Dart: A Fast Heuristic Algebraic Reconstruction Algorithm for Discrete Tomography

Batenburg, K. Joost; Sijbers, Jan

doi:10.1109/icip.2007.4379972

Cited by 52 publications

(49 citation statements)

References 5 publications

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“…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. Not only the costs of forward and backward projection and the memory usage scale linearly with N , the number of iterations required is also expected to scale linearly with N .…”

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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Section: Introductionmentioning

confidence: 99%

Adaptive Grid Refinement for Discrete Tomography

Leeuwen

Batenburg

2014

Advanced Information Systems Engineering

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“…Some techniques introduce post-processing steps for the discretization of the result of a continuous reconstruction algorithm [13,14,15]. Other approaches introduce steering mechanisms into the process of continuous reconstruction methods to gain discrete results [11,12,19,32,48], or reformulate the problem as an energy minimization task, and approximate the solution with some stochastic [6,7,8,16,30,41,51,52,68], or deterministic [44,45,55,56,67,68] optimization strategy. Moreover, the difficulties described at the Continuous Reconstruction problem -i.e., the possible inconsistency of the projections, and the non-uniqueness of the results -can still be present in the discrete case, which makes an even bigger need for approximate solutions capable of handling inconsistent and incomplete projection data.…”

Section: Reconstruction Algorithms For Tomographymentioning

confidence: 99%

“…In this case the iteration will stop in a semi-continuous solution, where some pixels are properly discretized, and the rest of them are left a) b) c) Figure 3.2: Some of the software phantoms used for testing. a) a binary image; b) a multivalued image from [11]; c) the well-known Shepp-Logan head phantom (see, e.g., page 53 of [39]). …”

Section: )mentioning

confidence: 99%

“…The Discrete Algebraic Reconstruction Technique (DART) [11], is a method for the general case of the Discrete Reconstruction problem, that is based on an iterated thresholding of continuous reconstructions. This algorithm starts out by producing a continuous reconstruction using an algebraic reconstruction method [70,71].…”

Section: Discrete Algebraic Reconstruction Techniquementioning

confidence: 99%

“…Some methods provide heuristic strategies for discretizing the results of continuous reconstructions [11,12,48], some other techniques reformulate the task as an optimization problem that can be solved by different meta-heuristics [6,7,8,44]. In this chapter we describe a reconstruction algorithm, that we developed for the general case of DT, and that can perform the reconstruction by minimizing a suitably constructed energy function.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Information Content of Projections and Reconstruction of Objects in Discrete Tomography

Varga

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A Multi-channel DART Algorithm

Zeegers

Lucka

Batenburg

2018

Lecture Notes in Computer Science

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Tomography deals with the reconstruction of objects from their projections, acquired along a range of angles. Discrete tomography is concerned with objects that consist of a small number of materials, which makes it possible to compute accurate reconstructions from highly limited projection data. For cases where the allowed intensity values in the reconstruction are known a priori, the discrete algebraic reconstruction technique (DART) has shown to yield accurate reconstructions from few projections. However, a key limitation is that the benefit of DART diminishes as the number of different materials increases. Many tomographic imaging techniques can simultaneously record tomographic data at multiple channels, each corresponding to a different weighting of the materials in the object. Whenever projection data from more than one channel is available, this additional information can potentially be exploited by the reconstruction algorithm. In this paper we present Multi-Channel DART (MC-DART), which deals effectively with multi-channel data. This class of algorithms is a generalization of DART to multiple channels and combines the information for each separate channelreconstruction in a multi-channel segmentation step. We demonstrate that in a range of simulation experiments, MC-DART is capable of producing more accurate reconstructions compared to single-channel DART.

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Dart: A Fast Heuristic Algebraic Reconstruction Algorithm for Discrete Tomography

Cited by 52 publications

References 5 publications

Adaptive Grid Refinement for Discrete Tomography

Adaptive Grid Refinement for Discrete Tomography

Information Content of Projections and Reconstruction of Objects in Discrete Tomography

A Multi-channel DART Algorithm

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