Phase Unwrapping Using Energy Minimization Methods for MRI Phase Image

Phase Unwrapping Using Energy Minimization Methods for MRI Phase Image

Kusworo Adi (ITB, Indonesia and UNDIP, Indonesia), Tati L. R. Mengko (ITB, Indonesia), Andriyan B. Suksmono (ITB, Indonesia) and H. Gunawan (ITB, Indonesia)
Copyright: © 2010 |Pages: 7
DOI: 10.4018/jehmc.2010070105
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Abstract

Phase Unwrapping (PU) is reconstruction of absolute phase data from its wrapped phase. The absolute phase cannot be extracted from the wrapped phase data directly. Without phase noise, singularity, and aliasing problems, the phase information can be unwrapped easily. However, the phase data are always contaminated by noise and discontinuities, making the PU process more complicated. Therefore, a suitable PU algorithm is required to address the problems properly. In this method, the energy difference between neighborhood pixels in level 3 is counted, followed by getting the probability value to obtain its total fringes. The capability of the proposed method to unwrap simulated and actual MRI phase images is also demonstrated. In actual MRI phase image, PU can be implemented for water and fat separation.
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Theory

The information about the value of 2π phase cycle in the absolute phase disappears. In this case, the fringe of phase process causes a sudden jump of artificial phase surrounds the edges. Mathematically, the concept of the estimation of the absolute phase image from a wrapped phase can be formulated as follows (Ghiglia & Pritt, 1998):

(1) where ϕu is the estimated absolute phase, ϕw is the principal value of the wrapped phase, and k(i,j) is an integer PU algorithm to be determined.

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