def test_max_level(self):
'''Make sure we clip the level at the high end.'''
with self.assertWarns(Warning):
high_level = np.random.randint(6, 10)
forward, _locs = cdf97_2d_forward(self.im, level=high_level)
forward_check, _locs = cdf97_2d_forward(self.im, level=5)
self.assertTrue(np.allclose(forward, forward_check))
# Get the encoding model
uft = UFT(mask)
# Load in the test data
kspace = load_test_data('mr_utils/test_data/tests/recon/reordering',
['coil1'])[0]
kspace = np.fft.fftshift(kspace)
imspace = uft.inverse(kspace)
# Undersample data to get prior
kspace_u = kspace * mask
imspace_u = uft.inverse(kspace_u)
# Sparsifying transforms
level = 3
wvlt, locations = cdf97_2d_forward(imspace, level)
sparsify = lambda x: cdf97_2d_forward(x, level)[0]
unsparsify = lambda x: cdf97_2d_inverse(x, locations)
# Decide how we'll be selective in our updates
percent_to_keep = .05
num_to_keep = int(percent_to_keep * imspace.size)
def select_n(x_hat, update):
'''Return indices of n largest updates each iteration.'''
return np.unravel_index(
np.argpartition(np.abs(x_hat - update).flatten(),
-num_to_keep)[-num_to_keep:], x_hat.shape)
# Shared recon params
prior = imspace_u.copy()
R = 4 # decimate so the matching will go more quickly
x = decimate(decimate(camera().astype(float), R, axis=0), R, axis=1)
# Let's try a few different transforms:
Ts = []
Tis = []
# Discrete cosine transform
norm = 'ortho'
Ts.append(lambda x: dct(dct(x, axis=0, norm=norm), axis=1, norm=norm))
Tis.append(lambda x: idct(idct(x, axis=0, norm=norm), axis=1, norm=norm))
assert np.allclose(x, Tis[-1](Ts[-1](x)))
# Wavelet transform
level = 3
_, locs = cdf97_2d_forward(x, level)
Ts.append(lambda x: cdf97_2d_forward(x, level)[0])
Tis.append(lambda x: cdf97_2d_inverse(x, locs))
assert np.allclose(x, Tis[-1](Ts[-1](x)))
# Tuning parameter for each transform and case, k -- percent of coeffs
nc = int(.2 * x.size) # number of coefficients to keep for comparison
ks = [
[.1, .9],
[.1, .9], # k for bulk_up, whittle_down for DCT
[.1, .9]
] # k for bulk_up, whittle_down for wavelet
for T, Ti, k in zip(Ts, Tis, ks):
# Try to "bulk up" the first k percent of coefficients
idx1 = bulk_up(x, T, Ti, k[0])
plt.show()
# Radial sampling pattern for retrospective undersampling
num_spokes = 16
samp = radial(im.shape, num_spokes, skinny=True, extend=True)
samp_percent = np.sum(samp.flatten()) / samp.size * 100
uft = UFT(samp)
kspace_u = np.fft.fft2(im) * samp
imspace_u = np.fft.ifft2(kspace_u)
# view(samp)
# view(imspace_u)
# view(kspace_u)
# Use wavelet transform
lvl = 3
_coeffs, locs = cdf97_2d_forward(im, lvl)
sparsify = lambda x0: cdf97_2d_forward(x0, lvl)[0]
unsparsify = lambda x0: cdf97_2d_inverse(x0, locs)
assert np.allclose(unsparsify(sparsify(im)), im)
# Recon params
ignore_mse = False
ignore_ssim = True
ignore_residual = True
thresh_sep = False
maxiter = 1000
disp = True
strikes = 10
# Do recon no ordering
recon = proximal_GD(
def test_forward_inverse(self):
'''Test forward transform invertibility.'''
forward, locs = cdf97_2d_forward(self.im, level=5)
inverse = cdf97_2d_inverse(forward, locs)
self.assertTrue(np.allclose(inverse, self.im))
if __name__ == '__main__':
# Get a phantom
N = 64
x = binary_smiley(N)
# Do some sampling
num_spokes = 12
mask = radial(x.shape, num_spokes)
uft = UFT(mask)
y = uft.forward_ortho(x)
# Sparsifying transforms
level = 3
wvlt, locations = cdf97_2d_forward(x, level)
sparsify = lambda x0: cdf97_2d_forward(x0, level)[0]
unsparsify = lambda x0: cdf97_2d_inverse(x0, locations)
# Do the recon
alpha = .15
disp = True
ignore = False
maxiter = 200
x_c = proximal_GD(y,
forward_fun=uft.forward_ortho,
inverse_fun=uft.inverse_ortho,
sparsify=sparsify,
unsparsify=unsparsify,
reorder_fun=None,
alpha=alpha,
def T(x0):
'''Wavelet transform.'''
return cdf97_2d_forward(x0, level=5)[0]