def update_S(self, new_S, update_spectral_radius=True):
""" Update current eigenPSFs."""
self.S = new_S
# Apply degradation operator to components
normfacs = self.flux / (np.median(self.flux) * self.sig)
self.FdS = np.array([[
nf * degradation_op(S_j, shift_ker, self.D)
for nf, shift_ker in zip(normfacs, utils.reg_format(self.ker))
] for S_j in utils.reg_format(self.S)])
if update_spectral_radius:
PowerMethod.get_spec_rad(self)
def MtX(self, x):
"""Adjoint to degradation operator :func:`MX`.
"""
normfacs = self.flux / (np.median(self.flux) * self.sig)
x = utils.reg_format(x)
upsamp_x = np.array([
nf * adjoint_degradation_op(x_i, shift_ker, self.D)
for nf, x_i, shift_ker in zip(normfacs, x,
utils.reg_format(self.ker_rot))
])
x, upsamp_x = utils.rca_format(x), utils.rca_format(upsamp_x)
return utils.apply_transform(upsamp_x.dot(self.A.T), self.filters)
def MX(self, transf_S):
"""Apply degradation operator and renormalize.
Parameters
----------
transf_S : np.ndarray
Current eigenPSFs in Starlet space.
Returns
-------
np.ndarray result
"""
normfacs = self.flux / (np.median(self.flux) * self.sig)
S = utils.rca_format(
np.array([
filter_convolve(transf_Sj, self.filters, filter_rot=True)
for transf_Sj in transf_S
]))
dec_rec = np.array([
nf * degradation_op(S.dot(A_i), shift_ker, self.D)
for nf, A_i, shift_ker in zip(normfacs, self.A.T,
utils.reg_format(self.ker))
])
self._current_rec = utils.rca_format(dec_rec)
return self._current_rec
def validation_stars(self, test_stars, test_pos):
""" Match PSF model to stars - in flux, shift and pixel sampling - for validation tests.
Returns both the matched PSFs' stamps and chi-square value.
Parameters
----------
test_stars: np.ndarray
Star stamps to be used for comparison with the PSF model. Should be in "rca" format,
i.e. with axises (n_pixels, n_pixels, n_stars).
test_pos: np.ndarray
Their corresponding positions.
"""
if not self.is_fitted:
raise ValueError(
'RCA instance has not yet been fitted to observations. Please run\
the fit method.')
cents = []
for star in utils.reg_format(test_stars):
cents += [utils.CentroidEstimator(star, sig=self.psf_size)]
test_shifts = np.array([ce.return_shifts() for ce in cents])
test_fluxes = utils.flux_estimate_stack(test_stars, rad=4)
matched_psfs = self.estimate_psf(test_pos,
apply_degradation=True,
shifts=test_shifts,
flux=test_fluxes)
return matched_psfs
def MtX(self, x):
"""Adjoint to degradation operator :func:`MX`.
Parameters
----------
x : np.ndarray
Set of finer-grid images.
"""
x = utils.reg_format(x)
STx = np.array([np.sum(FdS_i * x, axis=(1, 2)) for FdS_i in self.FdS])
return STx.dot(self.VT.T) #aka... "V"
def _initialize(self):
""" Initialization tasks related to noise levels, shifts and flux. Note it includes
renormalizing observed data, so needs to be ran even if all three are provided."""
