def covar_true(self):
eigs_true, lamdbas_true = self.eigs()
eigs_true = vol_to_vec(eigs_true)
covar_true = eigs_true @ lamdbas_true @ eigs_true.T
covar_true = vecmat_to_volmat(covar_true)
return covar_true
def src_backward(self, mean_vol, noise_variance, shrink_method=None):
"""
Apply adjoint mapping to source
:return: The sum of the outer products of the mean-subtracted images in `src`, corrected by the expected noise
contribution and expressed as coefficients of `basis`.
"""
covar_b = np.zeros((self.L, self.L, self.L, self.L, self.L, self.L),
dtype=self.as_type)
for i in range(0, self.n, self.batch_size):
im = self.src.images(i, self.batch_size)
batch_n = im.shape[-1]
im_centered = im - self.src.vol_forward(mean_vol, i,
self.batch_size)
im_centered_b = np.zeros((self.L, self.L, self.L, batch_n),
dtype=self.as_type)
for j in range(batch_n):
im_centered_b[:, :, :, j] = self.src.im_backward(
Image(im_centered[:, :, j]), i + j)
im_centered_b = vol_to_vec(im_centered_b)
covar_b += vecmat_to_volmat(
im_centered_b @ im_centered_b.T) / self.n
covar_b_coeff = self.basis.mat_evaluate_t(covar_b)
return self._shrink(covar_b_coeff, noise_variance, shrink_method)
def estimate(self, mean_vol, noise_variance, tol=None):
logger.info('Running Covariance Estimator')
b_coeff = self.src_backward(mean_vol, noise_variance)
est_coeff = self.conj_grad(b_coeff, tol=tol)
covar_est = self.basis.mat_evaluate(est_coeff)
covar_est = vecmat_to_volmat(make_symmat(volmat_to_vecmat(covar_est)))
return covar_est
def compute_kernel(self):
# TODO: Most of this stuff is duplicated in MeanEstimator - move up the hierarchy?
n = self.n
L = self.L
_2L = 2 * self.L
kernel = np.zeros((_2L, _2L, _2L, _2L, _2L, _2L), dtype=self.as_type)
filters_f = self.src.filters.evaluate_grid(L)
sq_filters_f = np.array(filters_f**2, dtype=self.as_type)
for i in tqdm(range(0, n, self.batch_size)):
pts_rot = rotated_grids(L, self.src.rots[:, :,
i:i + self.batch_size])
weights = sq_filters_f[:, :,
self.src.filters.indices[i:i +
self.batch_size]]
weights *= self.src.amplitudes[i:i + self.batch_size]**2
if L % 2 == 0:
weights[0, :, :] = 0
weights[:, 0, :] = 0
# TODO: This is where this differs from MeanEstimator
pts_rot = m_reshape(pts_rot, (3, L**2, -1))
weights = m_reshape(weights, (L**2, -1))
batch_n = weights.shape[-1]
factors = np.zeros((_2L, _2L, _2L, batch_n), dtype=self.as_type)
# TODO: Numpy has got to have a functional shortcut to avoid looping like this!
for j in range(batch_n):
factors[:, :, :, j] = anufft3(weights[:, j],
pts_rot[:, :, j],
(_2L, _2L, _2L),
real=True)
factors = vol_to_vec(factors)
kernel += vecmat_to_volmat(factors @ factors.T) / (n * L**8)
# Ensure symmetric kernel
kernel[0, :, :, :, :, :] = 0
kernel[:, 0, :, :, :, :] = 0
kernel[:, :, 0, :, :, :] = 0
kernel[:, :, :, 0, :, :] = 0
kernel[:, :, :, :, 0, :] = 0
kernel[:, :, :, :, :, 0] = 0
logger.info('Computing non-centered Fourier Transform')
kernel = mdim_ifftshift(kernel, range(0, 6))
kernel_f = fftn(kernel)
# Kernel is always symmetric in spatial domain and therefore real in Fourier
kernel_f = np.real(kernel_f)
return FourierKernel(kernel_f, centered=False)
def toeplitz(self, L=None):
"""
Compute the 3D Toeplitz matrix corresponding to this Fourier Kernel
:param L: The size of the volumes to be convolved (default M/2, where the dimensions of this Fourier Kernel
are MxMxM
:return: An six-dimensional Toeplitz matrix of size L describing the convolution of a volume with this kernel
"""
if L is None:
L = int(self.M / 2)
A = np.eye(L**3, dtype=self.as_type)
for i in range(L**3):
A[:, i] = vol_to_vec(self.convolve_volume(vec_to_vol(A[:, i])))
A = vecmat_to_volmat(A)
return A