Joint Bayesian separation and restoration of CMB from convolutional mixtures

TL;DR

This paper introduces a Bayesian method utilizing gradient-based priors and Langevin sampling to jointly separate and restore CMB and other astrophysical sources from convolutional mixtures, improving accuracy in astrophysical image analysis.

Contribution

It presents a novel Bayesian framework with t-distribution priors and Langevin sampling for joint separation and restoration of astrophysical sources, combining statistical modeling with efficient estimation techniques.

Findings

Effective separation of CMB from mixtures demonstrated

Model captures both smooth and sparse features in data

Improved estimation of source images and parameters

Abstract

We propose a Bayesian approach to joint source separation and restoration for astrophysical diffuse sources. We constitute a prior statistical model for the source images by using their gradient maps. We assume a t-distribution for the gradient maps in different directions, because it is able to fit both smooth and sparse data. A Monte Carlo technique, called Langevin sampler, is used to estimate the source images and all the model parameters are estimated by using deterministic techniques.