)
kbnufft_ob = KbNufft(im_size=im_size, numpoints=(2, 4, 6))
adjkbnufft_ob = AdjKbNufft(im_size=im_size, numpoints=(2, 4, 6))
real_mat, imag_mat = precomp_sparse_mats(ktraj, kbnufft_ob)
interp_mats = {'real_interp_mats': real_mat, 'imag_interp_mats': imag_mat}
y.requires_grad = True
x = adjkbnufft_ob.forward(y, ktraj, interp_mats)
((x**2) / 2).sum().backward()
y_grad = y.grad.clone().detach()
y_hat = kbnufft_ob.forward(x.clone().detach(), ktraj, interp_mats)
assert torch.norm(y_grad - y_hat) < norm_tol
def test_3d_kbnufft_adjoint_backward(params_3d, testing_tol, testing_dtype,
device_list):
dtype = testing_dtype
norm_tol = testing_tol
im_size = params_3d["im_size"]
numpoints = params_3d["numpoints"]
x = params_3d["x"]
y = params_3d["y"]
ktraj = params_3d["ktraj"]
for device in device_list:
x = x.detach().to(dtype=dtype, device=device)
y = y.detach().to(dtype=dtype, device=device)
ktraj = ktraj.detach().to(dtype=dtype, device=device)
kbnufft_ob = KbNufft(im_size=im_size,
numpoints=numpoints).to(dtype=dtype,
device=device)
adjkbnufft_ob = AdjKbNufft(im_size=im_size,
numpoints=numpoints).to(dtype=dtype,
device=device)
real_mat, imag_mat = precomp_sparse_mats(ktraj, kbnufft_ob)
interp_mats = {
"real_interp_mats": real_mat,
"imag_interp_mats": imag_mat
}
y.requires_grad = True
x = adjkbnufft_ob.forward(y, ktraj, interp_mats)
((x**2) / 2).sum().backward()
y_grad = y.grad.clone().detach()
y_hat = kbnufft_ob.forward(x.clone().detach(), ktraj, interp_mats)
assert torch.norm(y_grad - y_hat) < norm_tol
def test_3d_kbnufft_backward(params_3d, testing_tol, testing_dtype,
device_list):
dtype = testing_dtype
norm_tol = testing_tol
im_size = params_3d['im_size']
numpoints = params_3d['numpoints']
x = params_3d['x']
y = params_3d['y']
ktraj = params_3d['ktraj']
for device in device_list:
x = x.detach().to(dtype=dtype, device=device)
y = y.detach().to(dtype=dtype, device=device)
ktraj = ktraj.detach().to(dtype=dtype, device=device)
kbnufft_ob = KbNufft(im_size=im_size,
numpoints=numpoints).to(dtype=dtype,
device=device)
adjkbnufft_ob = AdjKbNufft(im_size=im_size,
numpoints=numpoints).to(dtype=dtype,
device=device)
real_mat, imag_mat = precomp_sparse_mats(ktraj, kbnufft_ob)
interp_mats = {
'real_interp_mats': real_mat,
'imag_interp_mats': imag_mat
}
x.requires_grad = True
y = kbnufft_ob.forward(x, ktraj, interp_mats)
((y**2) / 2).sum().backward()
x_grad = x.grad.clone().detach()
x_hat = adjkbnufft_ob.forward(y.clone().detach(), ktraj, interp_mats)
assert torch.norm(x_grad - x_hat) < norm_tol