Limited-angle computed tomography for sandwich structures using data fusion

Abstract

Both conventional and limited-angle computed-tomography (CT) are ill-posed problems, but where conventional CT has a small null space with few dimensions, limited-angle CT has a much larger null space and is severely ill-posed. The nature of the ill-posedness of limited-angle CT dictates that any limited-angle reconstruction method must interpolate from partial data in the Fourier domain. Large aluminum-core sandwich structures, such as those of aircraft control surfaces, simultaneously prevent full range data acquisition for CT and have face sheets that lie primarily in the limited-angle Radon transform null space. Consequently, interpolation of missing data is not possible and limited-angle CT for large sandwich structures is not feasible. This paper presents a novel method for limited-angle CT that addresses this problem. The method uses constraint-based data fusion to reduce the null space of the problem in a manner consistent with the specimen. Measurements of spatial support and face sheet thickness provide data for the additional constraints. By using the method, accurate reconstruction of sandwich structures becomes possible, where it would otherwise be impossible. The method of convex projections solves the inverse problem posed by the fusion system well because it is fast (for this problem) and easily incorporates the fusion constraints. Experimental results based on synthetic data show the improvement in reconstruction accuracy obtained by the fusion method. Real data results show the successful application of the method to a plexiglass phantom.