Healpy Smoothing Layer

[Arne-Thomsen]

Based off an idea by Tomek, I've implemented a non trainable layer to smooth healpy maps in real space. The smoothing is done in the following steps:

• An sklearn.neighbors.BallTree is used to find the nearest k neighbors for every pixel/index in the Healpix patch to be considered, where k is determined from a radius that is set as the number of standard deviations of the smoothing kernel
• A Gaussian smoothing kernel is evaluated for every nearest neighbor, according to its distance to the original pixel
• A sparse tensor of dense shape (n_pix, n_pix) is built such that every row corresponds to the k nearest neighbors and their Gaussian smoothing weights with respect to the original pixel
• The batch of images is multiplied with this tensor using tf.sparse.sparse_dense_matmul when the layer is called

This operation supports having multiple smoothing scales for the different channels, which are assumed to be in the last input tensor axis like (n_batch, n_pix, n_channels). To save GPU memory (the sparse kernel matrix can become quite large for large smoothing scales), the different smoothing scales are all implemented with the same sparse kernel matrix: Larger smoothing scales are achieved by smoothing repeatedly according to the rule the result of a convolution of two Gaussians with sigma_1 and sigma_2, the result is a Gaussian with sigma_3 = sqrt(sigma_1^2 + sigma_2^2). Since the number of times the smoothing is applied is restricted to integers, the layer automatically implements the closest conservative smoothing scale.

Two additional notes:

• With this, there comes the rather heavy additional dependency on sklearn
• Is it ok that the docstrings follow a different style than for the rest of the package? I can of course change that.

[jafluri]

Great, thanks a lot, looks really good.

I think the sklearn dependency is fine, since it a standard package for ML. However, is sklearn nowadays not in scikit-learn (the package name is still sklearn but the pip command uses scikit-learn)? If so, please adjust the dependency.

It would be good to keep the docstrings consistent in case we setup a proper documentation at some point.

[Arne-Thomsen]

Thanks for the fast response and pointing out the scikit-learn dependency, you're right. I've unified the format of the docstrings with the rest of the repo.