cartesian_wiener_filter.py 4.9 KB
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import numpy as np
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import nifty2go as ift
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if __name__ == "__main__":
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    signal_to_noise = 1.5  # The signal to noise ratio
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    # Setting up parameters
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    L_1 = 2.                   # Total side-length of the domain
    N_pixels_1 = 512           # Grid resolution (pixels per axis)
    L_2 = 2.                   # Total side-length of the domain
    N_pixels_2 = 512           # Grid resolution (pixels per axis)
    correlation_length_1 = 1.
    field_variance_1 = 2.      # Variance of field in position space
    response_sigma_1 = 0.05    # Smoothing length of response
    correlation_length_2 = 1.
    field_variance_2 = 2.      # Variance of field in position space
    response_sigma_2 = 0.01    # Smoothing length of response

    def power_spectrum_1(k):   # note: field_variance**2 = a*k_0/4.
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        a = 4 * correlation_length_1 * field_variance_1**2
        return a / (1 + k * correlation_length_1) ** 4.

    signal_space_1 = ift.RGSpace([N_pixels_1], distances=L_1/N_pixels_1)
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    harmonic_space_1 = signal_space_1.get_default_codomain()
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    signal_space_2 = ift.RGSpace([N_pixels_2], distances=L_2/N_pixels_2)
    harmonic_space_2 = signal_space_2.get_default_codomain()

    signal_domain = ift.DomainTuple.make((signal_space_1, signal_space_2))
    mid_domain = ift.DomainTuple.make((signal_space_1, harmonic_space_2))
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    harmonic_domain = ift.DomainTuple.make((harmonic_space_1,
                                            harmonic_space_2))
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    fft_1 = ift.FFTOperator(harmonic_domain, space=0)
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    power_space_1 = ift.PowerSpace(harmonic_space_1)
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    mock_power_1 = ift.PS_field(power_space_1, power_spectrum_1)
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    def power_spectrum_2(k):  # note: field_variance**2 = a*k_0/4.
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        a = 4 * correlation_length_2 * field_variance_2**2
        return a / (1 + k * correlation_length_2) ** 2.5

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    fft_2 = ift.FFTOperator(mid_domain, space=1)
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    power_space_2 = ift.PowerSpace(harmonic_space_2)
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    mock_power_2 = ift.PS_field(power_space_2, power_spectrum_2)
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    fft = fft_2*fft_1
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    mock_power = ift.Field(
        (power_space_1, power_space_2),
        val=ift.dobj.from_global_data(
            np.outer(ift.dobj.to_global_data(mock_power_1.val),
                     ift.dobj.to_global_data(mock_power_2.val))))
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    diagonal = ift.power_synthesize_nonrandom(mock_power, spaces=(0, 1))**2
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    S = ift.DiagonalOperator(diagonal)
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    np.random.seed(10)
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    mock_signal = fft(ift.power_synthesize(mock_power, real_signal=True))
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    # Setting up a exemplary response
    N1_10 = int(N_pixels_1/10)
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    mask_1 = np.ones(signal_space_1.shape)
    mask_1[N1_10*7:N1_10*9] = 0.
    mask_1 = ift.Field(signal_space_1, ift.dobj.from_global_data(mask_1))
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    N2_10 = int(N_pixels_2/10)
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    mask_2 = np.ones(signal_space_2.shape)
    mask_2[N2_10*7:N2_10*9] = 0.
    mask_2 = ift.Field(signal_space_2, ift.dobj.from_global_data(mask_2))
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    R = ift.ResponseOperator(signal_domain,
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                             sigma=(response_sigma_1, response_sigma_2),
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                             exposure=(mask_1, mask_2))
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    data_domain = R.target
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    R_harmonic = R*fft
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    # Setting up the noise covariance and drawing a random noise realization
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    ndiag = ift.Field.full(data_domain, mock_signal.var()/signal_to_noise)
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    N = ift.DiagonalOperator(ndiag.weight(1))
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    noise = ift.Field.from_random(
        domain=data_domain, random_type='normal',
        std=mock_signal.std()/np.sqrt(signal_to_noise), mean=0)
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    data = R(mock_signal) + noise
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    # Wiener filter
    j = R_harmonic.adjoint_times(N.inverse_times(data))
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    ctrl = ift.GradientNormController(verbose=True, tol_abs_gradnorm=0.1)
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    inverter = ift.ConjugateGradient(controller=ctrl)
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    wiener_curvature = ift.library.WienerFilterCurvature(
        S=S, N=N, R=R_harmonic, inverter=inverter)
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    m_k = wiener_curvature.inverse_times(j)
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    m = fft(m_k)

    # Probing the variance
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    class Proby(ift.DiagonalProberMixin, ift.Prober):
        pass
    proby = Proby((signal_space_1, signal_space_2), probe_count=1, ncpu=1)
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    proby(lambda z: fft(wiener_curvature.inverse_times(fft.inverse_times(z))))
#    sm = SmoothingOperator(signal_space, sigma=0.02)
#    variance = sm(proby.diagonal.weight(-1))
    variance = proby.diagonal.weight(-1)

    plot_space = ift.RGSpace((N_pixels_1, N_pixels_2))
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    sm = ift.FFTSmoothingOperator(plot_space, sigma=0.03)
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    plotdict = {"xlabel": "Pixel index", "ylabel": "Pixel index",
                "colormap": "Planck-like"}
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    ift.plotting.plot(
        ift.log(ift.sqrt(sm(ift.Field(plot_space, val=variance.val.real)))),
        name='uncertainty.png', zmin=0., zmax=3., title="Uncertainty map",
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        **plotdict)
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    ift.plotting.plot(ift.Field(plot_space, val=mock_signal.val.real),
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                      name='mock_signal.png', **plotdict)
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    ift.plotting.plot(ift.Field(plot_space, val=data.val.real),
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                      name='data.png', **plotdict)
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    ift.plotting.plot(ift.Field(plot_space, val=m.val.real),
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                      name='map.png', **plotdict)