Bayesian Image Reconstruction Based on Voronoi Diagrams

Abstract

We present a Bayesian Voronoi image reconstruction (VIR) technique 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 χ2 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.