def eval_vol(self, vol_true, vol_est):
norm_true = anorm(vol_true)
err = anorm(vol_true - vol_est)
rel_err = err / norm_true
corr = acorr(vol_true, vol_est)
return {'err': err, 'rel_err': rel_err, 'corr': corr}
def testPhaseFlip(self):
self.sim.phase_flip()
imgs_pf = self.sim.images(start=0, num=self.n)
# check energy conservation
self.assertTrue(
np.allclose(
anorm(self.imgs_org.asnumpy(), axes=(1, 2)),
anorm(imgs_pf.asnumpy(), axes=(1, 2)),
))
def eval_volmat(self, volmat_true, volmat_est):
"""
Evaluate volume matrix estimation accuracy
:param volmat_true: The true volume matrices in the form of an L-by-L-by-L-by-L-by-L-by-L-by-K array.
:param volmat_est: The estimated volume matrices in the same form.
:return:
"""
norm_true = anorm(volmat_true)
err = anorm(volmat_true - volmat_est)
rel_err = err / norm_true
corr = acorr(volmat_true, volmat_est)
return {'err': err, 'rel_err': rel_err, 'corr': corr}
def testDownsample(self):
# generate a 3D map with density decays as Gaussian function
g3d = grid_3d(self.L, dtype=self.dtype)
coords = np.array(
[g3d["x"].flatten(), g3d["y"].flatten(), g3d["z"].flatten()])
sigma = 0.2
vol = np.exp(-0.5 * np.sum(np.abs(coords / sigma)**2, axis=0)).astype(
self.dtype)
vol = np.reshape(vol, g3d["x"].shape)
vols = Volume(vol)
# set noise to zero and CFT filters to unity for simulation object
noise_var = 0
noise_filter = ScalarFilter(dim=2, value=noise_var)
sim = Simulation(
L=self.L,
n=self.n,
vols=vols,
offsets=0.0,
amplitudes=1.0,
unique_filters=[
ScalarFilter(dim=2, value=1)
for d in np.linspace(1.5e4, 2.5e4, 7)
],
noise_filter=noise_filter,
dtype=self.dtype,
)
# get images before downsample
imgs_org = sim.images(start=0, num=self.n)
# get images after downsample
max_resolution = 32
sim.downsample(max_resolution)
imgs_ds = sim.images(start=0, num=self.n)
# Check individual grid points
self.assertTrue(
np.allclose(
imgs_org[:, 32, 32],
imgs_ds[:, 16, 16],
atol=utest_tolerance(self.dtype),
))
# check resolution
self.assertTrue(np.allclose(max_resolution, imgs_ds.shape[1]))
# check energy conservation after downsample
self.assertTrue(
np.allclose(
anorm(imgs_org.asnumpy(), axes=(1, 2)) / self.L,
anorm(imgs_ds.asnumpy(), axes=(1, 2)) / max_resolution,
atol=utest_tolerance(self.dtype),
))
def eval_eigs(self, eigs_est, lambdas_est):
"""
Evaluate covariance eigendecomposition accuracy
:param eigs_est: The estimated volume eigenvectors in an L-by-L-by-L-by-K array.
:param lambdas_est: The estimated eigenvalues in a K-by-K diagonal matrix (default `diag(ones(K, 1))`).
:return:
"""
eigs_true, lambdas_true = self.eigs()
B = vol_to_vec(eigs_est).T @ vol_to_vec(eigs_true)
norm_true = anorm(lambdas_true)
norm_est = anorm(lambdas_est)
inner = ainner(B @ lambdas_true, lambdas_est @ B)
err = np.sqrt(norm_true**2 + norm_est**2 - 2 * inner)
rel_err = err / norm_true
corr = inner / (norm_true * norm_est)
# TODO: Determine Principal Angles and return as a dict value
return {'err': err, 'rel_err': rel_err, 'corr': corr}
def setUp(self):
L = 8
n = 32
C = 1
SNR = 1
pixel_size = 5
voltage = 200
defocus_min = 1.5e4
defocus_max = 2.5e4
defocus_ct = 7
Cs = 2.0
alpha = 0.1
filters = [
RadialCTFFilter(pixel_size, voltage, defocus=d, Cs=2.0, alpha=0.1)
for d in np.linspace(defocus_min, defocus_max, defocus_ct)
]
# Since FFBBasis2D doesn't yet implement dtype, we'll set this to double to match its built in types.
sim = Simulation(n=n, C=C, filters=filters, dtype='double')
vols = np.load(os.path.join(DATA_DIR, 'clean70SRibosome_vol.npy'))
vols = vols[..., np.newaxis]
vols = downsample(vols, (L * np.ones(3, dtype=int)))
sim.vols = vols
self.basis = FFBBasis2D((L, L))
# use new methods to generate random rotations and clean images
sim.rots = qrand_rots(n, seed=0)
self.imgs_clean = vol2img(vols[..., 0], sim.rots)
self.h_idx = np.array([filters.index(f) for f in sim.filters])
self.filters = filters
self.h_ctf_fb = [filt.fb_mat(self.basis) for filt in self.filters]
self.imgs_ctf_clean = sim.eval_filters(self.imgs_clean)
sim.cache(self.imgs_ctf_clean)
power_clean = anorm(self.imgs_ctf_clean)**2 / np.size(
self.imgs_ctf_clean)
self.noise_var = power_clean / SNR
self.imgs_ctf_noise = self.imgs_ctf_clean + np.sqrt(
self.noise_var) * randn(L, L, n, seed=0)
self.cov2d = RotCov2D(self.basis)
self.coeff_clean = self.basis.evaluate_t(self.imgs_clean)
self.coeff = self.basis.evaluate_t(self.imgs_ctf_noise)
def vol_coords(self, mean_vol=None, eig_vols=None):
"""
Coordinates of simulation volumes in a given basis
:param mean_vol: A mean volume in the form of an L-by-L-by-L array (default `mean_true`).
