def get_cwf_coeffs(
self,
coeffs,
ctf_fb=None,
ctf_idx=None,
mean_coeff=None,
covar_coeff=None,
noise_var=1,
):
"""
Estimate the expansion coefficients using the Covariance Wiener Filtering (CWF) method.
:param coeffs: A coefficient vector (or an array of coefficient vectors) to be calculated.
:param ctf_fb: The CFT functions in the FB expansion.
:param ctf_idx: An array of the CFT function indices for all 2D images.
If ctf_fb or ctf_idx is None, the identity filter will be applied.
:param mean_coeff: The mean value vector from all images.
:param covar_coeff: The block diagonal covariance matrix of the clean coefficients represented by a cell array.
:param noise_var: The estimated variance of noise. The value should be zero for `coeffs`
from clean images of simulation data.
:return: The estimated coefficients of the unfiltered images in certain math basis.
These are obtained using a Wiener filter with the specified covariance for the clean images
and white noise of variance `noise_var` for the noise.
"""
if mean_coeff is None:
mean_coeff = self.get_mean(coeffs, ctf_fb, ctf_idx)
if covar_coeff is None:
covar_coeff = self.get_covar(coeffs,
ctf_fb,
ctf_idx,
mean_coeff,
noise_var=noise_var)
# should be none or both
if (ctf_fb is None) or (ctf_idx is None):
ctf_idx = np.zeros(coeffs.shape[0], dtype=int)
ctf_fb = [BlkDiagMatrix.eye_like(covar_coeff)]
noise_covar_coeff = noise_var * BlkDiagMatrix.eye_like(covar_coeff)
coeffs_est = np.zeros_like(coeffs)
for k in np.unique(ctf_idx[:]):
coeff_k = coeffs[ctf_idx == k]
ctf_fb_k = ctf_fb[k]
ctf_fb_k_t = ctf_fb_k.T
sig_covar_coeff = ctf_fb_k @ covar_coeff @ ctf_fb_k_t
sig_noise_covar_coeff = sig_covar_coeff + noise_covar_coeff
mean_coeff_k = ctf_fb_k.apply(mean_coeff)
coeff_est_k = coeff_k - mean_coeff_k
coeff_est_k = sig_noise_covar_coeff.solve(coeff_est_k.T).T
coeff_est_k = (covar_coeff @ ctf_fb_k_t).apply(coeff_est_k.T).T
coeff_est_k = coeff_est_k + mean_coeff
coeffs_est[ctf_idx == k] = coeff_est_k
return coeffs_est
def _build(self):
src = self.src
if self.basis is None:
from aspire.basis import FFBBasis2D
self.basis = FFBBasis2D((src.L, src.L), dtype=self.dtype)
if src.unique_filters is None:
logger.info("CTF filters are not included in Cov2D denoising")
# set all CTF filters to an identity filter
self.ctf_idx = np.zeros(src.n, dtype=int)
self.ctf_fb = [
BlkDiagMatrix.eye_like(RadialCTFFilter().fb_mat(self.basis))
]
else:
logger.info("Represent CTF filters in FB basis")
unique_filters = src.unique_filters
self.ctf_idx = src.filter_indices
self.ctf_fb = [f.fb_mat(self.basis) for f in unique_filters]
def get_mean(self, coeffs, ctf_fb=None, ctf_idx=None):
"""
Calculate the mean vector from the expansion coefficients with CTF information.
:param coeffs: A coefficient vector (or an array of coefficient vectors) to be averaged.
:param ctf_fb: The CFT functions in the FB expansion.
:param ctf_idx: An array of the CFT function indices for all 2D images.
If ctf_fb or ctf_idx is None, the identity filter will be applied.
:return: The mean value vector for all images.
"""
if coeffs.size == 0:
raise RuntimeError("The coefficients need to be calculated!")
