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Convolving with un-normalized kernels
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There are some tasks, such as source finding, where you want to apply a filter
with a kernel that is not normalized.

For data that are well-behaved (contain no missing or infinite values), this is
easy and can be done in one step::

    convolve(image, kernel)

For example, we can try to run a commonly-used peak enhancing kernel:

.. plot::
   :context: reset
   :include-source:
   :align: center

    import numpy as np
    import matplotlib.pyplot as plt

    from astropy.io import fits
    from astropy.utils.data import get_pkg_data_filename
    from astropy.convolution import CustomKernel
    from scipy.signal import convolve as scipy_convolve
    from astropy.convolution import convolve, convolve_fft


    # Load the data from data.astropy.org
    filename = get_pkg_data_filename('galactic_center/gc_msx_e.fits')
    hdu = fits.open(filename)[0]

    # Scale the file to have reasonable numbers
    # (this is mostly so that colorbars don't have too many digits)
    # Also, we crop it so you can see individual pixels
    img = hdu.data[50:90, 60:100] * 1e5

    kernel = CustomKernel([[-1,-1,-1], [-1, 8, -1], [-1,-1,-1]])

    astropy_conv = convolve(img, kernel, normalize_kernel=False, nan_treatment='fill')
    #astropy_conv_fft = convolve_fft(img, kernel, normalize_kernel=False, nan_treatment='fill')

    plt.figure(1, figsize=(12, 12)).clf()
    ax1 = plt.subplot(1, 2, 1)
    im = ax1.imshow(img, vmin=-6., vmax=5.e1, origin='lower',
                    interpolation='nearest', cmap='viridis')

    ax2 = plt.subplot(1, 2, 2)
    im = ax2.imshow(astropy_conv, vmin=-6., vmax=5.e1, origin='lower',
                    interpolation='nearest', cmap='viridis')

If you have an image with missing values (NaNs), you have to replace them with
real values first.  Often, the best way to do this is to replace the NaN values
with interpolated values.  In the example below, we use a Gaussian kernel
with a size similar to that of our peak-finding kernel to replace the bad data
before applying the peak-finding kernel.

.. plot::
   :context:
   :include-source:
   :align: center

   from astropy.convolution import Gaussian2DKernel, interpolate_replace_nans

   # Select a random set of pixels that were affected by some sort of artifact
   # and replaced with NaNs (e.g., cosmic-ray-affected pixels)
   np.random.seed(42)
   yinds, xinds = np.indices(img.shape)
   img[np.random.choice(yinds.flat, 50), np.random.choice(xinds.flat, 50)] = np.nan

   # We smooth with a Gaussian kernel with x_stddev=1 (and y_stddev=1)
   # It is a 9x9 array
   kernel = Gaussian2DKernel(x_stddev=1)

   # interpolate away the NaNs
   reconstructed_image = interpolate_replace_nans(img, kernel)


   # apply peak-finding
   kernel = CustomKernel([[-1,-1,-1], [-1, 8, -1], [-1,-1,-1]])

   # Use the peak-finding kernel
   # We have to turn off kernel normalization and set nan_treatment to "fill"
   # here because `nan_treatment='interpolate'` is incompatible with non-
   # normalized kernels
   peaked_image = convolve(reconstructed_image, kernel,
                           normalize_kernel=False,
                           nan_treatment='fill')

   plt.figure(1, figsize=(12, 12)).clf()
   ax1 = plt.subplot(1, 3, 1)
   ax1.set_title("Image with missing data")
   im = ax1.imshow(img, vmin=-6., vmax=5.e1, origin='lower',
                   interpolation='nearest', cmap='viridis')

   ax2 = plt.subplot(1, 3, 2)
   ax2.set_title("Interpolated")
   im = ax2.imshow(reconstructed_image, vmin=-6., vmax=5.e1, origin='lower',
                   interpolation='nearest', cmap='viridis')

   ax3 = plt.subplot(1, 3, 3)
   ax3.set_title("Peak-Finding")
   im = ax3.imshow(peaked_image, vmin=-6., vmax=5.e1, origin='lower',
                   interpolation='nearest', cmap='viridis')
