def curvelet_transform(x, num_bands, num_angles = 8, all_curvelets = True, as_complex = False):
ndims = len(x.shape)
# This file requires Curvelab and the PyCurveLab packages be installed on your system.
try:
import pyct
except ImportError:
raise NotImplementedError("Use of curvelets requires installation of CurveLab and the PyCurveLab package.\nSee: http://curvelet.org/ and https://www.slim.eos.ubc.ca/SoftwareLicensed/")
if ndims == 2:
ct = pyct.fdct2( n = x.shape,
nbs = num_bands, # Number of bands
nba = num_angles, # Number of discrete angles
ac = all_curvelets,# Return curvelets at the finest detail level
vec = False, # Return results as nested python vectors
cpx = as_complex) # Disable complex-valued curvelets
elif ndims == 3:
ct = pyct.fdct3( n = x.shape,
nbs = num_bands, # Number of bands
nba = num_angles, # Number of discrete angles
ac = all_curvelets,# Return curvelets at the finest detail level
vec = False, # Return results as nested python vectors
cpx = as_complex) # Disable complex-valued curvelets
else:
raise NotImplementedError("%dD Curvelets are not supported." % (ndims))
result = ct.fwd(x)
del ct
return result
def test_FDCT3D_3dsignal(par):
"""
Tests for FDCT3D operator for 3d signal.
"""
x = np.random.normal(0., 1., (par['nx'], par['ny'], par['nz'])) + \
np.random.normal(0., 1., (par['nx'], par['ny'], par['nz'])) * \
par['imag']
FDCTop = FDCT3D(dims=(par['nx'], par['ny'], par['nz']), dtype=par['dtype'])
assert dottest(FDCTop,
*FDCTop.shape,
tol=1e-12,
complexflag=0 if par['imag'] == 0 else 3)
y = FDCTop * x.ravel()
xinv = FDCTop.H * y
np.testing.assert_array_almost_equal(xinv.reshape(*x.shape), x, decimal=14)
if PYCT:
FDCTct = ct.fdct3(x.shape,
FDCTop.nbscales,
FDCTop.nbangles_coarse,
FDCTop.allcurvelets,
cpx=False if par['imag'] == 0 else True)
y_ct = np.array(FDCTct.fwd(x)).ravel()
np.testing.assert_array_almost_equal(y, y_ct, decimal=64)
assert y.dtype == y_ct.dtype
def normtest(dim=2, clen=10):
for i in range(clen):
print("-----------------------------------")
if dim == 2:
sz = np.arange(256, 513)
else:
sz = np.arange(64, 128)
np.random.shuffle(sz)
print(sz[:dim])
iscplx = [True, False]
np.random.shuffle(iscplx)
isac = [True, False]
np.random.shuffle(isac)
if isac[0]:
print("All curvelets")
else:
print("Wavelets at finest scale")
if dim == 2:
A = ct.fdct2(sz[:2], 6, 32, isac[0], norm=True, cpx=iscplx[0])
pos = np.arange(A.range())
np.random.shuffle(pos)
if iscplx[0]:
print("Complex input")
x = np.zeros(A.range(), dtype='complex')
v = np.random.rand()
x[pos[0]] = v + np.sqrt(1 - v**2) * 1j
else:
print("Real input")
x = np.zeros(A.range())
x[pos[0]] = 1.
elif dim == 3:
A = ct.fdct3(sz[:3], 4, 8, isac[0], norm=True, cpx=iscplx[0])
pos = np.arange(A.range())
np.random.shuffle(pos)
if iscplx[0]:
print("Complex input")
x = np.zeros(A.range(), dtype='complex')
v = np.random.rand()
x[pos[0]] = v + np.sqrt(1 - v**2) * 1j
else:
print("Real input")
x = np.zeros(A.range())
x[pos[0]] = 1.
f = A.inv(x)
if np.allclose(norm(f.flatten(), ord=2), norm(x, ord=2)):
print('Norm check ok!')