# should assert we require none or both...
if (ctf_fb is None) or (ctf_idx is None):
ctf_idx = np.zeros(coeffs.shape[0], dtype=int)
ctf_fb = [
BlkDiagMatrix.eye_like(RadialCTFFilter().fb_mat(self.basis),
dtype=self.dtype)
]
b = np.zeros(self.basis.count, dtype=coeffs.dtype)
A = BlkDiagMatrix.zeros_like(ctf_fb[0])
for k in np.unique(ctf_idx[:]).T:
coeff_k = coeffs[ctf_idx == k]
weight = coeff_k.shape[0] / coeffs.shape[0]
mean_coeff_k = self._get_mean(coeff_k)
ctf_fb_k = ctf_fb[k]
ctf_fb_k_t = ctf_fb_k.T
b += weight * ctf_fb_k_t.apply(mean_coeff_k)
A += weight * (ctf_fb_k_t @ ctf_fb_k)
mean_coeff = A.solve(b)
return mean_coeff
def get_covar(
self,
coeffs,
ctf_fb=None,
ctf_idx=None,
mean_coeff=None,
do_refl=True,
noise_var=1,
covar_est_opt=None,
make_psd=True,
):
"""
Calculate the covariance matrix from the expansion coefficients and CTF information.
:param coeffs: A coefficient vector (or an array of coefficient vectors) to be calculated.
:param ctf_fb: The CFT functions in the FB expansion.
:param ctf_idx: An array of the CFT function indices for all 2D images.
If ctf_fb or ctf_idx is None, the identity filter will be applied.
:param mean_coeff: The mean value vector from all images.
:param noise_var: The estimated variance of noise. The value should be zero for `coeffs`
from clean images of simulation data.
:param covar_est_opt: The optimization parameter list for obtaining the Cov2D matrix.
:param make_psd: If True, make the covariance matrix positive semidefinite
:return: The basis coefficients of the covariance matrix in
the form of cell array representing a block diagonal matrix. These
block diagonal matrices are implemented as BlkDiagMatrix instances.
The covariance is calculated from the images represented by the coeffs array,
along with all possible rotations and reflections. As a result, the computed covariance
matrix is invariant to both reflection and rotation. The effect of the filters in ctf_fb
are accounted for and inverted to yield a covariance estimate of the unfiltered images.
"""
if coeffs.size == 0:
raise RuntimeError("The coefficients need to be calculated!")
if (ctf_fb is None) or (ctf_idx is None):
ctf_idx = np.zeros(coeffs.shape[0], dtype=int)
ctf_fb = [
BlkDiagMatrix.eye_like(RadialCTFFilter().fb_mat(self.basis))
]
def identity(x):
return x
default_est_opt = {
"shrinker": "None",
"verbose": 0,
"max_iter": 250,
"iter_callback": [],
"store_iterates": False,
"rel_tolerance": 1e-12,
"precision": self.dtype,
"preconditioner": identity,
}
covar_est_opt = fill_struct(covar_est_opt, default_est_opt)
if mean_coeff is None:
mean_coeff = self.get_mean(coeffs, ctf_fb, ctf_idx)
b_coeff = BlkDiagMatrix.zeros_like(ctf_fb[0])
b_noise = BlkDiagMatrix.zeros_like(ctf_fb[0])
A = []
for _ in range(len(ctf_fb)):
A.append(BlkDiagMatrix.zeros_like(ctf_fb[0]))
M = BlkDiagMatrix.zeros_like(ctf_fb[0])
for k in np.unique(ctf_idx[:]):
coeff_k = coeffs[ctf_idx == k]
weight = coeff_k.shape[0] / coeffs.shape[0]
ctf_fb_k = ctf_fb[k]
ctf_fb_k_t = ctf_fb_k.T
mean_coeff_k = ctf_fb_k.apply(mean_coeff)
covar_coeff_k = self._get_covar(coeff_k, mean_coeff_k)
b_coeff += weight * (ctf_fb_k_t @ covar_coeff_k @ ctf_fb_k)
ctf_fb_k_sq = ctf_fb_k_t @ ctf_fb_k
b_noise += weight * ctf_fb_k_sq
A[k] = np.sqrt(weight) * ctf_fb_k_sq
M += A[k]
if not b_coeff.check_psd():
logger.warning(
"Left side b in Cov2D is not positive semidefinite.")
if covar_est_opt["shrinker"] == "None":
b = b_coeff - noise_var * b_noise
else:
b = self.shrink_covar_backward(
b_coeff,
b_noise,
np.size(coeffs, 1),
noise_var,
covar_est_opt["shrinker"],
)
if not b.check_psd():
logger.warning("Left side b after removing noise in Cov2D"
" is not positive semidefinite.")
