def test_adjoint_scaling(self):
vol_rn = Rn(self.geom.vol_size)
vol_rn_ones = vol_rn.element(1)
proj_rn = Rn(self.geom.proj_size)
proj_rn_ones = proj_rn.element(1)
projector = Projector(self.geom, vol_rn, proj_rn)
proj1 = projector.forward(vol_rn_ones)
vol1 = projector.backward(proj_rn_ones)
n1 = proj1.inner(proj_rn_ones)
n2 = vol_rn_ones.inner(vol1)
print('<A x, y> = <x, Ad y> : {0} = {1}'.format(n1, n2))
print('<A x, y> / <x, Ad y> - 1 = {0}'.format(n1/n2 - 1))
proj = projector.forward(vol_rn_ones)
vol = projector.backward(proj)
alpha = proj.norm()**2 / vol_rn._inner(vol, vol_rn_ones)
print alpha
projector.clear_astra_memory()
def test_parallel3d(self):
print('PARALLEL 3D')
data = ctdata.sets['parallel3d']
data.load()
print ' Data detector width:', data.detector_width_mm
print ' Data projections shape:', data.projections.shape
geom = self.geom(data, 3*(100,), 3*(100,))
projector = self.projector(geom)
# Adjoint <Ax,y>=<x,Ad y> with x[:]=1 and y[:]=1
rn_vol0 = Rn(geom.vol_size).element(1)
rn_proj0 = Rn(geom.proj_size).element(1)
rn_proj = projector.forward(rn_vol0)
rn_vol = projector.backward(rn_proj0)
l = rn_proj.inner(rn_proj0)
r = rn_vol0.inner(rn_vol)
print(' Adjoint with x[:]=1 and y[:]=1:')
print(' <Ax,y> = <x,Ad y> : {0} = {1}'.format(l, r))
print(' |<Ax,y> - <x,Ad y>| = {0}'.format(np.abs(l - r)))
print(' <Ax,y> / <x,Ad y> -1 = {0}'.format(l / r - 1))
# Back-project phantom data
rn_proj = Rn(geom.proj_size).element(data.projections.ravel())
rn_bp = projector.backward(rn_proj)
projector.clear_astra_memory()
def test_parallel3d(self):
print('PARALLEL 3D')
data = ctdata.sets['parallel3d']
data.load()
print ' Data detector width:', data.detector_width_mm
print ' Data projections shape:', data.projections.shape
geom = self.geom(data, 3 * (100, ), 3 * (100, ))
projector = self.projector(geom)
# Adjoint <Ax,y>=<x,Ad y> with x[:]=1 and y[:]=1
rn_vol0 = Rn(geom.vol_size).element(1)
rn_proj0 = Rn(geom.proj_size).element(1)
rn_proj = projector.forward(rn_vol0)
rn_vol = projector.backward(rn_proj0)
l = rn_proj.inner(rn_proj0)
r = rn_vol0.inner(rn_vol)
print(' Adjoint with x[:]=1 and y[:]=1:')
print(' <Ax,y> = <x,Ad y> : {0} = {1}'.format(l, r))
print(' |<Ax,y> - <x,Ad y>| = {0}'.format(np.abs(l - r)))
print(' <Ax,y> / <x,Ad y> -1 = {0}'.format(l / r - 1))
# Back-project phantom data
rn_proj = Rn(geom.proj_size).element(data.projections.ravel())
rn_bp = projector.backward(rn_proj)
projector.clear_astra_memory()
def test_ndim(self):
vshape = (88, 77)
vsize = np.prod(vshape)
cols = 99
angles = np.linspace(0, 2 * np.pi, 111, endpoint=False)
psize = cols * np.size(angles)
geom = Geometry(geometry_type='parallel', scale_factor=1,
volume_shape=vshape, det_col_count=cols,
det_row_count=1, angles=angles)
print 'Vol size: ', vsize
print 'Proj size:', psize
print 'Voxel size:', self.geom.voxel_size
vol_rn = Rn(vsize)
proj_rn = Rn(psize)
projector = Projector(geom, vol_rn, proj_rn)
proj = projector.forward(vol_rn.element(1))
