Ayan Sengupta edited Methods_cont.tex  over 9 years ago

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\subsection{Method 2}  As understood from the previous method that it may be quick but the veins mask thus generated is not of the best quality. The second method considers both the magnitude volume and the phase volume of SW images. Before the steps of processing are described its worthwhile to take a closer look at what are the magnitude volume and phase volume of the MR images \cite{16398421}. Generally complex MR image acquisition can be expressed as:   \begin{math} \[  I = |I|*exp(\phi)  \end{math}  Magnetic resonance (MR) phase images often contain useful  information, such as spatial inhomogeneities in the polarizing  magnetic field and the velocity of blood flow [1], [2]. Extracting  the phase image from its measured complex MR image  is nontrivial because is uniquely defined only in the  principal value range of . Any value outside this interval  will be folded back into the principal value range to produce the  so-called wrapped phase , which differs from by an unknown  integer multiple of . Formally, the phase unwrapping problem  is defined as: given the wrapped phase , find the  “true” phase , which is related to by \]  This method consists of the following steps.