MATLAB Phase Unwrapping Code with Branch Cuts Algorithm Implementation

This content discusses the branch cuts method for phase unwrapping in MATLAB, providing technical insights into algorithm implementation and mathematical foundations. In the context of phase unwrapping, the branch cuts algorithm represents a sophisticated approach to resolve phase discontinuities in complex data. For MATLAB implementation, this typically involves detecting phase jumps exceeding π radians and creating branch cuts to prevent propagation of unwrapping errors across these discontinuity boundaries. In mathematical terms, a branch cut is a curve or line in the complex plane that defines where a multi-valued function becomes discontinuous. Essentially, it establishes the domain boundaries for complex functions where phase transitions occur. The terminology originates from the tree-like structure of the complex plane, where branch cuts demarcate transitions between different Riemann surface branches. The phase unwrapping algorithm in MATLAB employs branch cuts to eliminate discontinuities from wrapped phase data, enabling continuous phase analysis and processing. MATLAB provides several built-in functions for phase manipulation, including the unwrap() function which automatically corrects phase jumps greater than π radians by adding appropriate multiples of 2π. However, custom branch cuts implementations may involve more advanced techniques such as: - Quality-guided unwrapping using phase derivative variance - Minimum spanning tree algorithms for optimal cut placement - Mask-based region isolation to handle noisy areas - Residual point detection and cut line generation For effective MATLAB implementation, developers typically utilize matrix operations for efficient phase gradient computation, employ morphological operations for branch cut refinement, and implement flood-fill algorithms for phase propagation across defined regions. The algorithm structure generally follows these key steps: phase gradient calculation, residue identification, branch cut placement, and quality-guided unwrapping path determination. While the original discussion provides fundamental concepts, practical MATLAB implementation requires additional considerations such as handling noise-affected regions, optimizing computational efficiency for large datasets, and validating results against known test cases. The branch cuts method remains particularly valuable in applications like interferometric SAR, MRI phase imaging, and optical metrology where robust phase unwrapping is critical for accurate measurements.