def test_3d_mrisensenufft_adjoint_backward():
dtype = torch.double
nslice = 2
ncoil = 4
im_size = (11, 33, 24)
klength = 112
x = np.random.normal(size=(nslice, 1) + im_size) + \
1j*np.random.normal(size=(nslice, 1) + 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)
smap_sz = (nslice, ncoil, 2) + im_size
smap = torch.randn(*smap_sz).to(dtype)
sensenufft_ob = MriSenseNufft(smap=smap, im_size=im_size)
adjsensenufft_ob = AdjMriSenseNufft(smap=smap, im_size=im_size)
y.requires_grad = True
x = adjsensenufft_ob.forward(y, ktraj)
((x**2) / 2).sum().backward()
y_grad = y.grad.clone().detach()
y_hat = sensenufft_ob.forward(x.clone().detach(), ktraj)
assert torch.norm(y_grad - y_hat) < norm_tol
def test_mrisensenufft_3d_coilpack_adjoint(
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"]
smap = params_2d["smap"]
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)
sensenufft_ob = MriSenseNufft(
smap=smap, im_size=im_size, numpoints=numpoints, coilpack=True
).to(dtype=dtype, device=device)
adjsensenufft_ob = AdjMriSenseNufft(
smap=smap, im_size=im_size, numpoints=numpoints, coilpack=True
).to(dtype=dtype, device=device)
x_forw = sensenufft_ob(x, ktraj)
y_back = adjsensenufft_ob(y, ktraj)
inprod1 = inner_product(y, x_forw, dim=2)
inprod2 = inner_product(y_back, x, dim=2)
assert torch.norm(inprod1 - inprod2) < norm_tol
def test_mrisensenufft_2d_adjoint():
dtype = torch.double
nslice = 2
ncoil = 4
im_size = (33, 24)
klength = 112
x = np.random.normal(size=(nslice, 1) + im_size) + \
1j*np.random.normal(size=(nslice, 1) + 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)
smap_sz = (nslice, ncoil, 2) + im_size
smap = torch.randn(*smap_sz).to(dtype)
sensenufft_ob = MriSenseNufft(smap=smap, im_size=im_size)
adjsensenufft_ob = AdjMriSenseNufft(smap=smap, im_size=im_size)
x_forw = sensenufft_ob(x, ktraj)
y_back = adjsensenufft_ob(y, ktraj)
inprod1 = inner_product(y, x_forw, dim=2)
inprod2 = inner_product(y_back, x, dim=2)
assert torch.norm(inprod1 - inprod2) < norm_tol
def test_mrisensenufft_3d_adjoint():
dtype = torch.double
nslice = 2
ncoil = 4
im_size = (11, 33, 24)
klength = 112
x = np.random.normal(size=(nslice, 1) + im_size) + \
1j*np.random.normal(size=(nslice, 1) + 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)
smap_sz = (nslice, ncoil, 2) + im_size
smap = torch.randn(*smap_sz).to(dtype)
sensenufft_ob = MriSenseNufft(smap=smap, im_size=im_size)
adjsensenufft_ob = AdjMriSenseNufft(smap=smap, im_size=im_size)
real_mat, imag_mat = precomp_sparse_mats(ktraj, sensenufft_ob)
interp_mats = {'real_interp_mats': real_mat, 'imag_interp_mats': imag_mat}
x_forw = sensenufft_ob(x, ktraj, interp_mats)
y_back = adjsensenufft_ob(y, ktraj, interp_mats)
inprod1 = inner_product(y, x_forw, dim=2)
inprod2 = inner_product(y_back, x, dim=2)
assert torch.norm(inprod1 - inprod2) < norm_tol
def test_3d_mrisensenufft_coilpack_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']
smap = params_2d['smap']
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)
sensenufft_ob = MriSenseNufft(smap=smap,
im_size=im_size,
numpoints=numpoints,
coilpack=True).to(dtype=dtype,
device=device)
adjsensenufft_ob = AdjMriSenseNufft(smap=smap,
im_size=im_size,
numpoints=numpoints,
coilpack=True).to(dtype=dtype,
device=device)