:param eig_vols: A set of eigenvolumes in an L-by-L-by-L-by-K array (default `eigs`).
:return:
"""
if mean_vol is None:
mean_vol = self.mean_true()
if eig_vols is None:
eig_vols = self.eigs()[0]
vols = self.vols - np.expand_dims(mean_vol, 3)
coords = vol_to_vec(eig_vols).T @ vol_to_vec(vols)
res = vols - vec_to_vol(vol_to_vec(eig_vols) @ coords)
res_norms = np.diag(anorm(res, (0, 1, 2)))
res_inners = vol_to_vec(mean_vol).T @ vol_to_vec(res)
return coords.squeeze(), res_norms, res_inners
def eval_coords(self, mean_vol, eig_vols, coords_est):
"""
Evaluate coordinate estimation
:param mean_vol: A mean volume in the form of an L-by-L-by-L array.
:param eig_vols: A set of eigenvolumes in an L-by-L-by-L-by-K array.
:param coords_est: The estimated coordinates in the affine space defined centered at `mean_vol` and spanned
by `eig_vols`.
:return:
"""
coords_true, res_norms, res_inners = self.vol_coords(
mean_vol, eig_vols)
# 0-indexed states vector
states = self.states - 1
coords_true = coords_true[states]
res_norms = res_norms[states]
res_inners = res_inners[states]
mean_eigs_inners = np.asscalar(
vol_to_vec(mean_vol).T @ vol_to_vec(eig_vols))
coords_err = coords_true - coords_est
err = np.hypot(res_norms, coords_err)
mean_vol_norm2 = anorm(mean_vol)**2
norm_true = np.sqrt(coords_true**2 + mean_vol_norm2 + 2 * res_inners +
2 * mean_eigs_inners * coords_true)
norm_true = np.hypot(res_norms, norm_true)
rel_err = err / norm_true
inner = mean_vol_norm2 + mean_eigs_inners * (
coords_true + coords_est) + coords_true * coords_est + res_inners
norm_est = np.sqrt(coords_est**2 + mean_vol_norm2 +
2 * mean_eigs_inners * coords_est)
corr = inner / (norm_true * norm_est)
return {'err': err, 'rel_err': rel_err, 'corr': corr}
logger.info(
f'Finish normal FB expansion of original images in {dtime:.4f} seconds.')
# Reconstruct images from the expansion coefficients based on FB basis
fb_images = fb_basis.evaluate(fb_coeffs)
logger.info(
'Finish reconstruction of images from normal FB expansion coefficients.')
# Calculate the mean value of maximum differences between the FB estimated images and the original images
fb_meanmax = np.mean(np.max(abs(fb_images - org_images), axis=2))
logger.info(
f'Mean value of maximum differences between FB estimated images and original images: {fb_meanmax}'
)
# Calculate the normalized RMSE of the FB estimated images
nrmse_ims = anorm(fb_images - org_images) / anorm(org_images)
logger.info(f'FB estimated images normalized RMSE: {nrmse_ims}')
# plot the first images using the normal FB method
plt.subplot(3, 4, 1)
plt.imshow(np.real(org_images[..., 0]), cmap='gray')
plt.title('Original')
plt.subplot(3, 4, 5)
plt.imshow(np.real(fb_images[..., 0]), cmap='gray')
plt.title('FB Image')
plt.subplot(3, 4, 9)
plt.imshow(np.real(org_images[..., 0] - fb_images[..., 0]), cmap='gray')
plt.title('Differences')
# Specify the fast FB basis method for expanding the 2D images
ffb_basis = FFBBasis2D((img_size, img_size))
h_idx = np.array([filters.index(f) for f in sim.filters])
# Evaluate CTF in the 8X8 FB basis
h_ctf_fb = [filt.fb_mat(ffbbasis) for filt in filters]
# Apply the CTF to the clean images.
logger.info('Apply CTF filters to clean images.')
imgs_ctf_clean = Image(sim.eval_filters(imgs_clean))
sim.cache(imgs_ctf_clean)
# imgs_ctf_clean is an Image object. Convert to numpy array for subsequent statements
imgs_ctf_clean = imgs_ctf_clean.asnumpy()
# Apply the noise at the desired singal-noise ratio to the filtered clean images
logger.info('Apply noise filters to clean images.')
power_clean = anorm(imgs_ctf_clean)**2 / np.size(imgs_ctf_clean)
noise_var = power_clean / sn_ratio
imgs_noise = imgs_ctf_clean + np.sqrt(noise_var) * randn(
img_size, img_size, num_imgs, seed=0)
# Expand the images, both clean and noisy, in the Fourier-Bessel basis. This
# can be done exactly (that is, up to numerical precision) using the
# `basis.expand` function, but for our purposes, an approximation will do.
# Since the basis is close to orthonormal, we may approximate the exact
# expansion by applying the adjoint of the evaluation mapping using
# `basis.evaluate_t`.
logger.info('Get coefficients of clean and noisy images in FFB basis.')
coeff_clean = ffbbasis.evaluate_t(imgs_clean)
coeff_noise = ffbbasis.evaluate_t(imgs_noise)
# Create the Cov2D object and calculate mean and covariance for clean images without CTF.
def norm(self):
return anorm(self.data)