if self.default_filters:
init_filters = get_mr_filters(self.shap[:2],
opt=self.opt,
coarse=True)
else:
init_filters = self.Phi_filters
# noise levels
if self.sigs is None:
transf_data = utils.apply_transform(self.obs_data, init_filters)
transf_mask = utils.transform_mask(self.obs_weights,
init_filters[0])
sigmads = np.array([
1.4826 * utils.mad(fs[0], w)
for fs, w in zip(transf_data, utils.reg_format(transf_mask))
])
self.sigs = sigmads / np.linalg.norm(init_filters[0])
else:
self.sigs = np.copy(self.sigs)
self.sig_min = np.min(self.sigs)
# intra-pixel shifts
if self.shifts is None:
thresh_data = np.copy(self.obs_data)
cents = []
for i in range(self.shap[2]):
# don't allow thresholding to be over 80% of maximum observed pixel
nsig_shifts = min(
self.ksig_init,
0.8 * self.obs_data[:, :, i].max() / self.sigs[i])
thresh_data[:, :, i] = utils.HardThresholding(
thresh_data[:, :, i], nsig_shifts * self.sigs[i])
cents += [
utils.CentroidEstimator(thresh_data[:, :, i],
sig=self.psf_size)
]
self.shifts = np.array([ce.return_shifts() for ce in cents])
self.shift_ker_stack, self.shift_ker_stack_adj = utils.shift_ker_stack(
self.shifts, self.upfact)
# flux levels
if self.flux is None:
#TODO: could actually pass on the centroids to flux estimator since we have them at this point
self.flux = utils.flux_estimate_stack(self.obs_data, rad=4)
self.flux_ref = np.median(self.flux)
# Normalize noise levels observed data
self.sigs /= self.sig_min
self.obs_data /= self.sigs.reshape(1, 1, -1)
def _fit(self):
weights = self.A
comp = self.S
alpha = self.alpha
#### Source updates set-up ####
# initialize dual variable and compute Starlet filters for Condat source updates
dual_var = np.zeros((self.im_hr_shape))
if self.default_filters:
self.Phi_filters = get_mr_filters(self.im_hr_shape[:2],
opt=self.opt,
coarse=True)
rho_phi = np.sqrt(
np.sum(np.sum(np.abs(self.Phi_filters), axis=(1, 2))**2))
# Set up source updates, starting with the gradient
source_grad = grads.SourceGrad(self.obs_data, self.obs_weights,
weights, self.flux, self.sigs,
self.shift_ker_stack,
self.shift_ker_stack_adj, self.upfact,
self.Phi_filters)
# sparsity in Starlet domain prox (this is actually assuming synthesis form)
sparsity_prox = rca_prox.StarletThreshold(
0) # we'll update to the actual thresholds later
# and the linear recombination for the positivity constraint
lin_recombine = rca_prox.LinRecombine(weights, self.Phi_filters)
#### Weight updates set-up ####
# gradient
weight_grad = grads.CoeffGrad(self.obs_data, self.obs_weights, comp,
self.VT, self.flux, self.sigs,
self.shift_ker_stack,
self.shift_ker_stack_adj, self.upfact)
# cost function
weight_cost = costObj([weight_grad], verbose=self.modopt_verb)
source_cost = costObj([source_grad], verbose=self.modopt_verb)
# k-thresholding for spatial constraint
iter_func = lambda x: np.floor(np.sqrt(x)) + 1
coeff_prox = rca_prox.KThreshold(iter_func)
for k in range(self.nb_iter):
#### Eigenpsf update ####
# update gradient instance with new weights...
source_grad.update_A(weights)
# ... update linear recombination weights...
lin_recombine.update_A(weights)
