def objfunc_scattering(self, minvec):
N = self.prior_next.xdim
imvec = minvec[:N**2]
EpsilonList = minvec[N**2:]
if self.transform_next == 'log':
imvec = np.exp(imvec)
IM = ehtim.image.Image(imvec.reshape(N,N), self.prior_next.psize, self.prior_next.ra, self.prior_next.dec, rf=self.obs_next.rf, source=self.prior_next.source, mjd=self.prior_next.mjd)
scatt_im = self.scattering_model.Scatter(IM, Epsilon_Screen=so.MakeEpsilonScreenFromList(EpsilonList, N), ea_ker = self._ea_ker, sqrtQ=self._sqrtQ, Linearized_Approximation=True).imvec #the scattered image vector
# Calculate the chi^2 using the scattered image
datterm = 0.
chi2_term_dict = self.make_chisq_dict(scatt_im)
for dname in sorted(self.dat_term_next.keys()):
datterm += self.dat_term_next[dname] * (chi2_term_dict[dname] - 1.)
# Calculate the entropy using the unscattered image
regterm = 0
reg_term_dict = self.make_reg_dict(imvec)
for regname in sorted(self.reg_term_next.keys()):
regterm += self.reg_term_next[regname] * reg_term_dict[regname]
# Scattering screen regularization term
chisq_epsilon = sum(EpsilonList*EpsilonList)/((N*N-1.0)/2.0)
regterm_scattering = self.alpha_phi_next * (chisq_epsilon - 1.0)
return datterm + regterm + regterm_scattering
def plotcur_scattering(self, minvec):
if self._show_updates:
N = self.prior_next.xdim
imvec = minvec[:N**2]
EpsilonList = minvec[N**2:]
if self.transform_next == 'log':
imvec = np.exp(imvec)
IM = ehtim.image.Image(imvec.reshape(N, N),
self.prior_next.psize,
self.prior_next.ra,
self.prior_next.dec,
rf=self.obs_next.rf,
source=self.prior_next.source,
mjd=self.prior_next.mjd)
#the scattered image vector
scatt_im = self.scattering_model.Scatter(
IM,
Epsilon_Screen=so.MakeEpsilonScreenFromList(EpsilonList, N),
ea_ker=self._ea_ker,
sqrtQ=self._sqrtQ,
Linearized_Approximation=True).imvec
# Calculate the chi^2 using the scattered image
datterm = 0.
chi2_term_dict = self.make_chisq_dict(scatt_im)
for dname in sorted(self.dat_term_next.keys()):
datterm += self.dat_term_next[dname] * (chi2_term_dict[dname] -
1.)
# Calculate the entropy using the unscattered image
regterm = 0
reg_term_dict = self.make_reg_dict(imvec)
for regname in sorted(self.reg_term_next.keys()):
regterm += self.reg_term_next[regname] * reg_term_dict[regname]
# Scattering screen regularization term
chisq_epsilon = sum(EpsilonList * EpsilonList) / (
(N * N - 1.0) / 2.0)
regterm_scattering = self.alpha_phi_next * (chisq_epsilon - 1.0)
outstr = "i: %d " % self._nit
for dname in sorted(self.dat_term_next.keys()):
outstr += "%s : %0.2f " % (dname, chi2_term_dict[dname])
for regname in sorted(self.reg_term_next.keys()):
outstr += "%s : %0.2f " % (regname, reg_term_dict[regname])
outstr += "Epsilon chi^2 : %0.2f " % (chisq_epsilon)
outstr += "Max |Epsilon| : %0.2f " % (max(abs(EpsilonList)))
print(outstr)
self._nit += 1
imgr_deblur.make_image_I()
imgr_deblur.out_last().display()
# Now image using stochastic optics
imgr_so = eh.imager.Imager(obs,
gaussprior,
prior_im=gaussprior,
maxit=200,
flux=total_flux,
clipfloor=-1.)
imgr_so.make_image_I_stochastic_optics()
# Now look at the unscattered image, the scattered image, and replicate the scattering using the solved screen
imgr_so.out_last().display()
imgr_so.out_scattered_last().display()
imgr_so.scattering_model.Scatter(imgr_so.out_last(),
Epsilon_Screen=so.MakeEpsilonScreenFromList(
imgr_so.out_epsilon_last(), npix),
ea_ker=imgr_so._ea_ker,
sqrtQ=imgr_so._sqrtQ,
Linearized_Approximation=True,
DisplayImage=True)
#Note that only the scattered image will fit the measured visibilities!
eh.comp_plots.plotall_obs_im_compare(obs, imgr_so.out_last(), 'uvdist', 'amp')
eh.comp_plots.plotall_obs_im_compare(obs, imgr_so.out_scattered_last(),
'uvdist', 'amp')
# Decrease the scattering regularization slightly and re-image (desired max |Epsilon| is ~2.5)
imgr_so.alpha_phi_next /= 2.0
imgr_so.init_next = imgr_so.out_last().blur_circ(obs.res())
imgr_so.epsilon_list_next = imgr_so.out_epsilon_last()
imgr_so.make_image_I_stochastic_optics()
def make_image_I_stochastic_optics(self, grads=True, show_updates=True):
"""Reconstructs an image of total flux density using the stochastic optics scattering mitigation technique.
