Discrete tomography by convex–concave regularization and D.C. programming

Schüle, Thomas; Schnörr, Christoph; Weber, Stefan; Hornegger, Joachim

doi:10.1016/j.dam.2005.02.028

Cited by 108 publications

(92 citation statements)

References 20 publications

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“…Although the TCLGS reconstruction is typically inferior to reconstructions computed by more specialized Discrete Tomography algorithms [11,12], its computation is straightforward as a byproduct of the proposed angle selection method, and the general shape of the rNMP curve seems to be similar compared to more advanced methods.…”

Section: Experiments I: Selecting One New Anglementioning

confidence: 99%

“…Following a different approach, the field of discrete tomography focuses on the reconstruction of images that consist of a small, discrete set of gray values [9,10]. By exploiting the knowledge of these gray values in the reconstruction algorithm, it is often possible to compute accurate reconstructions from far fewer projections than required by classical ''continuous'' tomography algorithms [11,12].…”

Section: Introductionmentioning

confidence: 99%

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Dynamic angle selection in binary tomography

Batenburg

Palenstijn

Balázs

et al. 2013

Computer Vision and Image Understanding

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a b s t r a c tIn this paper, we present an algorithm for the dynamic selection of projection angles in binary tomography. Based on the information present in projections that have already been measured, a new projection angle is computed, which aims to maximize the information gained by adding this projection to the set of measurements. The optimization model used for angle selection is based on a characterization of solutions of the binary reconstruction problem, and a related definition of information gain. From this formal model, an algorithm is obtained by several approximation steps. Results from a series of simulation experiments demonstrate that the proposed angle selection scheme is indeed capable of finding angles for which the reconstructed image is much more accurate than for the standard angle selection scheme.

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Section: Experiments I: Selecting One New Anglementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic angle selection in binary tomography

Batenburg

Palenstijn

Balázs

et al. 2013

Computer Vision and Image Understanding

View full text Add to dashboard Cite

show abstract

“…Examples can be found in sparse reconstruction techniques and discrete tomography [4,14,16,31,33,34]. The benefit of these methods is their ability to produce accurate reconstructions from limited projection data.…”

Section: Introductionmentioning

confidence: 99%

Easy implementation of advanced tomography algorithms using the ASTRA toolbox with Spot operators

et al. 2015

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Mathematical scripting languages are commonly used to develop new tomographic reconstruction algorithms. For large experimental datasets, high performance parallel (GPU) implementations are essential, requiring a re-implementation of the algorithm using a language that is closer to the computing hardware. In this paper, we introduce a new MATLAB interface to the ASTRA toolbox, a high performance toolbox for building tomographic reconstruction algorithms. By exposing the ASTRA linear tomography operators through a standard MATLAB matrix syntax, existing and new reconstruction algorithms implemented in MATLAB can now be applied directly to large experimental datasets. This is achieved by using the Spot toolbox, which wraps external code for linear operations into MATLAB objects that can be used as matrices. We provide a series of examples that demonstrate how this Spot operator can be used in combination with existing algorithms implemented in MATLAB and how it can be used for rapid development of new algorithms, resulting in direct applicability to large-scale experimental datasets.

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“…Solving such problems exactly is not feasible for large-scale problems due to their combinatorial nature and often not desirable due to noise. Many heuristic reconstruction have been developed over the years, which fall into two basic classes: methods that aim directly at solving the discrete optimization problem [3,4] and methods that solve (a series) of continuous optimization problems [5,6]. Even state-of-the-art iterative algorithms such as DART [6,7] are computationally very expensive as they are based on iterative reconstruction algorithms.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Grid Refinement for Discrete Tomography

Leeuwen

Batenburg

2014

Advanced Information Systems Engineering

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Abstract. Discrete tomography has proven itself as a powerful approach to image reconstruction from limited data. In recent years, algebraic reconstruction methods have been applied successfully to a range of experimental data sets. However, the computational cost of such reconstruction techniques currently prevents routine application to large data-sets. In this paper we investigate the use of adaptive refinement on QuadTree grids to reduce the number of pixels (or voxels) needed to represent an image. Such locally refined grids match well with the domain of discrete tomography as they are optimally suited for representing images containing large homogeneous regions. Reducing the number of pixels ultimately promises a reduction in both the computation time of discrete algebraic reconstruction techniques as well as reduced memory requirements. At the same time, a reduction of the number of unknowns can reduce the influence of noise on the reconstruction. The resulting refined grid can be used directly for further post-processing (such as segmentation, feature extraction or metrology). The proposed approach can also be used in a non-adaptive manner for region-of-interest tomography. We present a computational approach for automatic determination of the locations where the grid must be defined. We demonstrate how algebraic discrete tomography algorithms can be constructed based on the QuadTree data structure, resulting in reconstruction methods that are fast, accurate and memory efficient.

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Discrete tomography by convex–concave regularization and D.C. programming

Cited by 108 publications

References 20 publications

Dynamic angle selection in binary tomography

Dynamic angle selection in binary tomography

Easy implementation of advanced tomography algorithms using the ASTRA toolbox with Spot operators

Adaptive Grid Refinement for Discrete Tomography

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