else:
print('Problem w norm test')
print("||f|| = ", norm(f.flatten(), ord=2), f.dtype)
print("||x|| = ", norm(x, ord=2), x.dtype)
def test(dim=2,clen=10): for i in xrange(clen): print "-----------------------------------" if dim==2: sz = np.arange(256,513) elif dim==3: sz = np.arange(64,128) np.random.shuffle(sz) iscplx = [True,False] np.random.shuffle(iscplx) if iscplx[0]: print "Complex input" f = np.array(sc.randn(*sz[:dim])+sc.randn(*sz[:dim])*1j) else: print "Real input" f = np.array(sc.randn(*sz[:dim])) isac = [True,False] np.random.shuffle(isac) if isac[0]: print "All curvelets" else: print "Wavelets at finest scale" print f.shape if dim==2: A = ct.fdct2(f.shape,6,32,isac[0],cpx=iscplx[0]) elif dim==3: A = ct.fdct3(f.shape,4,8,isac[0],cpx=iscplx[0]) x = A.fwd(f) if np.allclose(norm(f.flatten(),ord=2),norm(x,ord=2) ): print 'Energy check ok!' else: print 'Problem w energy test' fr = A.inv(x) if np.allclose(f.flatten(),fr.flatten() ): print 'Inverse check ok!' else: print 'Problem w inverse test' print "||f|| = ",norm(f.flatten(),ord=2),f.dtype print "||x|| = ",norm(x,ord=2),x.dtype print "||fr|| = ",norm(fr.flatten(),ord=2),fr.dtype
def curvelet_decomposition(vol, n_scales, n_angles):
# Create a Curvelet object
A = ct.fdct3(vol.shape,
nbs=n_scales,
nba=n_angles,
ac=True,
norm=False,
vec=True,
cpx=False)
# Apply curvelet to volume
f = A.fwd(vol)
# Assembly feature vector
feats = pd.Series()
for scale in range(n_scales):
for angle in range(n_angles):
# Get values in respective scale/angle
try:
ix = A.index(scale, angle)
data = f[ix[0]:ix[1]] # Extract magnitude
# Extract several statistics
n, (mi, ma), mea, var, skew, kurt = stats.describe(data)
# Assign to series
feats['%d_%d_n' % (scale, angle)] = n
feats['%d_%d_min' % (scale, angle)] = mi
feats['%d_%d_max' % (scale, angle)] = ma
feats['%d_%d_mean' % (scale, angle)] = mea
feats['%d_%d_var' % (scale, angle)] = var
feats['%d_%d_skew' % (scale, angle)] = skew
feats['%d_%d_kurtosis' % (scale, angle)] = kurt
except IndexError:
pass
return feats
def inverse_curvelet_transform(coefs, x_shape, num_bands, num_angles, all_curvelets, as_complex):
# This file requires Curvelab and the PyCurveLab packages be installed on your system.
try:
import pyct
except ImportError:
raise NotImplementedError("Use of curvelets requires installation of CurveLab and the PyCurveLab package.\nSee: http://curvelet.org/ and https://www.slim.eos.ubc.ca/SoftwareLicensed/")
if len(x_shape) == 2:
ct = pyct.fdct2( n = x_shape,
nbs = num_bands, # Number of bands
nba = num_angles,
ac = all_curvelets,
vec = False,
cpx = as_complex)
else:
ct = pyct.fdct3( n = x_shape,
nbs = num_bands, # Number of bands
nba = num_angles,
ac = all_curvelets,
vec = False,
cpx = as_complex)
result = ct.inv(coefs)
del ct
return result
filename = os.path.join(root, 'param', 'fsaverage', 'brainmask.mgz')
img = nb.load(filename).get_data().astype(np.float)
img = img[50:150, 50:150, 50:150]
print('Image shape: ', img.shape)
print('Number of elements: ', np.prod(img.shape))
# Parameters
number_of_scales = 7
number_of_angles = 4
# Setup curvelet params
print('Applying Curvelet Transform...')
A = ct.fdct3(img.shape,
nbs=number_of_scales,
nba=number_of_angles,
ac=True,
norm=False,
vec=True,
cpx=False)
# Apply curvelet to the image
f = A.fwd(img)
print('Coefficients array:\n\t', f)
print('Shape: ', f.shape)
# Print Information
for scale in range(0, number_of_scales):
if scale == 0:
angles = [0]
elif scale == 1: