Bayesian Image Reconstruction Based on Voronoi Diagrams

TL;DR

This paper introduces a Bayesian Voronoi diagram-based method for interferometric image reconstruction, which models images with fewer parameters and improves reconstruction quality over fixed grid methods.

Contribution

The paper proposes a novel Bayesian Voronoi image reconstruction technique that uses variable polygons to model interferometric images, optimizing both the diagram and intensity quantization.

Findings

VIR produces better reconstructed images with fewer parameters.

The method effectively deconvolves simulated interferometric data.

VIR outperforms fixed grid models in residuals and chi^2 metrics.

Abstract

We present a Bayesian Voronoi image reconstruction technique (VIR) for interferometric data. Bayesian analysis applied to the inverse problem allows us to derive the a-posteriori probability of a novel parameterization of interferometric images. We use a variable Voronoi diagram as our model in place of the usual fixed pixel grid. A quantization of the intensity field allows us to calculate the likelihood function and a-priori probabilities. The Voronoi image is optimized including the number of polygons as free parameters. We apply our algorithm to deconvolve simulated interferometric data. Residuals, restored images and chi^2 values are used to compare our reconstructions with fixed grid models. VIR has the advantage of modeling the image with few parameters, obtaining a better image from a Bayesian point of view.