Shape recovery from sparse tomographic X-ray data

TL;DR

This paper presents a Bayesian NURBS-based approach for reconstructing the shape of homogeneous objects from sparse X-ray tomography data, effectively recovering shape and attenuation with improved accuracy over traditional methods.

Contribution

It introduces a nonlinear inverse problem solution using NURBS parameterization and MCMC sampling, enhancing shape recovery in sparse tomography.

Findings

Outperforms baseline total variation regularization in shape and attenuation recovery

Successfully reconstructs shapes from both simulated and real X-ray data

Provides CAD-compatible boundary representations

Abstract

A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. This approach conveniently provides the result in a format readily compatible with computer-aided design (CAD) software. However, the linear tomography task becomes a nonlinear inverse problem due to the NURBS-based parameterization. Therefore, Bayesian inversion with Markov chain Monte Carlo (MCMC) sampling is used for calculating an estimate of the NURBS control points. The reconstruction method is tested with both simulated data and measured X-ray projection data. The proposed method recovers the shape and the attenuation coefficient significantly better than the baseline algorithm (optimally thresholded total variation regularization), but at the cost of heavier computation.