Spatial Filtering Applications from Medical Images to 2D Turbulence Using the Fourth-Order and Shock PDEs Methods in Complex Domain
The complex fourth-order as well as the complex shock partial differential equations (PDEs) is introduced for noise removal from medical images and 2D turbulent flow. The Lattice Boltzmann method (LBM) with a single relaxation model is used to obtain the velocity field. The two filtering methods are applied against the vorticity field of the flow. Comparisons between the results of the two methods for medical images and 2D turbulence are extensively studied. Investigation and identification of the filtering parameters are also considered. It is shown that the proposed filtering methods are effective for noise removal in both applications. Results indicate that the complex fourth-order PDE method extracts the coherent and incoherent parts more clearly compared with the shock method.
Keywords: Complex fourth-order and shock PDEs filtering methods, medical images, 2D turbulence
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ABOUT THE AUTHORS
Tamer Nabil
Faculty of Science, Helwan University at Cairo, Egypt, in 1997, the M.Sc. degree in pure Mathematics from Helwan university at Cairo, Egypt, in 2000, and Ph.D. degree in Computational Mathematics from Suez Canal University at Ismailia, Egypt, in 2005. Currently, he is an Assistant Professor in Mathematics Department, faculty of Science, King Khalid University, Abha, Saudi Arabia. Also, his permanent work is Assistant Professor at Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt. His research interests are computational harmonic analysis, Numerical methods in Fluid mechanics, and Mathematical methods in image analysis.
Tamer Nabil
Faculty of Science, Helwan University at Cairo, Egypt, in 1997, the M.Sc. degree in pure Mathematics from Helwan university at Cairo, Egypt, in 2000, and Ph.D. degree in Computational Mathematics from Suez Canal University at Ismailia, Egypt, in 2005. Currently, he is an Assistant Professor in Mathematics Department, faculty of Science, King Khalid University, Abha, Saudi Arabia. Also, his permanent work is Assistant Professor at Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt. His research interests are computational harmonic analysis, Numerical methods in Fluid mechanics, and Mathematical methods in image analysis.
Waleed Abdel Kareem
Waleed Abdel Kareem received his B.Sc. (1996) and M.Sc. (2001) in Mathematics from Menoufiya University, Faculty of Science, Department of Mathematics, Egypt. In 2006, he received his PhD from Tohoku University, Graduate School of Engineering, Department of Mechanical Systems and Design, Sendai, Japan. Currently, he is Assistant Professor at King Khalid University, Faculty of Science, Department of Mathematics, Abha, Saudi Arabia. His permanent work is Assistant Professor at Suez University, Faculty of Science, Department of Mathematics, Suez, Egypt. His research interests are Lattice Boltzmann method, Turbulent flow and computational harmonic analysis.
Tamer Nabil
Faculty of Science, Helwan University at Cairo, Egypt, in 1997, the M.Sc. degree in pure Mathematics from Helwan university at Cairo, Egypt, in 2000, and Ph.D. degree in Computational Mathematics from Suez Canal University at Ismailia, Egypt, in 2005. Currently, he is an Assistant Professor in Mathematics Department, faculty of Science, King Khalid University, Abha, Saudi Arabia. Also, his permanent work is Assistant Professor at Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt. His research interests are computational harmonic analysis, Numerical methods in Fluid mechanics, and Mathematical methods in image analysis.
Tamer Nabil
Faculty of Science, Helwan University at Cairo, Egypt, in 1997, the M.Sc. degree in pure Mathematics from Helwan university at Cairo, Egypt, in 2000, and Ph.D. degree in Computational Mathematics from Suez Canal University at Ismailia, Egypt, in 2005. Currently, he is an Assistant Professor in Mathematics Department, faculty of Science, King Khalid University, Abha, Saudi Arabia. Also, his permanent work is Assistant Professor at Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt. His research interests are computational harmonic analysis, Numerical methods in Fluid mechanics, and Mathematical methods in image analysis.
Waleed Abdel Kareem
Waleed Abdel Kareem received his B.Sc. (1996) and M.Sc. (2001) in Mathematics from Menoufiya University, Faculty of Science, Department of Mathematics, Egypt. In 2006, he received his PhD from Tohoku University, Graduate School of Engineering, Department of Mechanical Systems and Design, Sendai, Japan. Currently, he is Assistant Professor at King Khalid University, Faculty of Science, Department of Mathematics, Abha, Saudi Arabia. His permanent work is Assistant Professor at Suez University, Faculty of Science, Department of Mathematics, Suez, Egypt. His research interests are Lattice Boltzmann method, Turbulent flow and computational harmonic analysis.
