Two-dimensional phase unwrapping using a minimum spanning tree algorithm

Area of Science:

• Image processing
• Computational physics
• Medical imaging

Background:

• Phase unwrapping is essential for determining phase from modulo 2pi data.
• Existing methods struggle with unreliable data and complex, non-connected regions.
• Magnetic Resonance Imaging (MRI) phase maps benefit significantly from accurate phase unwrapping.

Purpose of the Study:

• To develop a robust 2D phase unwrapping algorithm for arbitrarily shaped and non-connected regions.
• To address challenges posed by unreliable phase data and nonconvex boundaries.
• To enhance the utility of phase maps in applications like MRI.

Main Methods:

• Segmentation to identify connectivity within phase data.
• Taylor series expansion for phase unwrapping within individual segments.
• Minimum spanning tree algorithm to determine optimal paths for intersegment unwrapping.
• Phase information void filling techniques.

Main Results:

• The algorithm successfully unwraps 2D phase data within disconnected regions of arbitrary shapes.
• It effectively handles nonconvex boundaries and unreliable phase information.
• The minimum spanning tree approach optimizes intersegment unwrapping paths.

Conclusions:

• The presented phase unwrapping algorithm is effective for complex 2D data, particularly in MRI.
• It provides a reliable method for determining phase from noisy and incomplete data.
• The algorithm's ability to handle disconnected regions expands its applicability in scientific imaging.