On local tomography

Kuchment, Peter; Lancaster, Kirk E.; Mogilevskaya, L

doi:10.1088/0266-5611/11/3/006

Cited by 81 publications

(66 citation statements)

References 17 publications

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“…Basic discussions of microlocal analysis in tomography are in [27,42] and microlocal analysis is used in more general settings (e.g., [17]), seismics (e.g., [6]) radar (e.g., [26,48]) and X-ray CT (e.g., [11,25,28,37]). …”

Section: Basic Microlocal Analysismentioning

confidence: 99%

Artifacts and Visible Singularities in Limited Data X-Ray Tomography

Quinto

2017

Sens Imaging

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We describe a principle to determine which features of an object will be easy to reconstruct from limited X-ray CT data and which will be difficult. The principle depends on the geometry of the data set, and it applies to any limited data set. We also describe a characterization of Frikel and the author explaining artifacts that can be added to limited angle reconstructions, and we provide an easy-to-implement method to decrease them. These ideas are justified using microlocal analysis, deep mathematics that involves Fourier theory. Reconstructions from simulated and real limited data are given to illustrate our ideas.

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Section: Basic Microlocal Analysismentioning

confidence: 99%

Artifacts and Visible Singularities in Limited Data X-Ray Tomography

Quinto

2017

Sens Imaging

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“…Pseudo-differential operators are known not to shift locations of any singularities, including boundaries. 19,28,30 This means that although the backprojection formula might give imprecise values of , it will present the locations of the boundaries of all inclusions correctly.…”

Section: ͑7͒mentioning

confidence: 99%

“…This leads to a local tomography type formula. 25,28 The result of the procedure also produces an expression of the form ⌳, where ⌳ is a pseudo-differential operator defined in Eq. ͑6͒.…”

Section: ͑7͒mentioning

confidence: 99%

Reconstructions in limited‐view thermoacoustic tomography

et al. 2004

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The limited-view problem is studied for thermoacoustic tomography, which is also referred to as photoacoustic or optoacoustic tomography depending on the type of radiation for the induction of acoustic waves. We define a ''detection region,'' within which all points have sufficient detection views. It is explained analytically and shown numerically that the boundaries of any objects inside this region can be recovered stably. Otherwise some sharp details become blurred. One can identify in advance the parts of the boundaries that will be affected if the detection view is insufficient. If the detector scans along a circle in a two-dimensional case, acquiring a sufficient view might require covering more than a -, or less than a -arc of the trajectory depending on the position of the object. Similar results hold in a three-dimensional case. In order to support our theoretical conclusions, three types of reconstruction methods are utilized: a filtered backprojection ͑FBP͒ approximate inversion, which is shown to work well for limited-view data, a local-tomography-type reconstruction that emphasizes sharp details ͑e.g., the boundaries of inclusions͒, and an iterative algebraic truncated conjugate gradient algorithm used in conjunction with FBP. Computations are conducted for both numerically simulated and experimental data. The reconstructions confirm our theoretical predictions.

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“…These algorithms comprise λ -tomography, where local inversion formulae ensure that space-continuously defined functions and their theoretical reconstructions have the same jumps. One should however point out that λ -tomography does not reconstruct the density distribution f itself but the function Λ f , where Λ = √ −△ denotes the Calderon operator which does not preserve gray values (for details see Louis and Maass, 1993;Kuchment et al, 1995;Faridani et al, 1997). An innovative and computationally efficient reconstruction technique has been proposed by Louis (2008).…”

Section: Discussionmentioning

confidence: 99%

Statistical Analysis of Tomographic Reconstruction Algorithms by Morphological Image Characteristics

Lück¹,

Kupsch²,

Lange³

et al. 2011

Image Anal Stereol

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We suggest a procedure for quantitative quality control of tomographic reconstruction algorithms. Our task-oriented evaluation focuses on the correct reproduction of phase boundary length and has thus a clear implication for morphological image analysis of tomographic data. Indirectly the method monitors accurate reproduction of a variety of locally defined critical image features within tomograms such as interface positions and microstructures, debonding, cracks and pores. Tomographic errors of such local nature are neglected if only global integral characteristics such as mean squared deviation are considered for the evaluation of an algorithm. The significance of differences in reconstruction quality between algorithms is assessed using a sample of independent random scenes to be reconstructed. These are generated by a Boolean model and thus exhibit a substantial stochastic variability with respect to image morphology. It is demonstrated that phase boundaries in standard reconstructions by filtered backprojection exhibit substantial errors. In the setting of our simulations, these could be significantly reduced by the use of the innovative reconstruction algorithm DIRECTT.

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On local tomography

Cited by 81 publications

References 17 publications

Artifacts and Visible Singularities in Limited Data X-Ray Tomography

Artifacts and Visible Singularities in Limited Data X-Ray Tomography

Reconstructions in limited‐view thermoacoustic tomography

Statistical Analysis of Tomographic Reconstruction Algorithms by Morphological Image Characteristics

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