Quantifying the spatial resolution of the maximum a posteriori estimate in linear, rank-deficient, Bayesian hard field tomography

TL;DR

This paper introduces a statistical measure for spatial resolution in Bayesian tomography, accounting for prior information and aiding system design, moving beyond traditional deterministic point-spread function methods.

Contribution

It proposes a covariance-based spatial resolution measure that incorporates prior information, providing a more accurate assessment for rank-deficient tomographic reconstructions.

Findings

Prior information sets a lower bound for spatial resolution.

The measure accounts for spatial inhomogeneity in resolution.

Design insights for tomographic systems considering resolution limitations.

Abstract

Image based diagnostics are interpreted in the context of spatial resolution. The same is true for tomographic image reconstruction. Current empirically driven approaches to quantify spatial resolution rely on a deterministic formulation based on point-spread functions which neglect the statistical prior information, that is integral to rank-deficient tomography. We propose a statistical spatial resolution measure based on the covariance of the reconstruction (point estimate) and show that the prior information acts as a lower limit for the spatial resolution. Furthermore, the spatial resolution measure can be employed for designing tomographic systems under consideration of spatial inhomogeneity of spatial resolution.