p = proj.data.reshape(geom.proj_shape)
print 'Proj at 0 degree: max = ', p[0, :].max()
vol = projector.backward(proj_rn.element(1))
print vol.data.max()
projector.clear_astra_memory()
def test_adjoint_scaling(self):
vol_rn = Rn(self.geom.vol_size)
vol_rn_ones = vol_rn.element(1)
proj_rn = Rn(self.geom.proj_size)
proj_rn_ones = proj_rn.element(1)
projector = Projector(self.geom, vol_rn, proj_rn)
proj1 = projector.forward(vol_rn_ones)
vol1 = projector.backward(proj_rn_ones)
n1 = proj1.inner(proj_rn_ones)
n2 = vol_rn_ones.inner(vol1)
print('<A x, y> = <x, Ad y> : {0} = {1}'.format(n1, n2))
print('<A x, y> / <x, Ad y> - 1 = {0}'.format(n1 / n2 - 1))
proj = projector.forward(vol_rn_ones)
vol = projector.backward(proj)
alpha = proj.norm()**2 / vol_rn._inner(vol, vol_rn_ones)
print alpha
projector.clear_astra_memory()
def test_fanflat(self):
print('FANFLAT')
data = ctdata.sets['fanflat']
data.load()
print 'Data detector width:', data.detector_width_mm
print 'Data projections shape:', data.projections.shape
wr = data.roi_cubic_width_mm
print ' ROI width:', wr
# geom = self.geom(data, 2*(100,), 2*(np.floor(wr),))
geom = self.geom(data, 2*(100,), 2*(100,))
print ' Detector pixel width:', geom.det_col_spacing, geom.det_row_spacing
print ' Vol width:', geom.vol_width_mm
print ' Voxel width:', geom.voxel_width
projector = self.projector(geom)
# Adjoint <Ax,y>=<x,Ad y> with x[:]=1 and y[:]=1
rn_vol0 = Rn(geom.vol_size).element(1)
rn_proj0 = Rn(geom.proj_size).element(1)
rn_proj = projector.forward(rn_vol0)
rn_vol = projector.backward(rn_proj0)
l = rn_proj.inner(rn_proj0)
r = rn_vol0.inner(rn_vol)
print(' Adjoint with x[:]=1 and y[:]=1:')
print(' <Ax,y> = <x,Ad y> : {0} = {1}'.format(l, r))
print(' |<Ax,y> - <x,Ad y>| = {0}'.format(np.abs(l - r)))
print(' <Ax,y> / <x,Ad y> -1 = {0}'.format(l / r - 1))
# Back-project phantom data
rn_proj = Rn(geom.proj_size).element(data.projections.ravel())
rn_bp = projector.backward(rn_proj)
# FBP
rn_fbp = projector.fbp(rn_proj)
rec = np.reshape(rn_fbp.data, geom.vol_shape)
# plt.imshow(rec, cmap=plt.cm.Greys)
# plt.show()
projector.clear_astra_memory()
def test_fanflat(self):
print('FANFLAT')
data = ctdata.sets['fanflat']
data.load()
print 'Data detector width:', data.detector_width_mm
print 'Data projections shape:', data.projections.shape
wr = data.roi_cubic_width_mm
print ' ROI width:', wr
# geom = self.geom(data, 2*(100,), 2*(np.floor(wr),))
geom = self.geom(data, 2 * (100, ), 2 * (100, ))
print ' Detector pixel width:', geom.det_col_spacing, geom.det_row_spacing
print ' Vol width:', geom.vol_width_mm
print ' Voxel width:', geom.voxel_width
projector = self.projector(geom)
# Adjoint <Ax,y>=<x,Ad y> with x[:]=1 and y[:]=1
rn_vol0 = Rn(geom.vol_size).element(1)
rn_proj0 = Rn(geom.proj_size).element(1)
rn_proj = projector.forward(rn_vol0)
rn_vol = projector.backward(rn_proj0)
l = rn_proj.inner(rn_proj0)
r = rn_vol0.inner(rn_vol)
print(' Adjoint with x[:]=1 and y[:]=1:')
