Improving the Solution of an Incomplete Problem in Computed Tomography
type: CreativeWork
description: Computed Tomography (CT) is an imaging method that uses radiation, such as Xrays, to scan an object from di erent orientations to provide projection-measurements to reconstruct a pixelated image of the interior of the object using mathematical algorithms. To successfully recover an unambiguous image of the scanned object, the number of measurements should be equal or higher than the number of the pixels (unknowns). This requires relatively long data acquisition time and high radiation exposure. To reduce radiation exposure, particularly in medical applications, this thesis investigates whether credible CT images can be recovered from a lower number of radiation projections; particularly when the CT problem is incomplete, i.e. when the number of measurements is less than the number of unknowns. In practice images are typically piece-wise constant i.e. consist of a limited number of materials in a few regions and consequently have a small set of image attributes. Then, constrained optimization methods, such as total-variation (TV) regularization and compressed sensing, can produce credible images in incomplete (underdetermined) CT problems. However, the uniqueness of such solutions cannot always i be assured, since an incomplete problem can have multiple solutions that match the input measurements. Therefore, it is proposed in this work to produce a unique image reconstructed by formulating the problem as an overdetermined problem. This was done by reconstructing a coarse image from the same CT data so that the number of pixels (unknowns) is higher than the number of available measurements. The reliable coarse image was then fused with the ne image reconstructed from incomplete data, in an attempt to improve the quality of the latter image. Several common image fusion methods were applied, but were found not to be e ective due to the inevitable smoothing of the image attributes due to the larger size of the pixels of the coarse image. Therefore, a new fuzzy image re n…
abstract: Computed Tomography (CT) is an imaging method that uses radiation, such as Xrays, to scan an object from di erent orientations to provide projection-measurements to reconstruct a pixelated image of the interior of the object using mathematical algorithms. To successfully recover an unambiguous image of the scanned object, the number of measurements should be equal or higher than the number of the pixels (unknowns). This requires relatively long data acquisition time and high radiation exposure. To reduce radiation exposure, particularly in medical applications, this thesis investigates whether credible CT images can be recovered from a lower number of radiation projections; particularly when the CT problem is incomplete, i.e. when the number of measurements is less than the number of unknowns. In practice images are typically piece-wise constant i.e. consist of a limited number of materials in a few regions and consequently have a small set of image attributes. Then, constrained optimization methods, such as total-variation (TV) regularization and compressed sensing, can produce credible images in incomplete (underdetermined) CT problems. However, the uniqueness of such solutions cannot always i be assured, since an incomplete problem can have multiple solutions that match the input measurements. Therefore, it is proposed in this work to produce a unique image reconstructed by formulating the problem as an overdetermined problem. This was done by reconstructing a coarse image from the same CT data so that the number of pixels (unknowns) is higher than the number of available measurements. The reliable coarse image was then fused with the ne image reconstructed from incomplete data, in an attempt to improve the quality of the latter image. Several common image fusion methods were applied, but were found not to be e ective due to the inevitable smoothing of the image attributes due to the larger size of the pixels of the coarse image. Therefore, a new fuzzy image re n…
author: Malik, Varinder
language: en
date published: 2020-08
date modified: 2026-07-24T04:03:32Z
provider: University of Regina
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Faculty of Graduate Studies and Research, University of Regina

PropertyValue
property ID: Handle
value: https://hdl.handle.net/10294/14393

PropertyValue
property ID: DOI
value: 10.82465/4164