real_mat, imag_mat = precomp_sparse_mats(ktraj, sensenufft_ob)
interp_mats = {
'real_interp_mats': real_mat,
'imag_interp_mats': imag_mat
}
x.requires_grad = True
y = sensenufft_ob.forward(x, ktraj, interp_mats)
((y**2) / 2).sum().backward()
x_grad = x.grad.clone().detach()
x_hat = adjsensenufft_ob.forward(y.clone().detach(), ktraj,
interp_mats)
assert torch.norm(x_grad - x_hat) < norm_tol
def test_3d_mrisensenufft_coilpack_adjoint_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"]
smap = params_2d["smap"]
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)
sensenufft_ob = MriSenseNufft(smap=smap,
im_size=im_size,
numpoints=numpoints,
coilpack=True).to(dtype=dtype,
device=device)
adjsensenufft_ob = AdjMriSenseNufft(smap=smap,
im_size=im_size,
numpoints=numpoints,
coilpack=True).to(dtype=dtype,
device=device)
real_mat, imag_mat = precomp_sparse_mats(ktraj, sensenufft_ob)
interp_mats = {
"real_interp_mats": real_mat,
"imag_interp_mats": imag_mat
}
y.requires_grad = True
x = adjsensenufft_ob.forward(y, ktraj, interp_mats)
((x**2) / 2).sum().backward()
y_grad = y.grad.clone().detach()
y_hat = sensenufft_ob.forward(x.clone().detach(), ktraj, interp_mats)
assert torch.norm(y_grad - y_hat) < norm_tol
def test_3d_mrisensenufft_coilpack_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"]
smap = params_2d["smap"]
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)
sensenufft_ob = MriSenseNufft(smap=smap,
im_size=im_size,
numpoints=numpoints,
coilpack=True).to(dtype=dtype,
device=device)
adjsensenufft_ob = AdjMriSenseNufft(smap=smap,
im_size=im_size,
numpoints=numpoints,
coilpack=True).to(dtype=dtype,
device=device)
x.requires_grad = True
y = sensenufft_ob.forward(x, ktraj)
((y**2) / 2).sum().backward()
x_grad = x.grad.clone().detach()
x_hat = adjsensenufft_ob.forward(y.clone().detach(), ktraj)
assert torch.norm(x_grad - x_hat) < norm_tol
def test_3d_mrisensenufft_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"]
smap = params_3d["smap"]
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)
sensenufft_ob = MriSenseNufft(smap=smap,
im_size=im_size,
numpoints=numpoints).to(dtype=dtype,
device=device)
adjsensenufft_ob = AdjMriSenseNufft(smap=smap,
im_size=im_size,
numpoints=numpoints).to(
dtype=dtype, device=device)
y.requires_grad = True
x = adjsensenufft_ob.forward(y, ktraj)
((x**2) / 2).sum().backward()
y_grad = y.grad.clone().detach()
y_hat = sensenufft_ob.forward(x.clone().detach(), ktraj)
assert torch.norm(y_grad - y_hat) < norm_tol
def test_3d_mrisensenufft_backward():
dtype = torch.double
nslice = 2
ncoil = 4
im_size = (11, 33, 24)
klength = 112
x = np.random.normal(size=(nslice, 1) + im_size) + \
1j*np.random.normal(size=(nslice, 1) + 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)
smap_sz = (nslice, ncoil, 2) + im_size
smap = torch.randn(*smap_sz).to(dtype)
sensenufft_ob = MriSenseNufft(smap=smap, im_size=im_size)
adjsensenufft_ob = AdjMriSenseNufft(smap=smap, im_size=im_size)
real_mat, imag_mat = precomp_sparse_mats(ktraj, sensenufft_ob)
interp_mats = {'real_interp_mats': real_mat, 'imag_interp_mats': imag_mat}
x.requires_grad = True
y = sensenufft_ob.forward(x, ktraj, interp_mats)
((y**2) / 2).sum().backward()
x_grad = x.grad.clone().detach()
x_hat = adjsensenufft_ob.forward(y.clone().detach(), ktraj, interp_mats)
