QR-Factorization Algorithm for Computed Tomography (CT): Comparison With FDK and Conjugate Gradient (CG) Algorithms

Even though QR-factorization of the system matrix for tomographic devices has been already used for medical imaging, to date, no satisfactory solution has been found for solving large linear systems, such as those used in computed tomography (CT) (in the order of <inline-formula> <tex-math...

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Vydané v:IEEE transactions on radiation and plasma medical sciences Ročník 2; číslo 5; s. 459 - 469
Hlavní autori: Rodriguez-Alvarez, Maria Jose, Sanchez, Filomeno, Soriano, Antonio, Moliner, Laura, Sanchez, Sebastian, Benlloch, Jose
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Piscataway IEEE 01.09.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
3-D images reconstruction
Algorithms
Biomedical imaging
Computation
Computed tomography
computed tomography (CT)
Computer applications
conjugate gradient (CG)
Conjugates
Davis
Detectors
Factorization
Feldkamp
Image contrast
Image processing
Image quality
Image reconstruction
Iterative methods
Kress (FDK)
Linear systems
Mathematical analysis
Mathematical model
Matrices
Matrix algebra
Matrix methods
Medical imaging
Noise
QR-factorization algorithm
Quality assessment
Quality control
reconstruction algorithms
reconstruction toolkit (RTK)
Sharpness
Tomography
ISSN:2469-7311, 2469-7303
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Popis
Shrnutí:Even though QR-factorization of the system matrix for tomographic devices has been already used for medical imaging, to date, no satisfactory solution has been found for solving large linear systems, such as those used in computed tomography (CT) (in the order of <inline-formula> <tex-math notation="LaTeX">10^{6} </tex-math></inline-formula> equations). In CT, the Feldkamp, Davis, and Kress back projection algorithm (FDK) and iterative methods like conjugate gradient (CG) are the standard methods used for image reconstruction. As the image reconstruction problem can be modeled by a large linear system of equations, QR-factorization of the system matrix could be used to solve this system. Current advances in computer science enable the use of direct methods for solving such a large linear system. The QR-factorization is a numerically stable direct method for solving linear systems of equations, which is beginning to emerge as an alternative to traditional methods, bringing together the best from traditional methods. QR-factorization was chosen because the core of the algorithm, from the computational cost point of view, is precalculated and stored only once for a given CT system, and from then on, each image reconstruction only involves a backward substitution process and the product of a vector by a matrix. Image quality assessment was performed comparing contrast to noise ratio and noise power spectrum; performances regarding sharpness were evaluated by the reconstruction of small structures using data measured from a small animal 3-D CT. Comparisons of QR-factorization with FDK and CG methods show that QR-factorization is able to reconstruct more detailed images for a fixed voxel size.
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ISSN:2469-7311
2469-7303
DOI:10.1109/TRPMS.2018.2843803