Date on Master's Thesis/Doctoral Dissertation


Document Type

Master's Thesis

Degree Name

M. Eng.


Electrical and Computer Engineering

Degree Program

JB Speed School of Engineering

Committee Chair

Amini, Amir

Committee Co-Chair (if applicable)

Inanc, Tamer

Committee Member

Inanc, Tamer

Committee Member

Robinson, Brian

Author's Keywords

Phase Contrast MRI; 4D flow MRI; Phase Unwrapping; Graph Cuts; Max-flow Min-cut Thereom


A common issue when measuring velocity utilizing 4D flow magnetic resonance imaging (MRI) is aliasing that occurs because of a low velocity encoding parameter (VENC). Aliasing can be avoided if the velocity encoding parameter is set above the largest velocity quantity. However, when this is done the velocity to noise ratio is lowered less detail is acquired in the image. Thusly, it is sometimes desirable to have a below the maximum velocity to acquire higher quality data.

Consequently, an efficient and robust algorithm is needed to unwrap the aliased data. This paper proposes an iterative graph cuts algorithm to perform the phase unwrapping on the 4D flow data. This graph cuts algorithm utilizes a global energy minimization framework and is largely based on the Phase Unwrapping Max-Flow Algorithm (PUMA) proposed in [1]. However, the algorithm presented in this paper is extended to account for the added dimensions of data. Previous methods that have been utilized for 4D phase unwrapping include the Laplacian method and the Spatial Gradients method presented in [2] and [3] respectively. Of these, the Laplacian method has proven the most successful in phase unwrapping quality and time. The proposed graph cuts method is shown to unwrap aliased 4D data more accurately than these existing techniques. This includes unwrapping synthetic data with values down to 20% of the max velocity and SNRs down to 2.

Included in

Biomedical Commons