assert torch.norm(x_grad - x_hat) < norm_tol
def test_mrisensenufft_3d_coilpack_adjoint(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']
smap = params_2d['smap']
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)
sensenufft_ob = MriSenseNufft(smap=smap,
im_size=im_size,
numpoints=numpoints,
coilpack=True).to(dtype=dtype,
device=device)
adjsensenufft_ob = AdjMriSenseNufft(smap=smap,
im_size=im_size,
numpoints=numpoints,
coilpack=True).to(dtype=dtype,
device=device)
real_mat, imag_mat = precomp_sparse_mats(ktraj, sensenufft_ob)
interp_mats = {
'real_interp_mats': real_mat,
'imag_interp_mats': imag_mat
}
x_forw = sensenufft_ob(x, ktraj, interp_mats)
y_back = adjsensenufft_ob(y, ktraj, interp_mats)
inprod1 = inner_product(y, x_forw, dim=2)
inprod2 = inner_product(y_back, x, dim=2)
assert torch.norm(inprod1 - inprod2) < norm_tol
def test_mrisensenufft_3d_adjoint(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"]
smap = params_3d["smap"]
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)
sensenufft_ob = MriSenseNufft(smap=smap,
im_size=im_size,
numpoints=numpoints).to(dtype=dtype,
device=device)
adjsensenufft_ob = AdjMriSenseNufft(smap=smap,
im_size=im_size,
numpoints=numpoints).to(
dtype=dtype, device=device)
real_mat, imag_mat = precomp_sparse_mats(ktraj, sensenufft_ob)
interp_mats = {
"real_interp_mats": real_mat,
"imag_interp_mats": imag_mat
}
x_forw = sensenufft_ob(x, ktraj, interp_mats)
y_back = adjsensenufft_ob(y, ktraj, interp_mats)
inprod1 = inner_product(y, x_forw, dim=2)
inprod2 = inner_product(y_back, x, dim=2)
assert torch.norm(inprod1 - inprod2) < norm_tol
def test_kb_matching(testing_tol):
norm_tol = testing_tol
def check_tables(table1, table2):
for ind, table in enumerate(table1):
assert np.linalg.norm(table - table2[ind]) < norm_tol
im_szs = [(256, 256), (10, 256, 256)]
kbwidths = [2.34, 5]
orders = [0, 2]
for kbwidth in kbwidths:
for order in orders:
for im_sz in im_szs:
smap = torch.randn(*((1,) + im_sz))
base_table = AdjKbNufft(
im_sz, order=order, kbwidth=kbwidth).table
cur_table = KbNufft(im_sz, order=order, kbwidth=kbwidth).table
check_tables(base_table, cur_table)
cur_table = KbInterpBack(
im_sz, order=order, kbwidth=kbwidth).table
check_tables(base_table, cur_table)
cur_table = KbInterpForw(
im_sz, order=order, kbwidth=kbwidth).table
check_tables(base_table, cur_table)
cur_table = MriSenseNufft(
smap, im_sz, order=order, kbwidth=kbwidth).table
check_tables(base_table, cur_table)
cur_table = AdjMriSenseNufft(
smap, im_sz, order=order, kbwidth=kbwidth).table
check_tables(base_table, cur_table)
def test_toeplitz_mrisensenufft_2d(params_2d, testing_tol, testing_dtype, device_list):
dtype = testing_dtype
# this tolerance looks really bad, but toep struggles with random traj
# for radial it's more like 1e-06
norm_tol = 1e-3
im_size = params_2d["im_size"]
numpoints = params_2d["numpoints"]
x = params_2d["x"]
y = params_2d["y"]
ktraj = params_2d["ktraj"]
smap = params_2d["smap"]
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)
sensenufft_ob = MriSenseNufft(
smap=smap, im_size=im_size, numpoints=numpoints
).to(dtype=dtype, device=device)
adjsensenufft_ob = AdjMriSenseNufft(
smap=smap, im_size=im_size, numpoints=numpoints
).to(dtype=dtype, device=device)
toep_ob = ToepSenseNufft(smap=smap).to(dtype=dtype, device=device)