Uses the scattering model of the imager. If none has been specified, it will default to a standard model for Sgr A*.
Returns the estimated unscattered image.
Args:
grads (bool): Flag for whether or not to use analytic gradients.
show_updates (bool): Flag for whether or not to show updates for each step of convergence.
Returns:
out (Image): The estimated *unscattered* image.
"""
N = self.prior_next.xdim
# Checks and initialize
self.check_params()
self.check_limits()
self.init_imager_I()
self.init_imager_scattering()
# Generate the initial image+screen vector. By default, the screen is re-initialized to zero each time.
if self.transform_next == 'log':
xinit = np.log(self._ninit_I)
else:
xinit = self._ninit_I
if len(self.epsilon_list_next) == 0:
xinit = np.concatenate((xinit, np.zeros(N**2 - 1)))
else:
xinit = np.concatenate((xinit, self.epsilon_list_next))
self._nit = 0
# Print stats
if show_updates:
self._show_updates = True
else:
self._show_updates = False
self.plotcur_scattering(xinit)
# Minimize
optdict = {'maxiter': self.maxit_next, 'ftol': STOP, 'maxcor': NHIST}
tstart = time.time()
if grads:
res = opt.minimize(self.objfunc_scattering,
xinit,
method='L-BFGS-B',
jac=self.objgrad_scattering,
options=optdict,
callback=self.plotcur_scattering)
else:
res = opt.minimize(self.objfunc_scattering,
xinit,
method='L-BFGS-B',
options=optdict,
callback=self.plotcur_scattering)
tstop = time.time()
# Format output
out = res.x[:N**2]
if self.transform_next == 'log': out = np.exp(out)
if np.any(np.invert(self._embed_mask)):
raise Exception("Embedding is not currently implemented!")
out = embed(out, self._embed_mask)
outim = image.Image(out.reshape(N, N),
self.prior_next.psize,
self.prior_next.ra,
self.prior_next.dec,
rf=self.prior_next.rf,
source=self.prior_next.source,
mjd=self.prior_next.mjd,
pulse=self.prior_next.pulse)
outep = res.x[N**2:]
outscatt = self.scattering_model.Scatter(
outim,
Epsilon_Screen=so.MakeEpsilonScreenFromList(outep, N),
ea_ker=self._ea_ker,
sqrtQ=self._sqrtQ,
Linearized_Approximation=True)
# Preserving image complex polarization fractions
if len(self.prior_next.qvec):
qvec = self.prior_next.qvec * out / self.prior_next.imvec
uvec = self.prior_next.uvec * out / self.prior_next.imvec
outim.add_qu(qvec.reshape(N, N), uvec.reshape(N, N))
# Print stats
print("time: %f s" % (tstop - tstart))
print("J: %f" % res.fun)
print(res.message)
# Append to history
logstr = str(self.nruns) + ": make_image_I_stochastic_optics()"
self._append_image_history(outim, logstr)
self._out_list_epsilon.append(res.x[N**2:])
self._out_list_scattered.append(outscatt)
self.nruns += 1
# Return Image object
return outim
def objgrad_scattering(self, minvec):
"""Current stochastic optics objective function gradient
"""
wavelength = C / self.obs_next.rf * 100.0 #Observing wavelength [cm]
wavelengthbar = wavelength / (2.0 * np.pi) #lambda/(2pi) [cm]
N = self.prior_next.xdim
#Field of view, in cm, at the scattering screen
FOV = self.prior_next.psize * N * self.scattering_model.observer_screen_distance
rF = self.scattering_model.rF(wavelength)
imvec = minvec[:N**2]
EpsilonList = minvec[N**2:]
if self.transform_next == 'log':
imvec = np.exp(imvec)
IM = ehtim.image.Image(imvec.reshape(N, N),
self.prior_next.psize,
self.prior_next.ra,
self.prior_next.dec,
rf=self.obs_next.rf,
source=self.prior_next.source,
mjd=self.prior_next.mjd)
#the scattered image vector
scatt_im = self.scattering_model.Scatter(
IM,
Epsilon_Screen=so.MakeEpsilonScreenFromList(EpsilonList, N),
ea_ker=self._ea_ker,
sqrtQ=self._sqrtQ,
Linearized_Approximation=True).imvec
EA_Image = self.scattering_model.Ensemble_Average_Blur(
IM, ker=self._ea_ker)
EA_Gradient = so.Wrapped_Gradient(
(EA_Image.imvec / (FOV / N)).reshape(N, N))
#The gradient signs don't actually matter, but let's make them match intuition (i.e., right to left, bottom to top)
EA_Gradient_x = -EA_Gradient[1]
EA_Gradient_y = -EA_Gradient[0]
Epsilon_Screen = so.MakeEpsilonScreenFromList(EpsilonList, N)
phi = self.scattering_model.MakePhaseScreen(
Epsilon_Screen,
IM,
obs_frequency_Hz=self.obs_next.rf,
sqrtQ_init=self._sqrtQ).imvec.reshape((N, N))
phi_Gradient = so.Wrapped_Gradient(phi / (FOV / N))
phi_Gradient_x = -phi_Gradient[1]
phi_Gradient_y = -phi_Gradient[0]
#Entropy gradient; wrt unscattered image so unchanged by scattering
regterm = 0
reg_term_dict = self.make_reggrad_dict(imvec)
for regname in sorted(self.reg_term_next.keys()):
regterm += self.reg_term_next[regname] * reg_term_dict[regname]
# Chi^2 gradient wrt the unscattered image
# First, the chi^2 gradient wrt to the scattered image
datterm = 0.
