add nonlinear Wiener filter demo

demos/nonlinear_wiener_filter.py

+import nifty4 as ift
+from nifty4.library.nonlinearities import Linear, Exponential, Tanh
+import numpy as np
+np.random.seed(20)
+
+if __name__ == "__main__":
+
+    noise_level = 0.3
+    correlation_length = 0.1
+    p_spec = lambda k: (1. / (k*correlation_length + 1) ** 4)
+
+    nonlinearity = Tanh()
+    #nonlinearity = Linear()
+    #nonlinearity = Exponential()
+
+    # Set up position space
+    s_space = ift.RGSpace(1024)
+    h_space = s_space.get_default_codomain()
+
+    # Define harmonic transformation and associated harmonic space
+    HT = ift.HarmonicTransformOperator(h_space, target=s_space)
+
+    S = ift.ScalingOperator(1., h_space)
+
+    # Drawing a sample sh from the prior distribution in harmonic space
+    sh = S.draw_sample()
+
+    # Choosing the measurement instrument
+    # Instrument = SmoothingOperator(s_space, sigma=0.01)
+    mask = np.ones(s_space.shape)
+    mask[600:800] = 0.
+    mask = ift.Field.from_global_data(s_space, mask)
+
+    R = ift.GeometryRemover(s_space) * ift.DiagonalOperator(mask)
+
+    d_space = R.target
+
+    power = ift.sqrt(ift.create_power_operator(h_space, p_spec).diagonal)
+
+    # Creating the mock data
+    true_sky = nonlinearity(HT(power*sh))
+    noiseless_data = R(true_sky)
+    noise_amplitude = noiseless_data.val.std()*noise_level
+    N = ift.ScalingOperator(noise_amplitude**2, d_space)
+    n = N.draw_sample()
+    # Creating the mock data
+    d = noiseless_data + n
+
+    IC1 = ift.GradientNormController(name="IC1", iteration_limit=100,
+                                     tol_abs_gradnorm=1e-4)
+    LS = ift.LineSearchStrongWolfe(c2=0.02)
+    minimizer = ift.RelaxedNewton(IC1, line_searcher=LS)
+
+    ICI = ift.GradientNormController(iteration_limit=2000,
+                                     tol_abs_gradnorm=1e-3)
+    inverter = ift.ConjugateGradient(controller=ICI)
+
+    # initial guess
+    m = ift.Field.full(h_space, 1e-7)
+    map_energy = ift.library.NonlinearWienerFilterEnergy(
+        m, d, R, nonlinearity, HT, power, N, S, inverter=inverter)
+
+    # Minimization with chosen minimizer
+    map_energy, convergence = minimizer(map_energy)
+    m = map_energy.position
+
+    recsky = nonlinearity(HT(power*m))
+    data = R.adjoint_times(d)
+    lo = np.min([true_sky.min(), recsky.min(), data.min()])
+    hi = np.max([true_sky.max(), recsky.max(), data.max()])
+    plotdict = {"colormap": "Planck-like", "ymin": lo, "ymax": hi}
+    ift.plot(true_sky, name="true_sky.png", **plotdict)
+    ift.plot(recsky, name="reconstructed_sky.png", **plotdict)
+    ift.plot(data, name="data.png", **plotdict)

nifty4/library/nonlinear_wiener_filter_energy.py

@@ -31,7 +31,7 @@ class NonlinearWienerFilterEnergy(Energy):
         self.nonlinearity = nonlinearity
         self.ht = ht
         self.power = power
-        m = self.ht(self.power * self.position)
+        m = self.ht(self.power*self.position)
         self.LinearizedResponse = LinearizedSignalResponse(
             Instrument, nonlinearity, ht, power, m)