print(' <Ax,y> = <x,Ad y> : {0} = {1}'.format(l, r))
print(' |<Ax,y> - <x,Ad y>| = {0}'.format(np.abs(l - r)))
print(' <Ax,y> / <x,Ad y> -1 = {0}'.format(l / r - 1))
# Back-project phantom data
rn_proj = Rn(geom.proj_size).element(data.projections.ravel())
rn_bp = projector.backward(rn_proj)
# FBP
rn_fbp = projector.fbp(rn_proj)
rec = np.reshape(rn_fbp.data, geom.vol_shape)
# plt.imshow(rec, cmap=plt.cm.Greys)
# plt.show()
projector.clear_astra_memory()
def test_ndim(self):
vshape = (88, 77)
vsize = np.prod(vshape)
cols = 99
angles = np.linspace(0, 2 * np.pi, 111, endpoint=False)
psize = cols * np.size(angles)
geom = Geometry(geometry_type='parallel',
scale_factor=1,
volume_shape=vshape,
det_col_count=cols,
det_row_count=1,
angles=angles)
print 'Vol size: ', vsize
print 'Proj size:', psize
print 'Voxel size:', self.geom.voxel_size
vol_rn = Rn(vsize)
proj_rn = Rn(psize)
projector = Projector(geom, vol_rn, proj_rn)
proj = projector.forward(vol_rn.element(1))
p = proj.data.reshape(geom.proj_shape)
print 'Proj at 0 degree: max = ', p[0, :].max()
vol = projector.backward(proj_rn.element(1))
print vol.data.max()
projector.clear_astra_memory()
def test_parallel(self):
print('PARALLEL')
data = ctdata.sets['parallel']
data.load()
print ' Data detector width:', data.detector_width_mm
print ' Data projections shape:', data.projections.shape
geom = self.geom(data, 2*(100,), 2*(100,))
print ' Detector pixel width:', geom.det_col_spacing, geom.det_row_spacing
projector = self.projector(geom)
# Adjoint <Ax,y>=<x,Ad y> with x[:]=1 and y[:]=1
rn_vol0 = Rn(geom.vol_size).element(1)
rn_proj0 = Rn(geom.proj_size).element(1)
rn_proj = projector.forward(rn_vol0)
rn_vol = projector.backward(rn_proj0)
l = rn_proj.inner(rn_proj0)
r = rn_vol0.inner(rn_vol)
print(' Adjoint with x[:]=1 and y[:]=1:')
print(' <Ax,y> = <x,Ad y> : {0} = {1}'.format(l, r))
print(' |<Ax,y> - <x,Ad y>| = {0}'.format(np.abs(l - r)))
print(' <Ax,y> / <x,Ad y> -1 = {0}'.format(l / r -1))
# Back-project phantom data
rn_proj = Rn(geom.proj_size).element(data.projections.ravel())
rn_bp = projector.backward(rn_proj)
# FBP
rn_fbp = projector.fbp(rn_proj)
rec = np.reshape(rn_fbp.data, geom.vol_shape)
import scipy.io as sio
sio.savemat(self.matfile, {'parallel_fbp': rec})
# plt.imshow(rec, cmap=plt.cm.Greys)
# plt.show()
projector.clear_astra_memory()
def test_parallel(self):
print('PARALLEL')
data = ctdata.sets['parallel']
data.load()
print ' Data detector width:', data.detector_width_mm
print ' Data projections shape:', data.projections.shape
geom = self.geom(data, 2 * (100, ), 2 * (100, ))
print ' Detector pixel width:', geom.det_col_spacing, geom.det_row_spacing
projector = self.projector(geom)
# Adjoint <Ax,y>=<x,Ad y> with x[:]=1 and y[:]=1
rn_vol0 = Rn(geom.vol_size).element(1)
rn_proj0 = Rn(geom.proj_size).element(1)
rn_proj = projector.forward(rn_vol0)
rn_vol = projector.backward(rn_proj0)
l = rn_proj.inner(rn_proj0)
r = rn_vol0.inner(rn_vol)
print(' Adjoint with x[:]=1 and y[:]=1:')
