Mathematics and Physics of Computed Tomography (CT): Demonstrations and Practical Examples

Kharfi, Fayçal

doi:10.5772/52351

Cited by 9 publications

(8 citation statements)

References 3 publications

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“…In practice, S is the number of pixels in a single detector row. 19 For current experiments, there were 768 pixels in each row. This would require 1207 projection angles.…”

Section: Resultsmentioning

confidence: 99%

“…For a parallel beam, the minimum number of projections to ensure adequate reconstruction is P ≥ S π 2 where P is the number of projections and S is the number of points per projection line. In practice, S is the number of pixels in a single detector row . For current experiments, there were 768 pixels in each row.…”

Section: Experimental Results and Discussionmentioning

confidence: 99%

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Liquid Holdup Profiles in Structured Packing Determined via Neutron Radiography

Basden

Eldridge

Farone

et al. 2013

Ind. Eng. Chem. Res.

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Neutron scans of an operating air−water contactor were performed at the NIST Center for Neutron Research (NCNR). Averaged radiographs were used to determine local and average liquid holdup profiles in three stainless steel structured packings (Sulzer Mellapak 250.Y, Mellapak 500.Y, and MellpakPlus 752.Y). Experiments were conducted with liquid loads ranging from 5.4 to 48.9 m 3 /m 2 •h (2.2 to 20 GPM/ft 2 ) and F-factors ranging from 0.61 to 1.65 Pa 0.5 [0.5 to 1.35 (ft/s)(lb m / ft 3 ) 0.5 ] in a column with an inner diameter (ID) of 14.6 cm (5.75 in.). The average holdup in Mellapak 250.Y is validated against previous X-ray computed tomography (CT) and pilot plant experiments. Local holdup profiles exhibited a strong dependency on vertical position in the column, generating a periodic profile in the bulk of all packings. The largest values for holdup were observed at the interface (joint region) between two layers of packing. The joint region in MellapakPlus 752.Y exhibited lower holdup when compared to Mellapak 500.Y.

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“…In practice, S is the number of pixels in a single detector row. 19 For current experiments, there were 768 pixels in each row. This would require 1207 projection angles.…”

Section: Resultsmentioning

confidence: 99%

Section: Experimental Results and Discussionmentioning

confidence: 99%

Liquid Holdup Profiles in Structured Packing Determined via Neutron Radiography

Basden

Eldridge

Farone

et al. 2013

Ind. Eng. Chem. Res.

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show abstract

“…La teoría se basa en considerar una muestra como una superposición de planos transversales µ(x,y) (ver Fig. 4), todos de un mismo espesor sobre el eje z, donde cada uno representa una sección que se va a reconstruir [9] a partir de múltiples imágenes radiográficas (proyecciones) que se obtienen en Cuando la muestra es atravesada por un haz de rayos X paralelos entre sí y perpendiculares al detector, con intensidad incidente I 0 , la intensidad que llega al detector en un sistema de coordenadas polares, con un eje "s" paralelo a los rayos, un eje "r" perpendicular a la radiación, y un angulo θ que forman los rayos X con el eje Y de la muestra, se describe en la fórmula I = I 0 e − µ(x,y) ds = I 0 e − µ(rcosθ −ssinθ ,rsinθ +scosθ ) ds.…”

Section: Reconstrucción Tomográficaunclassified

X-Ray Microtomography to Characterize the Root Canal Volume Extracted in Endodontic Instrumentation

Gilli¹,

Mattea²,

Martin³

et al. 2022

AnAFA

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During the last decades, the analytical techniques of X-ray absorption contrast imaging have systematically gained greater relevance, mainly due to the ability to attain non-destructive exploration of the sample interior. The significant improvement in spatial resolution offered by X-ray micro-tomography, as compared to conventional computed tomography, has motivated its insertion in many biomedical fields, among which dentistry stands out. Particularly, for endodontics, microCT appears as a method of remarkable potential interest to study procedures involved in root canal treatments, where one of the main needs is the anatomical characterization of the root canal in the teeth. The present work reports on the adaptation of the microCT equipment of the LIIFAMIRx⃝laboratory at the E. Gaviola Physics Institute, CONICET and UNC, thus allowing to acquire of radiographic images of dental samples of interest, to be later used in the implementation of algorithms, intended to tomographic reconstruction and volume segmentation. As a result, radiographic images of premolar teeth were obtained with good contrast between the different materials present, and three-dimensional representations, whose visualization is comparable with the real samples. Moreover, it was possible to characterize the root canal volume of the tooth both in its natural form and after having undergone the instrumentation process in which the pulp tissue is extracted.

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“…On the one hand, the FBP is not ideal for reconstructing noisy projections caused by low imaging dose (Ziegler et al 2007). The algorithm also requires the angular sampling rate of projections not to exceed the lower limit of the Shannon-Nyquist theorem (Kharfi 2013). On the other hand, the iterative nature of iterative methods requires many iterations and extended computation time for CT image reconstruction (Willemink and Noël 2019).…”

Section: Introductionmentioning

confidence: 99%

A geometry-guided multi-beamlet deep learning technique for CT reconstruction

Lu¹,

Ren²,

Yin³

2022

Biomed. Phys. Eng. Express

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Purpose: Previous studies have proposed deep-learning techniques to reconstruct CT images from sinograms. However, these techniques employ large fully-connected (FC) layers for projection-to-image domain transformation, producing large models requiring substantial computation power, potentially exceeding the computation memory limit. Our previous work proposed a geometry-guided-deep-learning (GDL) technique for CBCT reconstruction that reduces model size and GPU memory consumption. This study further develops the technique and proposes a novel multi-beamlet deep learning (GMDL) technique of improved performance. The study compares the proposed technique with the FC layer-based deep learning (FCDL) method and the GDL technique through low-dose real-patient CT image reconstruction. Methods: Instead of using a large FC layer, the GMDL technique learns the projection-to-image domain transformation by constructing many small FC layers. In addition to connecting each pixel in the projection domain to beamlet points along the central beamlet in the image domain as GDL does, these smaller FC layers in GMDL connect each pixel to beamlets peripheral to the central beamlet based on the CT projection geometry. We compare ground truth images with low-dose images reconstructed with the GMDL, the FCDL, the GDL, and the conventional FBP methods. The images are quantitatively analyzed in terms of peak-signal-to-noise-ratio (PSNR), structural-similarity-index-measure (SSIM), and root-mean-square-error (RMSE). Results: Compared to other methods, the GMDL reconstructed low-dose CT images show improved image quality in terms of PSNR, SSIM, and RMSE. The optimal number of peripheral beamlets for the GMDL technique is two beamlets on each side of the central beamlet. The model size and memory consumption of the GMDL model is less than 1/100 of the FCDL model. Conclusion: Compared to the FCDL method, the GMDL technique is demonstrated to be able to reconstruct real patient low-dose CT images of improved image quality with significantly reduced model size and GPU memory requirement.

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Mathematics and Physics of Computed Tomography (CT): Demonstrations and Practical Examples

Cited by 9 publications

References 3 publications

Liquid Holdup Profiles in Structured Packing Determined via Neutron Radiography

Liquid Holdup Profiles in Structured Packing Determined via Neutron Radiography

X-Ray Microtomography to Characterize the Root Canal Volume Extracted in Endodontic Instrumentation

A geometry-guided multi-beamlet deep learning technique for CT reconstruction

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