wiener_filter_easy.py 2.41 KB
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import numpy as np
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import nifty4 as ift
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if __name__ == "__main__":
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    np.random.seed(43)
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    # 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)
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    h_space = s_space.get_default_codomain()
    ht = ift.HarmonicTransformOperator(h_space, s_space)
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    p_space = ift.PowerSpace(h_space)

    # Create mock data

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

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

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    R = ht*ift.create_harmonic_smoothing_operator((h_space,),0,response_sigma)
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    noiseless_data = R(sh)
    signal_to_noise = 1.
    noise_amplitude = noiseless_data.std()/signal_to_noise
    N = ift.DiagonalOperator(ift.Field.full(s_space, noise_amplitude**2))
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    n = ift.Field.from_random(domain=s_space,
                              random_type='normal',
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                              std=noise_amplitude,
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                              mean=0)

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    d = noiseless_data + n
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    # Wiener filter

    j = R.adjoint_times(N.inverse_times(d))
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    IC = ift.GradientNormController(name="inverter", iteration_limit=500,
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                                    tol_abs_gradnorm=0.1)
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    inverter = ift.ConjugateGradient(controller=IC)
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    D = (R.adjoint*N.inverse*R + Sh.inverse).inverse
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    # MR FIXME: we can/should provide a preconditioner here as well!
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    D = ift.InversionEnabler(D, inverter)
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    m = D(j)
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    plotdict = {"xlabel": "Pixel index", "ylabel": "Pixel index",
                "colormap": "Planck-like"}
    ift.plot(ht(sh), name="mock_signal.png", **plotdict)
    ift.plot(ift.Field(s_space, val=d.val),
             name="data.png", **plotdict)
    ift.plot(ht(m), name="map.png", **plotdict)