Discrete tomography (DT) focuses on the case where only few specimen projections are known and the images contain a small number of different colours (eg black-and-white). In this case, conventional reconstruction techniques all fail. Yet, several practical applications demand accurate reconstructions under these conditions. The reconstruction of images using more than two grey-levels, or the reconstruction of three-dimensional images are currently under consideration. On the other end, the general discipline of computational tomography (CT) has been used over the past 40 years, particularly in medical imaging (CAT-scanners), for making noninvasive images of patients. When a large number of projections (X-rays) is available, accurate reconstructions can be made by a wide spectrum of available methods. Applications of these methods are, among others, radiology (CT-, MRI- and PET- scans), geophysics and material science. The tomographic problems can be formulated as a system of linear equations. Unfortunately, these systems are not symmetric nor positive (semi)definite, rank deficient and not square. Furthermore, with every different kind of CT, and thus also with DT, one is faced with experimental noisy data. Because of this background noise in the data, the reconstruction process is more difficult since the system of equations becomes inconsistent easily. In fact the discrete inverse problem of reconstructing finite subsets of the n-dimensional integer lattice ℤn that are only accessible via their line sums (discrete X-rays) in a finite set of lattice directions results into an even more ill-posed problem from data got from noisy experimental environment, usually. Therefore, a tool, able to capture and reliably classify the subtle background noise characteristics of any real experimental tomography set-up could be quite useful to get better overall result by “data cleaning”. The first attempt to develop such a tool by combinatorial approach will be critically discussed in comparison to standard stochastic techniques. Two practical examples will be presented.

Background Information Noise Characterization for Discrete Tomography Application (Whiter than white data)

FIORINI, RODOLFO;
2013-01-01

Abstract

Discrete tomography (DT) focuses on the case where only few specimen projections are known and the images contain a small number of different colours (eg black-and-white). In this case, conventional reconstruction techniques all fail. Yet, several practical applications demand accurate reconstructions under these conditions. The reconstruction of images using more than two grey-levels, or the reconstruction of three-dimensional images are currently under consideration. On the other end, the general discipline of computational tomography (CT) has been used over the past 40 years, particularly in medical imaging (CAT-scanners), for making noninvasive images of patients. When a large number of projections (X-rays) is available, accurate reconstructions can be made by a wide spectrum of available methods. Applications of these methods are, among others, radiology (CT-, MRI- and PET- scans), geophysics and material science. The tomographic problems can be formulated as a system of linear equations. Unfortunately, these systems are not symmetric nor positive (semi)definite, rank deficient and not square. Furthermore, with every different kind of CT, and thus also with DT, one is faced with experimental noisy data. Because of this background noise in the data, the reconstruction process is more difficult since the system of equations becomes inconsistent easily. In fact the discrete inverse problem of reconstructing finite subsets of the n-dimensional integer lattice ℤn that are only accessible via their line sums (discrete X-rays) in a finite set of lattice directions results into an even more ill-posed problem from data got from noisy experimental environment, usually. Therefore, a tool, able to capture and reliably classify the subtle background noise characteristics of any real experimental tomography set-up could be quite useful to get better overall result by “data cleaning”. The first attempt to develop such a tool by combinatorial approach will be critically discussed in comparison to standard stochastic techniques. Two practical examples will be presented.
2013
Discrete Tomography
Discrete Tomography; denoising; Modular Arithmetic; computational information conservation theory; Biomedical Cybernetics; Biomedical Engineering; Healthcare; High Reliability Organization
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/821940
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