resurrect wiener_filter_easy

demos/wiener_filter_easy.py

+import numpy as np
+import nifty2go as ift
+
+
+# Note that the constructor of PropagatorOperator takes as arguments the
+# response R and noise covariance N operating on signal space and signal
+# covariance operating on harmonic space.
+class PropagatorOperator(ift.EndomorphicOperator):
+    def __init__(self, R, N, Sh):
+        super(PropagatorOperator, self).__init__()
+
+        self.R = R
+        self.N = N
+        self.Sh = Sh
+        self.fft = ift.FFTOperator(R.domain, target=Sh.domain)
+
+    def _inverse_times(self, x):
+        return self.R.adjoint_times(self.N.inverse_times(self.R(x))) \
+               + self.fft.adjoint_times(self.Sh.inverse_times(self.fft(x)))
+
+    @property
+    def domain(self):
+        return self.R.domain
+
+    @property
+    def unitary(self):
+        return False
+
+    @property
+    def self_adjoint(self):
+        return True
+
+
+if __name__ == "__main__":
+    # Set up physical constants
+    # Total length of interval or volume the field lives on, e.g. in meters
+    L = 2.
+    # Typical distance over which the field is correlated (in same unit as L)
+    correlation_length = 0.1
+    # Variance of field in position space sqrt(<|s_x|^2>) (in unit of s)
+    field_variance = 2.
+    # Smoothing length of response (in same unit as L)
+    response_sigma = 0.01
+
+    # Define resolution (pixels per dimension)
+    N_pixels = 256
+
+    # Set up derived constants
+    k_0 = 1./correlation_length
+    # Note that field_variance**2 = a*k_0/4. for this analytic form of power
+    # spectrum
+    a = field_variance**2/k_0*4.
+    pow_spec = (lambda k: a / (1 + k/k_0) ** 4)
+    pixel_width = L/N_pixels
+
+    # Set up the geometry
+    s_space = ift.RGSpace([N_pixels, N_pixels], distances=pixel_width)
+    fft = ift.FFTOperator(s_space)
+    h_space = fft.target[0]
+    p_space = ift.PowerSpace(h_space)
+
+    # Create mock data
+
+    Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)
+
+    sp = ift.Field(p_space, val=pow_spec(p_space.k_lengths))
+    sh = ift.power_synthesize(sp, real_signal=True)
+    ss = fft.inverse_times(sh)
+
+    R = ift.FFTSmoothingOperator(s_space, sigma=response_sigma)
+
+    signal_to_noise = 1
+    diag = ift.Field(s_space, ss.var()/signal_to_noise).weight(1)
+    N = ift.DiagonalOperator(diag)
+    n = ift.Field.from_random(domain=s_space,
+                              random_type='normal',
+                              std=ss.std()/np.sqrt(signal_to_noise),
+                              mean=0)
+
+    d = R(ss) + n
+
+    # Wiener filter
+
+    j = R.adjoint_times(N.inverse_times(d))
+    IC = ift.GradientNormController(iteration_limit=500, tol_abs_gradnorm=0.1)
+    inverter = ift.ConjugateGradient(controller=IC)
+    D = ift.InversionEnabler(PropagatorOperator(Sh=Sh, N=N, R=R),
+                             inverter=inverter)
+
+    m = D(j)