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Ayan Sengupta deleted file Methods_cont.tex
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\usepackage{mathtools}
\subsection{Method 1}
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:
\[
I = |I|*exp(\phi)
\]
where \(|I|\) is the magnitude part and \(\phi\) is the phase component of the image. The phase image conveys several important information like field inhomogeniety, venous blood flow etc. But extracting the phase image from the measured complex image is non-trivial, because the any phase component beyond the range of \(-(\pi, \pi]\) is wrapped back into the principal value range. So when the phase image is generated from the scanner it undergoes the \textit{Phase Wrapping} process, as mentioned above. The phase image provided here is in true sense a phase wrapped image in which the \textit{Wrapped Phase} is defined as:
\[
\psi = W(\phi)
\]
where \(W\) is the \textit{wrapping operator}. So for further image processing, we need to determine the true phase information which can be obtained by unwrapping the provided phase image. This image processing method consists of the following steps.
\begin{itemize}
\item \textbf{Step 1: Phase Unwrapping}
\end{itemize}
