Generic iterative subset algorithms for discrete tomography

AbstractDiscrete tomography deals with the reconstruction of images from their projections where the images are assumed to contain only a small number of grey values. In particular, there is a strong focus on the reconstruction of binary images (binary tomography). A variety of binary tomography problems have been considered in the literature, each using different projection models or additional constraints. In this paper, we propose a generic iterative reconstruction algorithm that can be used for many different binary reconstruction problems. In every iteration, a subproblem is solved based on at most two of the available projections. Each of the subproblems can be solved efficiently using network flow methods. We report experimental results for various reconstruction problems. Our results demonstrate that the algorithm is capable of reconstructing complex objects from a small number of projections

A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems

Classical iterative methods for tomographic reconstruction include the class of Algebraic Reconstruction Techniques (ART). Convergence of these stationary linear iterative methods is however notably slow. In this paper we propose the use of Krylov solvers for tomographic linear inversion problems. These advanced iterative methods feature fast convergence at the expense of a higher computational cost per iteration, causing them to be generally uncompetitive without the inclusion of a suitable preconditioner. Combining elements from standard multigrid (MG) solvers and the theory of wavelets, a novel wavelet-based multi-level (WMG) preconditioner is introduced, which is shown to significantly speed-up Krylov convergence. The performance of the WMG-preconditioned Krylov method is analyzed through a spectral analysis, and the approach is compared to existing methods like the classical Simultaneous Iterative Reconstruction Technique (SIRT) and unpreconditioned Krylov methods on a 2D tomographic benchmark problem. Numerical experiments are promising, showing the method to be competitive with the classical Algebraic Reconstruction Techniques in terms of convergence speed and overall performance (CPU time) as well as precision of the reconstruction.Comment: Journal of Computational and Applied Mathematics (2014), 26 pages, 13 figures, 3 table

A Multiresolution Approach to Discrete Tomography Using DART

In discrete tomography, a scanned object is assumed to consist of only a few different materials. This prior knowledge can be effectively exploited by a specialized discrete reconstruction algorithm such as the Discrete Algebraic Reconstruction Technique (DART), which is capable of providing more accurate reconstructions from limited data compared to conventional reconstruction algorithms. However, like most iterative reconstruction algorithms, DART suffers from long computation times. To increase the computational efficiency as well as the reconstruction quality of DART, a multiresolution version of DART (MDART) is proposed, in which the reconstruction starts on a coarse grid with big pixel (voxel) size. The resulting reconstruction is then resampled on a finer grid and used as an initial point for a subsequent DART reconstruction. This process continues until the target pixel size is reached. Experiments show that MDART can provide a significant spee