TVR-DART: A More Robust Algorithm for Discrete Tomography From Limited Projection Data With Automated Gray Value Estimation

Zhuge, Xiaodong; Palenstijn, Willem Jan; Batenburg, Kees Joost

doi:10.1109/tip.2015.2504869

Cited by 52 publications

(65 citation statements)

References 27 publications

(27 reference statements)

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“…In this data, the projections were only acquired from −75 • -75 °. We thus compared reconstructions using advanced reconstruction algorithms: total-variation minimization (TV-min) [10] , discrete algebraic reconstruction technique (DART) [14] and total variation regularized DART (TVR-DART) [15] , which incorporate the prior knowledge of image sparsity, discrete gray levels and image sparsity combined with discrete gray levels respectively. The images reconstructed from the nonlinear projections and the corrected projections are given in In Fig.…”

Section: Results: Au-ag Core-shell Nanoparticlementioning

confidence: 99%

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Automatic correction of nonlinear damping effects in HAADF–STEM tomography for nanomaterials of discrete compositions

et al. 2018

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a b s t r a c t HAADF-STEM tomography is a common technique for characterizing the three-dimensional morphology of nanomaterials. In conventional tomographic reconstruction algorithms, the image intensity is assumed to be a linear projection of a physical property of the specimen. However, this assumption of linearity is not completely valid due to the nonlinear damping of signal intensities. The nonlinear damping effects increase w.r.t the specimen thickness and lead to so-called "cupping artifacts", due to a mismatch with the linear model used in the reconstruction algorithm. Moreover, nonlinear damping effects can strongly limit the applicability of advanced reconstruction approaches such as Total Variation Minimization and discrete tomography.In this paper, we propose an algorithm for automatically correcting the nonlinear effects and the subsequent cupping artifacts. It is applicable to samples in which chemical compositions can be segmented based on image gray levels. The correction is realized by iteratively estimating the nonlinear relationship between projection intensity and sample thickness, based on which the projections are linearized. The correction and reconstruction algorithms are tested on simulated and experimental data.

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Section: Results: Au-ag Core-shell Nanoparticlementioning

confidence: 99%

“…In fact, these kinds of samples are commonly studied in materials science. For example, the samples typically studied in the context of discrete tomography [14,15] match the requirements.…”

Section: E-mail Address: Zhong@cwinl (Z Zhong)mentioning

confidence: 99%

Automatic correction of nonlinear damping effects in HAADF–STEM tomography for nanomaterials of discrete compositions

et al. 2018

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“…Discrete tomography (DT) is a class of tomographic reconstruction methods that are based on the assumption that the unknown object f consists of a few distinct materials, each producing a (almost) constant gray value in the reconstruction. The total variation regularized discrete algebraic reconstruction technique (TVR-DART) is a recent approach that is adapted towards discrete tomography [16,17], which has proven to be more robust than the original DART algorithm [4]. In particular, using the TVR-DART method allows one to significantly improve reconstruction quality and to drastically reduce the number of required projection images and/or exposure to the sample.…”

Section: Discrete Algebraic Reconstructionmentioning

confidence: 99%

“…The original formulation in [16,17] uses L 2 -norm as the data-fit term, which comes from the assumption that noise in data is additive Gaussian. This is however not always the case, e.g., in HAADF-STEM tomography [8] the noise in data is predominantly Poisson distributed, especially under very low exposure (electron dose) [10].…”

Section: Discrete Algebraic Reconstructionmentioning

confidence: 99%

“…Discrete tomography considers a specific type of prior knowledge, where it is assumed that the unknown object consists of a small number of different materials, each corresponding to a characteristic, approximately constant grey level in the reconstruction. A variety of reconstruction algorithms have been proposed for discrete tomography problems including primal-dual subgradient algorithms [12], network flow algorithms [3], statistical methods [2,7] and algebraic methods [4,17].…”

Section: Introductionmentioning

confidence: 99%

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High-Level Algorithm Prototyping: An Example Extending the TVR-DART Algorithm

