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Hybrid Vessel Extraction Method Based on Tight-Frame and EM Algorithms by Using 2D Dual Tree Complex Wavelet
Volume 32, Issue 1 (2021), pp. 1–22
Pub. online: 11 February 2021      Type: Research Article      Open accessOpen Access
Received
1 September 2019
Accepted
1 November 2020
Published
11 February 2021

Abstract

The vessel extraction is very important for the vascular disease diagnosis and grading of the stenoses and aneurysms in vessels. This aids in brain surgery and making angioplasty. The presence of noise in the MRA image, etc., turns the vessel extraction into a difficult problem. In this paper, we derive a vessel extraction algorithm based on TFA and EMS algorithms. We prove the convergence of the proposed method within a few iterations. Results of applying the presented method on real 2D MRA images demonstrate that our method is very efficient.

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Biographies

Abdollahi Farid
f.abdollahi@tabrizu.ac.ir

F. Abdollahi was born in 1988. He is a PhD student of Applied Mathematics at Faculty of Mathematical Sciences, University of Tabriz, Iran. His research interests include image processing and wavelets.

Lakestani Mehrdad
lakestani@tabrizu.ac.ir

M. Lakestani received his BSc in applied mathematics from Department of Mathematics at the University of Tabriz, in 1998, MSc and PhD in applied mathematics in 2000 and 2005, respectively, at Amirkabir University of Technology. He has been a professor of mathematics at the University of Tabriz since 2015. His research interests include wavelets, numerical methods, and image processing.

Razzaghi Mohsen
razzaghi@math.msstate.edu

M. Razzaghi received his BSc degree in mathematics and a PhD degree in applied mathematics both from the University of Sussex in England. Since 1986, he has been with the Department of Mathematics and Statistics at Mississippi State University, where he is currently a professor and the department head. He was the recipient of two Fulbright scholar programmes, one in 2011–2012 and another in 2015–2016, and one Fulbright specialist programme in 2019, in Romania. His current area of research centres on orthogonal functions, optimal control, wavelets, fractional calculus, and their applications in mathematical modelling, and engineering. He has over 190 refereed journal publications in mathematics, mathematical physics, and engineering. One of his papers, coauthored with one of his PhD students, was cited over 700 times.


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Open access article under the CC BY license.

Keywords
VESSEL extraction MRA images TFA algorithm EMS algorithm

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