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Noise characteristics and edge-enhan...

Alwehebi, Aisha Abdullah.

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Noise characteristics and edge-enhancing denoisers for the magnitude MRI imagery.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Noise characteristics and edge-enhancing denoisers for the magnitude MRI imagery./
Author:	Alwehebi, Aisha Abdullah.
Description:	65 p.
Notes:	Source: Dissertation Abstracts International, Volume: 70-12, Section: B, page: 7652.
Contained By:	Dissertation Abstracts International70-12B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3380497
ISBN:	9781109515695

Noise characteristics and edge-enhancing denoisers for the magnitude MRI imagery.
Alwehebi, Aisha Abdullah.

Noise characteristics and edge-enhancing denoisers for the magnitude MRI imagery. - 65 p.

Source: Dissertation Abstracts International, Volume: 70-12, Section: B, page: 7652.

Thesis (Ph.D.)--Mississippi State University, 2010.

Most of PDE-based restoration models and their numerical realizations show a common drawback: loss of fine structures. In particular, they often introduce an unnecessary numerical dissipation on regions where the image content changes rapidly such as on edges and textures. This thesis studies the magnitude data/imagery of magnetic resonance imaging (MRI) which follows Rician distribution. It analyzes statistically that the noise in the magnitude MRI data is approximately Gaussian of mean zero and of the same variance as in the frequency-domain measurements. Based on the analysis, we introduce a novel partial differential equation (PDE)-based denoising model which can restore fine structures satisfactorily and simultaneously sharpen edges as needed. For an efficient simulation we adopt an incomplete Crank-Nicolson (CN) time-stepping procedure along with the alternating direction implicit (ADI) method. The algorithm is analyzed for stability. It has been numerically verified that the new model can reduce the noise satisfactorily, outperforming the conventional PDE-based restoration models in 3-4 alternating direction iterations, with the residual (the difference between the original image and the restored image) being nearly edge-free. It has also been verified that the model can perform edge-enhancement effectively during the denoising of the magnitude MRI imagery. Numerical examples are provided to support the claim.

ISBN: 9781109515695Subjects--Topical Terms:

1669109
Applied Mathematics.

Noise characteristics and edge-enhancing denoisers for the magnitude MRI imagery.
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020 $a 9781109515695
035 $a (UMI)AAI3380497
035 $a AAI3380497
040 $a UMI $c UMI
100 1 $a Alwehebi, Aisha Abdullah. $3 1682212
245 1 0 $a Noise characteristics and edge-enhancing denoisers for the magnitude MRI imagery.
300 $a 65 p.
500 $a Source: Dissertation Abstracts International, Volume: 70-12, Section: B, page: 7652.
500 $a Adviser: Seongjai Kim.
502 $a Thesis (Ph.D.)--Mississippi State University, 2010.
520 $a Most of PDE-based restoration models and their numerical realizations show a common drawback: loss of fine structures. In particular, they often introduce an unnecessary numerical dissipation on regions where the image content changes rapidly such as on edges and textures. This thesis studies the magnitude data/imagery of magnetic resonance imaging (MRI) which follows Rician distribution. It analyzes statistically that the noise in the magnitude MRI data is approximately Gaussian of mean zero and of the same variance as in the frequency-domain measurements. Based on the analysis, we introduce a novel partial differential equation (PDE)-based denoising model which can restore fine structures satisfactorily and simultaneously sharpen edges as needed. For an efficient simulation we adopt an incomplete Crank-Nicolson (CN) time-stepping procedure along with the alternating direction implicit (ADI) method. The algorithm is analyzed for stability. It has been numerically verified that the new model can reduce the noise satisfactorily, outperforming the conventional PDE-based restoration models in 3-4 alternating direction iterations, with the residual (the difference between the original image and the restored image) being nearly edge-free. It has also been verified that the model can perform edge-enhancement effectively during the denoising of the magnitude MRI imagery. Numerical examples are provided to support the claim.
520 $a Key words: PDE based denoising models, Magnetic resonance imaging (MRI), Gaussian distribution, Rician distribution, equalized net diffusion, Crank-Nicolson (CN) alternating direction implicit (ADI) method.
590 $a School code: 0132.
650 4 $a Applied Mathematics. $3 1669109
690 $a 0364
710 2 $a Mississippi State University. $b Mathematics and Statistics. $3 1682213
773 0 $t Dissertation Abstracts International $g 70-12B.
790 1 0 $a Kim, Seongjai, $e advisor
790 1 0 $a Lim, Hyeona $e committee member
790 1 0 $a Razzaghi, Mohsen $e committee member
790 1 0 $a Shivaji, Ratnasingham $e committee member
790 1 0 $a Smith, Robert $e committee member
790 $a 0132
791 $a Ph.D.
792 $a 2010
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3380497