# RCOPT okay, this looks like a big batch, come back later
cg_opt = covar_est_opt
covar_coeff = BlkDiagMatrix.zeros_like(ctf_fb[0])
def precond_fun(S, x):
p = np.size(S, 0)
ensure(
np.size(x) == p * p,
"The sizes of S and x are not consistent.")
x = m_reshape(x, (p, p))
y = S @ x @ S
y = m_reshape(y, (p**2, ))
return y
def apply(A, x):
p = np.size(A[0], 0)
x = m_reshape(x, (p, p))
y = np.zeros_like(x)
for k in range(0, len(A)):
y = y + A[k] @ x @ A[k].T
y = m_reshape(y, (p**2, ))
return y
for ell in range(0, len(b)):
A_ell = []
for k in range(0, len(A)):
A_ell.append(A[k][ell])
p = np.size(A_ell[0], 0)
b_ell = m_reshape(b[ell], (p**2, ))
S = inv(M[ell])
cg_opt["preconditioner"] = lambda x: precond_fun(S, x)
covar_coeff_ell, _, _ = conj_grad(lambda x: apply(A_ell, x), b_ell,
cg_opt)
covar_coeff[ell] = m_reshape(covar_coeff_ell, (p, p))
if not covar_coeff.check_psd():
logger.warning(
"Covariance matrix in Cov2D is not positive semidefinite.")
if make_psd:
logger.info("Convert matrices to positive semidefinite.")
covar_coeff = covar_coeff.make_psd()
return covar_coeff
def testBlkDiagMatrixEye(self):
blk_eye = BlkDiagMatrix.eye(self.blk_partition)
self.allallfunc(blk_eye, self.blk_eyes)
blk_eye = BlkDiagMatrix.eye_like(self.blk_a)
self.allallfunc(blk_eye, self.blk_eyes)
def get_cwf_coeffs(self,
coeffs,
ctf_fb,
ctf_idx,
mean_coeff,
covar_coeff,
noise_var=0):
"""
Estimate the expansion coefficients using the Covariance Wiener Filtering (CWF) method.
:param coeffs: A coefficient vector (or an array of coefficient vectors) to be calculated.
:param ctf_fb: The CFT functions in the FB expansion.
:param ctf_idx: An array of the CFT function indices for all 2D images.
If ctf_fb or ctf_idx is None, the identity filter will be applied.
:param mean_coeff: The mean value vector from all images.
:param covar_coeff: The block diagonal covariance matrix of the clean coefficients represented by a cell array.
:param noise_var: The estimated variance of noise. The value should be zero for `coeffs`
from clean images of simulation data.
:return: The estimated coefficients of the unfiltered images in certain math basis.
These are obtained using a Wiener filter with the specified covariance for the clean images
and white noise of variance `noise_var` for the noise.
"""
if mean_coeff is None:
mean_coeff = self.get_mean()
if covar_coeff is None:
covar_coeff = self.get_covar(noise_var=noise_var,
mean_coeff=mean_coeff)
# Handle CTF arguments.
if (ctf_fb is None) ^ (ctf_idx is None):
raise RuntimeError(
"Both `ctf_fb` and `ctf_idx` should be provided,"
" or both should be `None`."
f' Given {"ctf_fb" if ctf_idx is None else "ctf_idx"}')
elif ctf_fb is None:
# Setup defaults for CTF
ctf_idx = np.zeros(coeffs.shape[0], dtype=int)
ctf_fb = [BlkDiagMatrix.eye_like(covar_coeff)]
noise_covar_coeff = noise_var * BlkDiagMatrix.eye_like(covar_coeff)
coeffs_est = np.zeros_like(coeffs)
for k in np.unique(ctf_idx[:]):
coeff_k = coeffs[ctf_idx == k]
ctf_fb_k = ctf_fb[k]
ctf_fb_k_t = ctf_fb_k.T
mean_coeff_k = ctf_fb_k.apply(mean_coeff)
coeff_est_k = coeff_k - mean_coeff_k
if noise_var == 0:
coeff_est_k = ctf_fb_k.solve(coeff_est_k.T).T
else:
sig_covar_coeff = ctf_fb_k @ covar_coeff @ ctf_fb_k_t
sig_noise_covar_coeff = sig_covar_coeff + noise_covar_coeff
coeff_est_k = sig_noise_covar_coeff.solve(coeff_est_k.T).T
coeff_est_k = (covar_coeff @ ctf_fb_k_t).apply(coeff_est_k.T).T
coeff_est_k = coeff_est_k + mean_coeff
coeffs_est[ctf_idx == k] = coeff_est_k
return coeffs_est