print(' <Ax,y> = <x,Ad y> : {0} = {1}'.format(l, r))
print(' |<Ax,y> - <x,Ad y>| = {0}'.format(np.abs(l - r)))
print(' <Ax,y> / <x,Ad y> -1 = {0}'.format(l / r - 1))
# Back-project phantom data
rn_proj = Rn(geom.proj_size).element(data.projections.ravel())
rn_bp = projector.backward(rn_proj)
# FBP
rn_fbp = projector.fbp(rn_proj)
rec = np.reshape(rn_fbp.data, geom.vol_shape)
import scipy.io as sio
sio.savemat(self.matfile, {'parallel_fbp': rec})
# plt.imshow(rec, cmap=plt.cm.Greys)
# plt.show()
projector.clear_astra_memory()
def test_odlprojector_instance(self):
# Create cubic unit volume
vol_rn = Rn(self.geom.vol_size)
vol = np.ones(self.geom.vol_shape)
vol_rn_vec = vol_rn.element(vol.ravel())
# Create projections
proj_rn = Rn(self.geom.proj_size)
proj = np.ones(self.geom.proj_size)
proj_rn_vec = proj_rn.element(proj.ravel())
vol_norm_0 = vol_rn_vec.norm()
self.assertEqual(vol_norm_0**2, np.sqrt(self.geom.vol_size)**2)
proj_norm_0 = proj_rn_vec.norm()
self.assertEqual(proj_norm_0**2, np.sqrt(self.geom.proj_size)**2)
# ODLProjector instance
projector = Projector(self.geom, vol_rn, proj_rn)
proj_rn_vec = projector.forward(vol_rn_vec)
proj_norm_1 = proj_rn_vec.norm()
self.assertNotEqual(proj_norm_0, proj_norm_1)
vol_rn_vec = projector.backward(proj_rn_vec)
vol_norm_1 = vol_rn_vec.norm()
self.assertNotEqual(vol_norm_0, vol_norm_1)
proj_rn_vec = projector.forward(vol_rn_vec)
proj_norm_2 = proj_rn_vec.norm()
self.assertNotEqual(proj_norm_1, proj_norm_2)
vol_rn_vec = projector.backward(proj_rn_vec)
vol_norm_2 = vol_rn_vec.norm()
self.assertNotEqual(vol_norm_2, vol_norm_1)
projector.clear_astra_memory()
print 'vol norms:', vol_norm_0, vol_norm_1, vol_norm_2
print 'proj norms', proj_norm_0, proj_norm_1, proj_norm_2
def test_odlprojector_instance(self):
# Create cubic unit volume
vol_rn = Rn(self.geom.vol_size)
vol = np.ones(self.geom.vol_shape)
vol_rn_vec = vol_rn.element(vol.ravel())
# Create projections
proj_rn = Rn(self.geom.proj_size)
proj = np.ones(self.geom.proj_size)
proj_rn_vec = proj_rn.element(proj.ravel())
vol_norm_0 = vol_rn_vec.norm()
self.assertEqual(vol_norm_0**2, np.sqrt(self.geom.vol_size)**2)
proj_norm_0 = proj_rn_vec.norm()
self.assertEqual(proj_norm_0**2, np.sqrt(self.geom.proj_size)**2)
# ODLProjector instance
projector = Projector(self.geom, vol_rn, proj_rn)
proj_rn_vec = projector.forward(vol_rn_vec)
proj_norm_1 = proj_rn_vec.norm()
self.assertNotEqual(proj_norm_0, proj_norm_1)
vol_rn_vec = projector.backward(proj_rn_vec)
vol_norm_1 = vol_rn_vec.norm()
self.assertNotEqual(vol_norm_0, vol_norm_1)
proj_rn_vec = projector.forward(vol_rn_vec)
proj_norm_2 = proj_rn_vec.norm()
self.assertNotEqual(proj_norm_1, proj_norm_2)
vol_rn_vec = projector.backward(proj_rn_vec)
vol_norm_2 = vol_rn_vec.norm()
self.assertNotEqual(vol_norm_2, vol_norm_1)
projector.clear_astra_memory()
print 'vol norms:', vol_norm_0, vol_norm_1, vol_norm_2
print 'proj norms', proj_norm_0, proj_norm_1, proj_norm_2
