Geometry-Free X-Ray Reconstruction Using the Theory of Convex Projections

Abstract

In problems involving inspection by x-ray tomography it may not always be possible to obtain a full set of parallel-beam or fan-beam views from which to reconstruct an image. This may occur because of: 1) external obstructions; 2) internal obstruction; and 3) restricted data acquisition times. Yet typical reconstruction algorithms such as convolution-back projection (CBP) or the direct Fourier method (DFM) are based on specific geometries and a full set of views.