A benchmark set for the reconstruction of hv-convex discrete sets

AbstractIn this paper we summarize the most important generation methods developed for the subclasses of hv-convex discrete sets. We also present some new generation techniques to complement the former ones thus making it possible to design a complete benchmark set for testing the performance of reconstruction algorithms on the class of hv-convex discrete sets and its subclasses. By using this benchmark set the paper also collects several statistics on hv-convex discrete sets, which are of great importance in the analysis of algorithms for reconstructing such kinds of discrete sets

Fast binary CT using Fourier null space regularization (FNSR)

X-ray CT is increasingly being adopted in manufacturing as a non destructive inspection tool. Traditionally, industrial workflows follow a two step procedure of reconstruction followed by segmentation. Such workflows suffer from two main problems: (1) the reconstruction typically requires thousands of projections leading to increased data acquisition times. (2) The application of the segmentation process a posteriori is dependent on the quality of the original reconstruction and often does not preserve data fidelity. We present a fast iterative x-ray CT method which simultaneously reconstructs and segments an image from a limited number of projections called Fourier null space regularization (FNSR). The novelty of the approach is in the explicit updating of the image null space with values derived from a regularized image from the previous iteration, thus compensating for any missing projections and effectively regularizing the reconstruction. The speed of the method is achieved by directly applying the Fourier Slice Theorem where the non-uniform fast Fourier transform (NUFFT) is used to compute the frequency spectrum of the projections at their positions in the image k-space. At each iteration a segmented image is computed which is used to populate the null values of the image k-space effectively steering the reconstruction towards a binary solution. The effectiveness of the method to generate accurate reconstructions is demonstrated and benchmarked against other iterative reconstruction techniques using a series of numerical examples. Finally, FNSR is validated using industrial x-ray CT data where accurate reconstructions were achieved with 18 or more projections, a significant reduction from the 5000 needed by filtered back projection

A genetic algorithm for discrete tomography reconstruction

The aim of this paper is the description of an experiment carried out to verify the robustness of two different approaches for the reconstruction of convex polyominoes in discrete tomography. This is a new field of research, because it differs from classic computerized tomography, and several problems are still open. In particular, the stability problem is tackled by using both a modified version of a known algorithm and a new genetic approach. The effect of both, instrumental and quantization noises has been considered too. © 2007 Springer Science+Business Media, LLC