wiener_filter_easy.py

import numpy as np
import nifty4 as ift


if __name__ == "__main__":
    np.random.seed(43)
    # 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)
    h_space = s_space.get_default_codomain()
    HT = ift.HarmonicTransformOperator(h_space, s_space)
    p_space = ift.PowerSpace(h_space)

    # Create mock data

    Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)

    sp = ift.PS_field(p_space, pow_spec)
    sh = ift.power_synthesize(sp, real_signal=True)

    R = HT*ift.create_harmonic_smoothing_operator((h_space,), 0,
                                                  response_sigma)

    noiseless_data = R(sh)
    signal_to_noise = 1.
    noise_amplitude = noiseless_data.val.std()/signal_to_noise
    N = ift.ScalingOperator(noise_amplitude**2, s_space)
    n = ift.Field.from_random(domain=s_space,
                              random_type='normal',
                              std=noise_amplitude,
                              mean=0)

    d = noiseless_data + n

    # Wiener filter

    j = R.adjoint_times(N.inverse_times(d))
    IC = ift.GradientNormController(name="inverter", iteration_limit=500,
                                    tol_abs_gradnorm=0.1)
    inverter = ift.ConjugateGradient(controller=IC)
    D = (R.adjoint*N.inverse*R + Sh.inverse).inverse
    # MR FIXME: we can/should provide a preconditioner here as well!
    D = ift.InversionEnabler(D, inverter)
    m = D(j)

    # Plotting
    d_field = ift.Field(s_space, val=d.val)
    zmax = max(HT(sh).max(), d_field.max(), HT(m).max())
    zmin = min(HT(sh).min(), d_field.min(), HT(m).min())
    plotdict = {"colormap": "Planck-like", "zmax": zmax, "zmin": zmin}
    ift.plot(HT(sh), name="mock_signal.png", **plotdict)
    ift.plot(d_field, name="data.png", **plotdict)
    ift.plot(HT(m), name="reconstruction.png", **plotdict)