Efficient Computation of Prolate Spheroidal Wave Functions in Radio Astronomical Source Modeling

TL;DR

This paper introduces a more efficient method for constructing Prolate Spheroidal Wave Functions (PSWF) in radio astronomy by using Delaunay triangulation to reduce computational costs without losing information.

Contribution

It proposes a novel approach using Delaunay triangulation for PSWF kernel construction, enhancing efficiency in radio astronomical source modeling.

Findings

Computational efficiency improved by using Delaunay triangulation.

No loss of information with the new method.

Enables faster high-fidelity imaging in radio astronomy.

Abstract

The application of orthonormal basis functions such as Prolate Spheroidal Wave Functions (PSWF) for accurate source modeling in radio astronomy has been comprehensively studied. They are of great importance for high fidelity, high dynamic range imaging with new radio telescopes as well as conventional ones. But the construction of PSWF is computationally expensive compared to other closed form basis functions. In this paper, we suggest a solution to reduce its computational cost by more efficient construction of the matrix kernel which relates the image domain to visibility (or Fourier) domain. Radio astronomical images are mostly represented using a regular grid of rectangular pixels. This is required for efficient storage and display purposes and moreover, comes naturally as a by product of the Fast Fourier Transform (FFT) in imaging. We propose the use of Delaunay triangulation as opposed to regular gridding of an image for a finer selection of the region of interest (signal support) during the PSWF kernel construction. We show that the computational efficiency improves without loss of information. Once the PSWF basis is constructed using the irregular grid, we revert back to the regular grid by interpolation and thereafter, conventional imaging techniques can be applied.