Interval estimate with probabilistic background constraints in deconvolution

TL;DR

This paper introduces a probabilistic background constraint method for astronomical image deconvolution, providing interval estimates that quantify uncertainty and improve source significance assessment.

Contribution

It presents a novel approach using probabilistic constraints and Monte Carlo analysis to derive interval estimates in image deconvolution, enhancing uncertainty quantification.

Findings

Confidence intervals effectively quantify background constraint uncertainties.

Monte Carlo simulations demonstrate the method's applicability to 1D deconvolution.

Significance levels for sources are reliably estimated from restored images.

Abstract

We present in this article the use of probabilistic background constraints in astronomical image deconvolution to approach to a solution as an interval estimate. We elaborate our objective -- the interval estimate of the unknown object from observed data and our approach -- monte-carlo experiment and analysis of marginal distributions of image values. One-dimensional observation and deconvolution using proposed approach are simulated. Confidence intervals reveal the uncertainties due to the background constraint are calculated and significance levels for sources retrieved from restored images are provided.