Spread spectrum for imaging techniques in radio interferometry

TL;DR

This paper explores the use of spread spectrum techniques in radio interferometry imaging, leveraging compressed sensing theory to improve reconstruction of sparse astrophysical signals from incomplete Fourier data.

Contribution

It analyzes the universality of the spread spectrum phenomenon in radio interferometry and its impact on sparse signal recovery, supported by theoretical and numerical evidence.

Findings

Spread spectrum enhances imaging quality for sparse signals.

Theoretical analysis shows reduced mutual coherence improves reconstruction.

Numerical simulations confirm the effectiveness of spread spectrum techniques.

Abstract

We consider the probe of astrophysical signals through radio interferometers with small field of view and baselines with non-negligible and constant component in the pointing direction. In this context, the visibilities measured essentially identify with a noisy and incomplete Fourier coverage of the product of the planar signals with a linear chirp modulation. In light of the recent theory of compressed sensing and in the perspective of defining the best possible imaging techniques for sparse signals, we analyze the related spread spectrum phenomenon and suggest its universality relative to the sparsity dictionary. Our results rely both on theoretical considerations related to the mutual coherence between the sparsity and sensing dictionaries, as well as on numerical simulations.