kern = calc_toep_kernel(adjsensenufft_ob, ktraj)
normal_forw = adjsensenufft_ob(sensenufft_ob(x, ktraj), ktraj)
toep_forw = toep_ob(x, kern)
diff = torch.norm(normal_forw - toep_forw) / torch.norm(normal_forw)
assert diff < norm_tol
def test_2d_init_inputs():
# all object initializations have assertions
# this should result in an error if any dimensions don't match
# test 2d scalar inputs
im_sz = (256, 256)
smap = torch.randn(*((1,) + im_sz))
grid_sz = (512, 512)
n_shift = (128, 128)
numpoints = 6
table_oversamp = 2 ** 10
kbwidth = 2.34
order = 0
norm = "None"
ob = KbInterpForw(
im_size=im_sz,
grid_size=grid_sz,
n_shift=n_shift,
numpoints=numpoints,
table_oversamp=table_oversamp,
kbwidth=kbwidth,
order=order,
)
ob = KbInterpBack(
im_size=im_sz,
grid_size=grid_sz,
n_shift=n_shift,
numpoints=numpoints,
table_oversamp=table_oversamp,
kbwidth=kbwidth,
order=order,
)
ob = KbNufft(
im_size=im_sz,
grid_size=grid_sz,
n_shift=n_shift,
numpoints=numpoints,
table_oversamp=table_oversamp,
kbwidth=kbwidth,
order=order,
norm=norm,
)
ob = AdjKbNufft(
im_size=im_sz,
grid_size=grid_sz,
n_shift=n_shift,
numpoints=numpoints,
table_oversamp=table_oversamp,
kbwidth=kbwidth,
order=order,
norm=norm,
)
ob = MriSenseNufft(
smap=smap,
im_size=im_sz,
grid_size=grid_sz,
n_shift=n_shift,
numpoints=numpoints,
table_oversamp=table_oversamp,
kbwidth=kbwidth,
order=order,
norm=norm,
)
ob = AdjMriSenseNufft(
smap=smap,
im_size=im_sz,
grid_size=grid_sz,
n_shift=n_shift,
numpoints=numpoints,
table_oversamp=table_oversamp,
kbwidth=kbwidth,
order=order,
norm=norm,
)
# test 2d tuple inputs
im_sz = (256, 256)
smap = torch.randn(*((1,) + im_sz))
grid_sz = (512, 512)
n_shift = (128, 128)
numpoints = (6, 6)
table_oversamp = (2 ** 10, 2 ** 10)
kbwidth = (2.34, 2.34)
order = (0, 0)
norm = "None"
ob = KbInterpForw(
im_size=im_sz,
grid_size=grid_sz,
n_shift=n_shift,
numpoints=numpoints,
table_oversamp=table_oversamp,
kbwidth=kbwidth,
order=order,
)
ob = KbInterpBack(
im_size=im_sz,
grid_size=grid_sz,
n_shift=n_shift,
numpoints=numpoints,
table_oversamp=table_oversamp,
kbwidth=kbwidth,
order=order,
)
ob = KbNufft(
im_size=im_sz,
grid_size=grid_sz,
n_shift=n_shift,
numpoints=numpoints,
table_oversamp=table_oversamp,
kbwidth=kbwidth,
order=order,
norm=norm,
)
ob = AdjKbNufft(
im_size=im_sz,
grid_size=grid_sz,
n_shift=n_shift,
numpoints=numpoints,
table_oversamp=table_oversamp,
kbwidth=kbwidth,
order=order,
norm=norm,
)
ob = MriSenseNufft(
smap=smap,
im_size=im_sz,
grid_size=grid_sz,
n_shift=n_shift,
numpoints=numpoints,
table_oversamp=table_oversamp,
kbwidth=kbwidth,
order=order,
norm=norm,
)
ob = AdjMriSenseNufft(
smap=smap,
im_size=im_sz,
grid_size=grid_sz,
n_shift=n_shift,
numpoints=numpoints,
table_oversamp=table_oversamp,
kbwidth=kbwidth,
order=order,
norm=norm,
)
def profile_torchkbnufft(image,
ktraj,
smap,
im_size,
device,
sparse_mats_flag=False,
use_toep=False):
# run double precision for CPU, float for GPU
# these seem to be present in reference implementations
if device == torch.device("cpu"):
dtype = torch.double
if use_toep:
num_nuffts = 20
else:
num_nuffts = 5
else:
dtype = torch.float
if use_toep:
num_nuffts = 50
else:
num_nuffts = 20
cpudevice = torch.device("cpu")
image = image.to(dtype=dtype)
ktraj = ktraj.to(dtype=dtype)
