Radio Astronomical Image Deconvolution Using Prolate Spheroidal Wave Functions

TL;DR

This paper proposes using generalized prolate spheroidal wave functions as an orthonormal basis for radio interferometric image deconvolution, enabling minimal basis functions and reduced artifacts for high dynamic range imaging.

Contribution

It introduces a method to construct an optimal basis using prolate spheroidal wave functions tailored to the source geometry and sampling, improving deconvolution accuracy.

Findings

Reduces the number of basis functions needed for modeling.

Minimizes artifacts outside the region of interest.

Enhances high dynamic range imaging quality.

Abstract

In order to produce high dynamic range images in radio interferometry, bright extended sources need to be removed with minimal error. However, this is not a trivial task because the Fourier plane is sampled only at a finite number of points. The ensuing deconvolution problem has been solved in many ways, mainly by algorithms based on CLEAN. However, such algorithms that use image pixels as basis functions have inherent limitations and by using an orthonormal basis that span the whole image, we can overcome them. The construction of such an orthonormal basis involves fine tuning of many free parameters that define the basis functions. The optimal basis for a given problem (or a given extended source) is not guaranteed. In this paper, we discuss the use of generalized prolate spheroidal wave functions as a basis. Given the geometry (or the region of interest) of an extended source and the sampling points on the visibility plane, we can construct the optimal basis to model the source. Not only does this gives us the minimum number of basis functions required but also the artifacts outside the region of interest are minimized.