# ... set optimization parameters...
beta = source_grad.spec_rad + rho_phi
tau = 1. / beta
sigma = 1. / lin_recombine.norm * beta / 2
# ... update sparsity prox thresholds...
thresh = utils.reg_format(
utils.acc_sig_maps(self.shap,
self.shift_ker_stack_adj,
self.sigs,
self.flux,
self.flux_ref,
self.upfact,
weights,
sig_data=np.ones(
(self.shap[2], )) * self.sig_min))
thresholds = self.ksig * np.sqrt(
np.array([
filter_convolve(Sigma_k**2, self.Phi_filters**2)
for Sigma_k in thresh
]))
sparsity_prox.update_threshold(tau * thresholds)
# and run source update:
transf_comp = utils.apply_transform(comp, self.Phi_filters)
if self.nb_reweight:
reweighter = cwbReweight(thresholds)
for _ in range(self.nb_reweight):
source_optim = optimalg.Condat(transf_comp,
dual_var,
source_grad,
sparsity_prox,
Positivity(),
linear=lin_recombine,
cost=source_cost,
max_iter=self.nb_subiter_S,
tau=tau,
sigma=sigma)
transf_comp = source_optim.x_final
reweighter.reweight(transf_comp)
thresholds = reweighter.weights
else:
source_optim = optimalg.Condat(transf_comp,
dual_var,
source_grad,
sparsity_prox,
Positivity(),
linear=lin_recombine,
cost=source_cost,
max_iter=self.nb_subiter_S,
tau=tau,
sigma=sigma)
transf_comp = source_optim.x_final
comp = utils.rca_format(
np.array([
filter_convolve(transf_compj, self.Phi_filters, True)
for transf_compj in transf_comp
]))
#TODO: replace line below with Fred's component selection (to be extracted from `low_rank_global_src_est_comb`)
ind_select = range(comp.shape[2])
#### Weight update ####
if k < self.nb_iter - 1:
# update sources and reset iteration counter for K-thresholding
weight_grad.update_S(comp)
coeff_prox.reset_iter()
weight_optim = optimalg.ForwardBackward(
alpha,
weight_grad,
coeff_prox,
cost=weight_cost,
beta_param=weight_grad.inv_spec_rad,
auto_iterate=False)
weight_optim.iterate(max_iter=self.nb_subiter_weights)
alpha = weight_optim.x_final
weights_k = alpha.dot(self.VT)
# renormalize to break scale invariance
weight_norms = np.sqrt(np.sum(weights_k**2, axis=1))
comp *= weight_norms
weights_k /= weight_norms.reshape(-1, 1)
#TODO: replace line below with Fred's component selection
ind_select = range(weights.shape[0])
weights = weights_k[ind_select, :]
supports = None #TODO
self.A = weights
self.S = comp
self.alpha = alpha
source_grad.MX(transf_comp)
self.current_rec = source_grad._current_rec
def estimate_psf(self,
test_pos,
n_neighbors=15,
rbf_function='thin_plate',
apply_degradation=False,
shifts=None,
flux=None,
upfact=None,
rca_format=False):
""" Estimate and return PSF at desired positions.
Parameters
----------
test_pos: np.ndarray
Positions where the PSF should be estimated. Should be in the same format (units,
etc.) as the ``obs_pos`` fed to :func:`RCA.fit`.
n_neighbors: int
Number of neighbors to use for RBF interpolation. Default is 15.
rbf_function: str
Type of RBF kernel to use. Default is ``'thin_plate'``.
apply_degradation: bool
Whether PSF model should be degraded (shifted and resampled on coarse grid),
for instance for comparison with stars. If True, expects shifts to be provided.
Default is False.
shifts: np.ndarray
Intra-pixel shifts to apply if ``apply_degradation`` is set to True.
flux: np.ndarray
Flux levels by which reconstructed PSF will be multiplied if provided. For comparison with
stars if ``apply_degradation`` is set to True.
upfact: int
Upsampling factor; default is None, in which case that of the RCA instance will be used.
rca_format: bool
If True, returns the PSF model in "rca" format, i.e. with axises
(n_pixels, n_pixels, n_stars). Otherwise, and by default, return them in
"regular" format, (n_stars, n_pixels, n_pixels).
"""
if not self.is_fitted:
raise ValueError(
'RCA instance has not yet been fitted to observations. Please run\
the fit method.')
if upfact is None:
upfact = self.upfact
ntest = test_pos.shape[0]
test_weights = np.empty((self.n_comp, ntest))
for j, pos in enumerate(test_pos):
# determine neighbors
nbs, pos_nbs = utils.return_neighbors(pos, self.obs_pos, self.A.T,
n_neighbors)
# train RBF and interpolate for each component
for i in range(self.n_comp):
rbfi = Rbf(pos_nbs[:, 0],
pos_nbs[:, 1],
nbs[:, i],
function=rbf_function)
test_weights[i, j] = rbfi(pos[0], pos[1])
PSFs = self._transform(test_weights)
if apply_degradation:
shift_kernels, _ = utils.shift_ker_stack(shifts, self.upfact)
deg_PSFs = np.array([
grads.degradation_op(PSFs[:, :, j], shift_kernels[:, :, j],
upfact) for j in range(ntest)
])
if flux is not None:
deg_PSFs *= flux.reshape(-1, 1, 1) / self.flux_ref
if rca_format:
return utils.rca_format(deg_PSFs)
else:
return deg_PSFs
elif rca_format:
return PSFs
else:
return utils.reg_format(PSFs)