smap = smap.to(dtype=dtype)
kbsense_ob = MriSenseNufft(smap=smap, im_size=im_size).to(dtype=dtype,
device=device)
adjkbsense_ob = AdjMriSenseNufft(smap=smap,
im_size=im_size).to(dtype=dtype,
device=device)
adjkbnufft_ob = AdjKbNufft(im_size=im_size).to(dtype=dtype, device=device)
# precompute toeplitz kernel if using toeplitz
if use_toep:
print("using toeplitz for forward/backward")
kern = calc_toep_kernel(adjkbsense_ob, ktraj)
toep_ob = ToepSenseNufft(smap=smap).to(dtype=dtype, device=device)
# precompute the sparse interpolation matrices
if sparse_mats_flag:
print("using sparse interpolation matrices")
real_mat, imag_mat = precomp_sparse_mats(ktraj, adjkbnufft_ob)
interp_mats = {
"real_interp_mats": real_mat,
"imag_interp_mats": imag_mat
}
else:
print("not using sparse interpolation matrices")
interp_mats = None
if use_toep:
# warm-up computation
for _ in range(num_nuffts):
x = toep_ob(image.to(device=device),
kern.to(device=device)).to(cpudevice)
# run the speed tests
if device == torch.device("cuda"):
torch.cuda.reset_max_memory_allocated()
torch.cuda.synchronize()
start_time = time.perf_counter()
for _ in range(num_nuffts):
x = toep_ob(image.to(device=device), kern.to(device=device))
if device == torch.device("cuda"):
torch.cuda.synchronize()
max_mem = torch.cuda.max_memory_allocated()
print("GPU forward max memory: {} GB".format(max_mem / 1e9))
end_time = time.perf_counter()
avg_time = (end_time - start_time) / num_nuffts
print("toeplitz forward/backward average time: {}".format(avg_time))
else:
# warm-up computation
for _ in range(num_nuffts):
y = kbsense_ob(image.to(device=device), ktraj.to(device=device),
interp_mats).to(cpudevice)
# run the forward speed tests
if device == torch.device("cuda"):
torch.cuda.reset_max_memory_allocated()
torch.cuda.synchronize()
start_time = time.perf_counter()
for _ in range(num_nuffts):
y = kbsense_ob(image.to(device=device), ktraj.to(device=device),
interp_mats)
if device == torch.device("cuda"):
torch.cuda.synchronize()
max_mem = torch.cuda.max_memory_allocated()
print("GPU forward max memory: {} GB".format(max_mem / 1e9))
end_time = time.perf_counter()
avg_time = (end_time - start_time) / num_nuffts
print("forward average time: {}".format(avg_time))
# warm-up computation
for _ in range(num_nuffts):
x = adjkbsense_ob(y.to(device), ktraj.to(device), interp_mats)
# run the adjoint speed tests
if device == torch.device("cuda"):
torch.cuda.reset_max_memory_allocated()
torch.cuda.synchronize()
start_time = time.perf_counter()
for _ in range(num_nuffts):
x = adjkbsense_ob(y.to(device), ktraj.to(device), interp_mats)
if device == torch.device("cuda"):
torch.cuda.synchronize()
max_mem = torch.cuda.max_memory_allocated()
print("GPU adjoint max memory: {} GB".format(max_mem / 1e9))
end_time = time.perf_counter()
avg_time = (end_time - start_time) / num_nuffts
print("backward average time: {}".format(avg_time))
def main():
dtype = torch.double
spokelength = 512
targ_size = (int(spokelength/2), int(spokelength/2))
nspokes = 405
image = shepp_logan_phantom().astype(np.complex)
im_size = image.shape
grid_size = tuple(2 * np.array(im_size))
# convert the phantom to a tensor and unsqueeze coil and batch dimension
image = np.stack((np.real(image), np.imag(image)))
image = torch.tensor(image).to(dtype).unsqueeze(0).unsqueeze(0)
