Commit 8bf61ef1 by Martin Reinecke

### Merge branch 'poisson_energy' into 'NIFTy_4'

Poisson energy

See merge request ift/NIFTy!242
parents 3f8ac11c c2e26750
Pipeline #27322 passed with stages
in 44 minutes and 50 seconds
 # Program to generate figures of article "Information theory for fields" # by Torsten Ensslin, Annalen der Physik, submitted to special edition # "Physics of Information" in April 2018 import numpy as np import nifty4 as ift import matplotlib.pyplot as plt class Exp3(object): def __call__(self, x): return ift.exp(3*x) def derivative(self, x): return 3*ift.exp(3*x) if __name__ == "__main__": np.random.seed(20) # Set up physical constants nu = 1. # excitation field level kappa = 10. # diffusion constant eps = 1e-8 # small number to tame zero mode sigma_n = 0.2 # noise level sigma_n2 = sigma_n**2 L = 1. # Total length of interval or volume the field lives on nprobes = 1000 # Number of probes for uncertainty quantification # Define resolution (pixels per dimension) N_pixels = 1024 # Define data gaps N1a = int(0.6*N_pixels) N1b = int(0.64*N_pixels) N2a = int(0.67*N_pixels) N2b = int(0.8*N_pixels) # Set up derived constants amp = nu/(2*kappa) # spectral normalization pow_spec = lambda k: amp / (eps + k**2) lambda2 = 2*kappa*sigma_n2/nu # resulting correlation length squared lambda1 = np.sqrt(lambda2) pixel_width = L/N_pixels x = np.arange(0, 1, pixel_width) # Set up the geometry s_domain = ift.RGSpace([N_pixels], distances=pixel_width) h_domain = s_domain.get_default_codomain() HT = ift.HarmonicTransformOperator(h_domain, s_domain) aHT = HT.adjoint # Create mock signal Phi_h = ift.create_power_operator(h_domain, power_spectrum=pow_spec) phi_h = Phi_h.draw_sample() # remove zero mode glob = phi_h.to_global_data() glob[0] = 0. phi_h = ift.Field.from_global_data(phi_h.domain, glob) phi = HT(phi_h) # Setting up an exemplary response GeoRem = ift.GeometryRemover(s_domain) d_domain = GeoRem.target[0] mask = np.ones(d_domain.shape) mask[N1a:N1b] = 0. mask[N2a:N2b] = 0. fmask = ift.Field.from_global_data(d_domain, mask) Mask = ift.DiagonalOperator(fmask) R0 = Mask*GeoRem R = R0*HT # Linear measurement scenario N = ift.ScalingOperator(sigma_n2, d_domain) # Noise covariance n = Mask(N.draw_sample()) # seting the noise to zero in masked region d = R(phi_h) + n # Wiener filter j = R.adjoint_times(N.inverse_times(d)) IC = ift.GradientNormController(name="inverter", iteration_limit=500, tol_abs_gradnorm=1e-3) inverter = ift.ConjugateGradient(controller=IC) D = (ift.SandwichOperator(R, N.inverse) + Phi_h.inverse).inverse D = ift.InversionEnabler(D, inverter, approximation=Phi_h) m = HT(D(j)) # Uncertainty D = ift.SandwichOperator(aHT, D) # real space propagator Dhat = ift.probe_with_posterior_samples(D.inverse, None, nprobes=nprobes)[1] sig = ift.sqrt(Dhat) # Plotting x_mod = np.where(mask > 0, x, None) plt.rcParams["text.usetex"] = True c1 = (m-sig).to_global_data() c2 = (m+sig).to_global_data() plt.fill_between(x, c1, c2, color='pink', alpha=None) plt.plot(x, phi.to_global_data(), label=r"$\varphi$", color='black') plt.scatter(x_mod, d.to_global_data(), label=r'$d$', s=1, color='blue', alpha=0.5) plt.plot(x, m.to_global_data(), label=r'$m$', color='red') plt.xlim([0, L]) plt.ylim([-1, 1]) plt.title('Wiener filter reconstruction') plt.legend() plt.savefig('Wiener_filter.pdf') plt.close() nonlin = Exp3() lam = R0(nonlin(HT(phi_h))) data = ift.Field.from_local_data( d_domain, np.random.poisson(lam.local_data).astype(np.float64)) # initial guess psi0 = ift.Field.full(h_domain, 1e-7) energy = ift.library.PoissonEnergy(psi0, data, R0, nonlin, HT, Phi_h, inverter) IC1 = ift.GradientNormController(name="IC1", iteration_limit=200, tol_abs_gradnorm=1e-4) minimizer = ift.RelaxedNewton(IC1) energy = minimizer(energy)[0] var = ift.probe_with_posterior_samples(energy.curvature, HT, nprobes)[1] sig = ift.sqrt(var) m = HT(energy.position) phi = HT(phi_h) plt.rcParams["text.usetex"] = True c1 = nonlin(m-sig).to_global_data() c2 = nonlin(m+sig).to_global_data() plt.fill_between(x, c1, c2, color='pink', alpha=None) plt.plot(x, nonlin(phi).to_global_data(), label=r"$e^{3\varphi}$", color='black') plt.scatter(x_mod, data.to_global_data(), label=r'$d$', s=1, color='blue', alpha=0.5) plt.plot(x, nonlin(m).to_global_data(), label=r'$e^{3\varphi_\mathrm{cl}}$', color='red') plt.xlim([0, L]) plt.ylim([-0.1, 7.5]) plt.title('Poisson log-normal reconstruction') plt.legend() plt.savefig('Poisson.pdf')
 ... ... @@ -3,4 +3,5 @@ from .wiener_filter_curvature import WienerFilterCurvature from .noise_energy import NoiseEnergy from .nonlinear_power_energy import NonlinearPowerEnergy from .nonlinear_wiener_filter_energy import NonlinearWienerFilterEnergy from .poisson_energy import PoissonEnergy from .nonlinearities import Exponential, Linear, Tanh, PositiveTanh
 ... ... @@ -24,11 +24,11 @@ from ..utilities import memo def _LinearizedPowerResponse(Instrument, nonlinearity, ht, Distributor, tau, xi): power = exp(0.5*tau) position = ht(Distributor(power)*xi) linearization = nonlinearity.derivative(position) return 0.5*Instrument*linearization*ht*xi*Distributor*power xi): power = exp(0.5*tau) position = ht(Distributor(power)*xi) linearization = nonlinearity.derivative(position) return 0.5*Instrument*linearization*ht*xi*Distributor*power class NonlinearPowerEnergy(Energy): ... ...