Ringh

Zhuge

Palenstijn

et al. 2017

Discrete Geometry for Computer Imagery

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Abstract. Operator Discretization Library (ODL) is an open-sourcePython library for prototyping reconstruction methods for inverse problems, and ASTRA is a high-performance Matlab/Python toolbox for large-scale tomographic reconstruction. The paper demonstrates the feasibility of combining ODL with ASTRA to prototype complex reconstruction methods for discrete tomography. As a case in point, we consider the total-variation regularized discrete algebraic reconstruction technique (TVR-DART). TVR-DART assumes that the object to be imaged consists of a limited number of distinct materials. The ODL/ASTRA implementation of this algorithm makes use of standardized building blocks, that can be combined in a plug-and-play manner. Thus, this implementation of TVR-DART can easily be adapted to account for application specific aspects, such as various noise statistics that come with different imaging modalities.

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A neural network with encoded visible edge prior for limited‐angle computed tomography reconstruction

Zhang

Zhao

et al. 2021

Medical Physics

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Purpose Limited‐angle computed tomography is a challenging but important task in certain medical and industrial applications for nondestructive testing. The limited‐angle reconstruction problem is highly ill‐posed and conventional reconstruction algorithms would introduce heavy artifacts. Various models and methods have been proposed to improve the quality of reconstructions by introducing different priors regarding to the projection data or ideal images. However, the assumed priors might not be practically applicable to all limited‐angle reconstruction problems. Convolutional neural network (CNN) exhibits great promise in the modeling of data coupling and has recently become an important technique in medical imaging applications. Although existing CNN methods have demonstrated promising results, their robustness is still a concern. In this paper, in light of the theory of visible and invisible boundaries, we propose an alternating edge‐preserving diffusion and smoothing neural network (AEDSNN) for limited‐angle reconstruction that builds the visible boundaries as priors into its structure. The proposed method generalizes the alternating edge‐preserving diffusion and smoothing (AEDS) method for limited‐angle reconstruction developed in the literature by replacing its regularization terms by CNNs, by which the piecewise constant assumption assumed by AEDS is effectively relaxed. Methods The AEDSNN is derived by unrolling the AEDS algorithm. AEDSNN consists of several blocks, and each block corresponds to one iteration of the AEDS algorithm. In each iteration of the AEDS algorithm, three subproblems are sequentially solved. So, each block of AEDSNN possesses three main layers: data matching layer, x‐direction regularization layer for visible edges diffusion, and y‐direction regularization layer for artifacts suppressing. The data matching layer is implemented by conventional ordered‐subset simultaneous algebraic reconstruction technique (OS‐SART) reconstruction algorithm, while the two regularization layers are modeled by CNNs for more intelligent and better encoding of priors regarding to the reconstructed images. To further strength the visible edge prior, the attention mechanism and the pooling layers are incorporated into AEDSNN to facilitate the procedure of edge‐preserving diffusion from visible edges. Results We have evaluated the performance of AEDSNN by comparing it with popular algorithms for limited‐angle reconstruction. Experiments on the medical dataset show that the proposed AEDSNN effectively breaks through the piecewise constant assumption usually assumed by conventional reconstruction algorithms, and works much better for piecewise smooth images with nonsharp edges. Experiments on the printed circuit board (PCB) dataset show that AEDSNN can better encode and utilize the visible edge prior, and its reconstructions are consistently better compared to the competing algorithms. Conclusions A deep‐learning approach for limited‐angle reconstruction is proposed in this paper, which significantly ...

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TVR-DART: A More Robust Algorithm for Discrete Tomography From Limited Projection Data With Automated Gray Value Estimation

Cited by 52 publications

References 27 publications

Automatic correction of nonlinear damping effects in HAADF–STEM tomography for nanomaterials of discrete compositions

Automatic correction of nonlinear damping effects in HAADF–STEM tomography for nanomaterials of discrete compositions

High-Level Algorithm Prototyping: An Example Extending the TVR-DART Algorithm

A neural network with encoded visible edge prior for limited‐angle computed tomography reconstruction

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