The LIRA-Ising Model: Estimating the boundaries of irregularly shaped X-ray sources

TL;DR

This paper introduces a Bayesian method combining LIRA and Ising models to accurately identify and analyze the boundaries and morphology of irregularly shaped X-ray sources in astronomical images, especially under challenging conditions.

Contribution

The paper presents a novel three-step Bayesian approach, LIRA-Ising, for boundary detection of irregular X-ray sources, integrating multiscale reconstruction and pixel grouping techniques.

Findings

Successfully applied to Chandra images of high redshift quasars

Revealed uniform brightness in one X-ray jet and knotty structures in another

Validated effectiveness through simulation studies

Abstract

Mapping the boundary of an extended source is a key step in the study of its morphology. The background contamination and statistical fluctuations of typical astronomical images make this a challenging statistical task, particularly for X-ray images with low surface brightness. We develop a three-step Bayesian procedure to identify the boundaries of irregularly shaped sources. We first apply a Bayesian multiscale reconstruction algorithm known as LIRA to obtain posterior pixelwise probability distributions of the source intensity that properly account for known structures, astrophysical background, and the effect of the telescope point spread function. Next, we adopt an Ising model to group pixels with similar intensities into cohesive regions corresponding to background and source. Finally, the boundary is derived on the basis of the most likely aggregation of pixels into the source region. Because the overall model combines LIRA and the Ising model, we call it LIRA-Ising. We verify the proposed method using a set of simulation studies. We then apply it to the Chandra X-ray Observatory images of two high redshift quasars, PKS J1421-0643 and 0730+257, to determine the extent and morphology of X-ray jets. Our method shows a uniform X-ray surface brightness of PKS J1421-0643 jet, and identifies knotty structure in the X-ray jet of 0730+257.