Shape recovery for sparse‐data tomography. (26th July 2017)

• Record Type: Journal Article
• Authors: Haario, Heikki; Kallonen, Aki; Laine, Marko; Niemi, Esa; Purisha, Zenith; Siltanen, Samuli
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 18(2018)
• Page Start: 6649
• Page End: 6669
• Publication Date: 2017-07-26
• Subjects: CAD -- MCMC -- NURBS -- reverse engineering -- shape recovery -- X‐ray tomography; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4480
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : A two‐dimensional sparse‐data tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A nonuniform rational basis splines (NURBS) curve is used as a computational representation of the boundary. This approach conveniently provides the result in a format readily compatible with computer‐aided design software. However, the linear tomography task becomes a nonlinear inverse problem because of the NURBS‐based parameterization. Therefore, Bayesian inversion with Markov chain Monte Carlo 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.