# create k-space trajectory
ga = np.deg2rad(180 / ((1 + np.sqrt(5)) / 2))
kx = np.zeros(shape=(spokelength, nspokes))
ky = np.zeros(shape=(spokelength, nspokes))
kmax = np.pi * ((spokelength/2) / im_size[0])
ky[:, 0] = np.linspace(-kmax, kmax, spokelength)
for i in range(1, nspokes):
kx[:, i] = np.cos(ga) * kx[:, i - 1] - np.sin(ga) * ky[:, i - 1]
ky[:, i] = np.sin(ga) * kx[:, i - 1] + np.cos(ga) * ky[:, i - 1]
ky = np.transpose(ky)
kx = np.transpose(kx)
ktraj = np.stack((ky.flatten(), kx.flatten()), axis=0)
ktraj = torch.tensor(ktraj).to(dtype).unsqueeze(0)
# sensitivity maps
ncoil = 8
smap = np.absolute(np.stack(mrisensesim(
im_size, coil_width=64))).astype(np.complex)
smap = np.stack((np.real(smap), np.imag(smap)), axis=1)
smap = torch.tensor(smap).to(dtype).unsqueeze(0)
# operators
sensenufft_ob = MriSenseNufft(
smap=smap, im_size=im_size, grid_size=grid_size).to(dtype)
kdata = sensenufft_ob(image, ktraj)
kdata = np.squeeze(kdata.numpy())
kdata = np.reshape(kdata[:, 0] + 1j*kdata[:, 1],
(ncoil, nspokes, spokelength))
ktraj = np.squeeze(ktraj.numpy())
ktraj = ktraj / np.max(ktraj) * np.pi
ktraj = np.reshape(ktraj, (2, nspokes, spokelength))
smap = np.squeeze(smap.numpy())
smap = smap[:, 0] + 1j*smap[:, 1]
smap_new = []
for coilind in range(smap.shape[0]):
smap_new.append(
resize(np.real(smap[coilind]), targ_size) +
1j*resize(np.imag(smap[coilind]), targ_size)
)
smap_new = np.array(smap_new)
data = {
'kdata': kdata,
'ktraj': ktraj,
'smap': smap_new
}
sio.savemat('demo_data.mat', data)
def __init__(self, im_size, ktraj, dcomp, csmap, norm='ortho'):
super(Dyn2DRadEncObj, self).__init__()
"""
inputs:
- im_size ... the shape of the object to be imaged
- ktraj ... the k-space tractories (torch tensor)
- csmap ... the coil-sensivity maps (torch tensor)
- dcomp ... the density compensation (torch tensor)
N.B. the shapes for the tensors are the following:
image (1,1,2,Nx,Ny,Nt),
ktraj (1,2,Nrad,Nt),
csmap (1,Nc,2,Nx,Ny),
dcomp (1,1,1,Nrad,Nt),
kdata (1,Nc,2,Nrad,Nt),
where
- Nx,Ny,Nt = im_size
- Nrad = 2*Ny*n_spokes
- n_spokes = the number of spokes per 2D frame
- Nc = the number of receiver coils
"""
dtype = torch.float
Nx, Ny, Nt = im_size
self.im_size = im_size
self.spokelength = im_size[1] * 2
self.Nrad = ktraj.shape[2]
self.ktraj_tensor = ktraj
self.dcomp_tensor = dcomp
#parameters for contstructing the operators
spokelength = im_size[1] * 2
grid_size = (spokelength, spokelength)
#single-coil/multi-coil NUFFTs
if csmap is not None:
self.NUFFT = MriSenseNufft(smap=csmap,
im_size=im_size[:2],
grid_size=grid_size,
norm=norm).to(dtype)
self.AdjNUFFT = AdjMriSenseNufft(smap=csmap,
im_size=im_size[:2],
grid_size=grid_size,
norm=norm).to(dtype)
self.ToepNUFFT = ToepSenseNufft(csmap).to(dtype)
else:
self.NUFFT = KbNufft(im_size=im_size[:2],
grid_size=grid_size,
norm=norm).to(dtype)
self.AdjNUFFT = AdjKbNufft(im_size=im_size[:2],
grid_size=grid_size,
norm=norm).to(dtype)
self.ToepNUFFT = ToepNufft().to(dtype)
#calculate Toeplitz kernels
# for E^{\dagger} \circ E
self.AdagA_toep_kernel_list = [
calc_toep_kernel(self.AdjNUFFT,
ktraj[..., kt],
weights=dcomp[..., kt]) for kt in range(Nt)
]
# for E^H \circ E
self.AHA_toep_kernel_list = [
calc_toep_kernel(self.AdjNUFFT, ktraj[..., kt]) for kt in range(Nt)
]