Maximal N-Ghosts and Minimal Information Recovery from N Projected Views of an Array

Svalbe, Imants; Ceko, Matthew

doi:10.1007/978-3-319-66272-5_12

Cited by 3 publications

(2 citation statements)

References 16 publications

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“…In this case no multiple point belongs to G = (G + , G − ), which is called bad configuration. See also [6,32,33,34] for recent results concerning ghosts in discrete tomography. Remark 1.…”

Section: Preliminariesmentioning

confidence: 99%

A rounding theorem for unique binary tomographic reconstruction

Dulio

Pagani

2019

Discrete Applied Mathematics

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Discrete tomography deals with the reconstruction of images from projections collected along a few given directions. Different approaches can be considered, according to different models. In this paper we adopt the grid model, where pixels are lattice points with integer coordinates, X-rays are discrete lattice lines, and projections are obtained by counting the number of lattice points intercepted by X-rays taken in the assigned directions.We move from a theoretical result that allows uniqueness of reconstruction in the grid with just four suitably selected X-ray directions. In this framework, the structure of the allowed ghosts is studied and described. This leads to a new result, stating that the unique binary solution can be explicitly and exactly retrieved from the minimum Euclidean norm solution by means of a rounding method based on some special entries, which are precisely determined. A corresponding iterative algorithm has been implemented, and tested on a few phantoms having different characteristics and structure.

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Section: Preliminariesmentioning

confidence: 99%

A rounding theorem for unique binary tomographic reconstruction

Dulio

Pagani

2019

Discrete Applied Mathematics

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“…Computational investigations related to the explicit construction of switching components can be found in [80]. Switching components for other projection models are considered in [127,128,129,130,136]. Special types of switching components in the context of superresolution imaging, hv-convex polynomioes, and, in a more algebraic setting, are studied in [65], [71], and [115], respectively.…”

Section: Theorem 4 ([120]mentioning

confidence: 99%

13. On the reconstruction of static and dynamic discrete structures

Alpers¹,

Gritzmann²

2019

The Radon Transform

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We study inverse problems of reconstructing static and dynamic discrete structures from tomographic data (with a special focus on the 'classical' task of reconstructing finite point sets in R d ). The main emphasis is on recent mathematical developments and new applications, which emerge in scientific areas such as physics and materials science, but also in inner mathematical fields such as number theory, optimization, and imaging. Along with a concise introduction to the field of discrete tomography, we give pointers to related aspects of computerized tomography in order to contrast the worlds of continuous and discrete inverse problems.

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