chi2_term_dict = self.make_chisqgrad_dict(scatt_im)
for dname in sorted(self.dat_term_next.keys()):
datterm += self.dat_term_next[dname] * (chi2_term_dict[dname] - 1.)
dchisq_dIa = datterm.reshape((N, N))
# Now the chain rule factor to get the chi^2 gradient wrt the unscattered image
gx = (rF**2.0 * so.Wrapped_Convolve(
self._ea_ker_gradient_x[::-1, ::-1], phi_Gradient_x *
(dchisq_dIa))).flatten()
gy = (rF**2.0 * so.Wrapped_Convolve(
self._ea_ker_gradient_y[::-1, ::-1], phi_Gradient_y *
(dchisq_dIa))).flatten()
chisq_grad_im = so.Wrapped_Convolve(self._ea_ker[::-1, ::-1],
(dchisq_dIa)).flatten() + gx + gy
# Gradient of the data chi^2 wrt to the epsilon screen
#Preliminary Definitions
chisq_grad_epsilon = np.zeros(N**2 - 1)
i_grad = 0
ell_mat = np.zeros((N, N))
m_mat = np.zeros((N, N))
for ell in range(0, N):
for m in range(0, N):
ell_mat[ell, m] = ell
m_mat[ell, m] = m
#Real part; top row
for t in range(1, (N + 1) / 2):
s = 0
grad_term = so.Wrapped_Gradient(
wavelengthbar / FOV * self._sqrtQ[s][t] * 2.0 *
np.cos(2.0 * np.pi / N *
(ell_mat * s + m_mat * t)) / (FOV / N))
grad_term_x = -grad_term[1]
grad_term_y = -grad_term[0]
chisq_grad_epsilon[i_grad] = np.sum(
dchisq_dIa * rF**2 *
(EA_Gradient_x * grad_term_x + EA_Gradient_y * grad_term_y))
i_grad = i_grad + 1
#Real part; remainder
for s in range(1, (N + 1) / 2):
for t in range(N):
grad_term = so.Wrapped_Gradient(
wavelengthbar / FOV * self._sqrtQ[s][t] * 2.0 *
np.cos(2.0 * np.pi / N *
(ell_mat * s + m_mat * t)) / (FOV / N))
grad_term_x = -grad_term[1]
grad_term_y = -grad_term[0]
chisq_grad_epsilon[i_grad] = np.sum(
dchisq_dIa * rF**2 * (EA_Gradient_x * grad_term_x +
EA_Gradient_y * grad_term_y))
i_grad = i_grad + 1
#Imaginary part; top row
for t in range(1, (N + 1) / 2):
s = 0
grad_term = so.Wrapped_Gradient(
-wavelengthbar / FOV * self._sqrtQ[s][t] * 2.0 *
np.sin(2.0 * np.pi / N *
(ell_mat * s + m_mat * t)) / (FOV / N))
grad_term_x = -grad_term[1]
grad_term_y = -grad_term[0]
chisq_grad_epsilon[i_grad] = np.sum(
dchisq_dIa * rF**2 *
(EA_Gradient_x * grad_term_x + EA_Gradient_y * grad_term_y))
i_grad = i_grad + 1
#Imaginary part; remainder
for s in range(1, (N + 1) / 2):
for t in range(N):
grad_term = so.Wrapped_Gradient(
-wavelengthbar / FOV * self._sqrtQ[s][t] * 2.0 *
np.sin(2.0 * np.pi / N *
(ell_mat * s + m_mat * t)) / (FOV / N))
grad_term_x = -grad_term[1]
grad_term_y = -grad_term[0]
chisq_grad_epsilon[i_grad] = np.sum(
dchisq_dIa * rF**2 * (EA_Gradient_x * grad_term_x +
EA_Gradient_y * grad_term_y))
i_grad = i_grad + 1
# Gradient of the chi^2 regularization term for the epsilon screen
chisq_epsilon_grad = self.alpha_phi_next * 2.0 * EpsilonList / (
(N * N - 1) / 2.0)
# chain rule term for change of variables
if self.transform_next == 'log':
regterm *= imvec
chisq_grad_im *= imvec
return np.concatenate(((regterm + chisq_grad_im),
(chisq_grad_epsilon + chisq_epsilon_grad)))