ARKCoS: Artifact-Suppressed Accelerated Radial Kernel Convolution on the Sphere

TL;DR

This paper introduces a GPU-accelerated hybrid Fourier/direct space convolution algorithm for radial kernels on the sphere, significantly speeding up high-resolution sky map processing while maintaining high accuracy.

Contribution

It presents a novel hybrid convolution method optimized for GPUs that suppresses ringing artifacts and is compatible with common pixelizations like HEALPix.

Findings

Speeds up beam convolution by two orders of magnitude on GPUs.

Suppresses ringing artifacts on HEALPix pixelization.

Maintains high fractional RMS accuracy (~1e-5).

Abstract

We describe a hybrid Fourier/direct space convolution algorithm for compact radial (azimuthally symmetric) kernels on the sphere. For high resolution maps covering a large fraction of the sky, our implementation takes advantage of the inexpensive massive parallelism afforded by consumer graphics processing units (GPUs). Applications involve modeling of instrumental beam shapes in terms of compact kernels, computation of fine-scale wavelet transformations, and optimal filtering for the detection of point sources. Our algorithm works for any pixelization where pixels are grouped into isolatitude rings. Even for kernels that are not bandwidth limited, ringing features are completely absent on an ECP grid. We demonstrate that they can be highly suppressed on the popular HEALPix pixelization, for which we develop a freely available implementation of the algorithm. As an example application, we show that running on a high-end consumer graphics card our method speeds up beam convolution for simulations of a characteristic Planck high frequency instrument channel by two orders of magnitude compared to the commonly used HEALPix implementation on one CPU core while maintaining at typical a fractional RMS accuracy of about 1 part in 10^5.