Mathematical Methods in Image Reconstruction

Natterer, Frank; Wübbeling, Frank

doi:10.1137/1.9780898718324

Cited by 928 publications

(771 citation statements)

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“…In order to get 69 views, 67 uneven views were picked and the other two views at −72.6° and 72.6° were added. In fact, it is the EA sampling that is popular in practice (Natterer and Wubbeling, 2001), even for missing wedge problems.…”

Section: Methodsmentioning

confidence: 99%

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Liu

Verbridge

et al. 2014

Scanning

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Summary Electron tomography usually suffers from so-called “missing wedge” artifacts caused by limited tilt angle range. An equally sloped tomography (EST) acquisition scheme (which should be called the linogram sampling scheme) was recently applied to achieve 2.4-angstrom resolution. On the other hand, a compressive sensing inspired reconstruction algorithm, known as adaptive dictionary based statistical iterative reconstruction (ADSIR), has been reported for X-ray computed tomography. In this paper, we evaluate the EST, ADSIR, and an ordered-subset simultaneous algebraic reconstruction technique (OS-SART), and compare the ES and equally angled (EA) data acquisition modes. Our results show that OS-SART is comparable to EST, and the ADSIR outperforms EST and OS-SART. Furthermore, the equally sloped projection data acquisition mode has no advantage over the conventional equally angled mode in this context.

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Section: Methodsmentioning

confidence: 99%

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Liu

Verbridge

et al. 2014

Scanning

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“…It can be viewed as a nonlinear generalization of the algebraic reconstruction technique (ART) in x-ray tomography [Nat86,NW01]. In contrary to the filtered backprojection method mentioned earlier, ART uses only part of the data in each step of the reconstruction.…”

Section: Sensitivities and The Adjoint Methodsmentioning

confidence: 99%

Adjoint Fields and Sensitivities for 3D Electromagnetic Imaging in Isotropic and Anisotropic Media

Dorn

Bertete‐Aguirre

Papanicolaou

2008

Inverse Problems and Imaging

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Summary. In this paper we give an overview of a recently developed method for solving an inverse Maxwell problem in environmental and geophysical imaging. Our main focus is on low-frequency cross-borehole electromagnetic induction tomography (EMIT), although related problems arise also in other applications in nondestructive testing and medical imaging. In typical applications (e.g. in environmental remediation), the isotropic or anisotropic conductivity distribution in the earth needs to be reconstructed from surface-to-borehole electromagnetic data. Our method uses a backpropagation strategy (based on adjoint fields) for solving this inverse problem. The method works iteratively, and can be considered as a nonlinear generalization of the Algebraic Reconstruction Technique (ART) in x-ray tomography, or as a nonlinear Kaczmarz-type approach. We will also propose a new regularization scheme for this method which is based on a proper choice of the function spaces for the inversion. A detailed sensitivity analysis for this problem is given, and a set of numerically calculated sensitiviy functions for homogeneous isotropic media is presented.

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“…The technique is based on the acquisition of X-ray shadow projections of a sample which is step-wise rotated over a wide range of angular orientations. The X-ray shadow projections are used to reconstruct 2D CT slices of the object through a back-projection procedure (s. Natterer and Wübbeling, 2001 for a review on back-projection algorithms). Because blurring is inherent to reconstruction by back-projection, the raw X-ray shadow projections have to be convoluted by high-pass filtering.…”

Section: Principles Of Conventional Vs Sem Micro-ctmentioning

confidence: 99%

High-resolution 3D analyses of the shape and internal constituents of small volcanic ash particles: The contribution of SEM micro-computed tomography (SEM micro-CT)

Vonlanthen

Rausch

Ketcham

et al. 2015

Journal of Volcanology and Geothermal Research

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The morphology of small volcanic ash particles is fundamental to our understanding of magma fragmentation, and in transport modeling of volcanic plumes and clouds. Until recently, the analysis of 3D features in small objects (b250 μm) was either restricted to extrapolations from 2D approaches, partial stereo-imaging, or CT methods having limited spatial resolution and/or accessibility. In this study, an X-ray computed-tomography technique known as SEM micro-CT, also called 3D X-ray ultramicroscopy (3D XuM), was used to investigate the 3D morphology of small volcanic ash particles (125-250 μm sieve fraction), as well as their vesicle and microcrystal distribution. The samples were selected from four stratigraphically well-established tephra layers of the Meerfelder Maar (West Eifel Volcanic Field, Germany). Resolution tests performed on a Beametr v1 pattern sample along with Monte Carlo simulations of X-ray emission volumes indicated that a spatial resolution of 0.65 μm was obtained for X-ray shadow projections using a standard thermionic SEM and a bulk brass target as X-ray source. Analysis of a smaller volcanic ash particle (64-125 μm sieve fraction) showed that features with volumes N 20 μm 3 (~3.5 μm in diameter) can be successfully reconstructed and quantified. In addition, new functionalities of the Blob3D software were developed to allow the particle shape factors frequently used as input parameters in ash transport and dispersion models to be calculated. This study indicates that SEM micro-CT is very well suited to quantify the various aspects of shape in fine volcanic ash, and potentially also to investigate the 3D morphology and internal structure of any object b 0.1 mm 3 .

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Mathematical Methods in Image Reconstruction

Cited by 928 publications

References 0 publications

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Adjoint Fields and Sensitivities for 3D Electromagnetic Imaging in Isotropic and Anisotropic Media

High-resolution 3D analyses of the shape and internal constituents of small volcanic ash particles: The contribution of SEM micro-computed tomography (SEM micro-CT)

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