def eval_vol(self, vol_true, vol_est):
norm_true = anorm(vol_true)
err = anorm(vol_true - vol_est)
rel_err = err / norm_true
# RCOPT
corr = acorr(vol_true.asnumpy(), vol_est.asnumpy())
return {"err": err, "rel_err": rel_err, "corr": corr}
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 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 a Volume Instance (default `mean_true`).
:param eig_vols: A set of k volumes in a Volume instance (default `eigs`).
:return:
"""
if mean_vol is None:
mean_vol = self.mean_true()
if eig_vols is None:
eig_vols = self.eigs()[0]
assert isinstance(mean_vol, Volume)
assert isinstance(eig_vols, Volume)
vols = self.vols - mean_vol # note, broadcast
V = vols.to_vec()
EV = eig_vols.to_vec()
coords = EV @ V.T
res = vols - Volume.from_vec(coords.T @ EV)
res_norms = anorm(res.asnumpy(), (1, 2, 3))
res_inners = mean_vol.to_vec() @ res.to_vec().T
return coords.squeeze(), res_norms, res_inners
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 = eigs_est.to_vec() @ eigs_true.to_vec().T
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 eval_coords(self, mean_vol, eig_vols, coords_est):
"""
Evaluate coordinate estimation
:param mean_vol: A mean volume in the form of a Volume instance.
:param eig_vols: A set of eigenvolumes in an Volume instance.
:param coords_est: The estimated coordinates in the affine space defined centered at `mean_vol` and spanned
by `eig_vols`.
:return:
"""
assert isinstance(mean_vol, Volume)
assert isinstance(eig_vols, Volume)
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 = (mean_vol.to_vec() @ eig_vols.to_vec().T).item()
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}
mean_coeff=mean_coeff_est,
covar_coeff=covar_coeff_est,
noise_var=noise_var,
)
# Convert Fourier-Bessel coefficients back into 2D images
imgs_est = ffbbasis.evaluate(coeff_est)
# Evaluate the results
# Calculate the difference between the estimated covariance and the "true"
# covariance estimated from the clean Fourier-Bessel coefficients.
covar_coeff_diff = covar_coeff - covar_coeff_est
# Calculate the deviation between the clean estimates and those obtained from
# the noisy, filtered images.
diff_mean = anorm(mean_coeff_est - mean_coeff) / anorm(mean_coeff)
diff_covar = covar_coeff_diff.norm() / covar_coeff.norm()
# Calculate the normalized RMSE of the estimated images.
nrmse_ims = (imgs_est - imgs_clean).norm() / imgs_clean.norm()
logger.info(f"Deviation of the noisy mean estimate: {diff_mean}")
logger.info(f"Deviation of the noisy covariance estimate: {diff_covar}")
logger.info(f"Estimated images normalized RMSE: {nrmse_ims}")
# plot the first images at different stages
idm = 0
plt.subplot(2, 2, 1)
plt.imshow(-imgs_noise[idm], cmap="gray")
plt.colorbar()
plt.title("Noise")
plt.subplot(2, 2, 2)
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
fb_nrmse_ims = anorm(fb_images - org_images) / anorm(org_images)
logger.info(f"FB estimated images normalized RMSE: {fb_nrmse_ims}")
# plot the first images using the normal FB method
plt.subplot(1, 3, 1)
plt.imshow(np.real(org_images[0]), cmap="gray")
plt.title("Original")
plt.subplot(1, 3, 2)
plt.imshow(np.real(fb_images[0]), cmap="gray")
plt.title("FB Image")
plt.subplot(1, 3, 3)
plt.imshow(np.real(org_images[0] - fb_images[0]), cmap="gray")
plt.title("Differences")
plt.tight_layout()
# %%