Several Phase Unwrapping Algorithms

Phase unwrapping is a critical technique in optical measurement and interferometric imaging, primarily addressing the 2π ambiguity issue in phase data. Various unwrapping algorithms possess distinct characteristics suited for different scenarios:

DCT Least-Squares Algorithm Based on discrete cosine transform (DCT) theory, this method transforms unwrapping into a least-squares optimization problem. The algorithm suppresses noise through frequency-domain processing and is ideal for phase fields with good global smoothness. However, it may cause error propagation near local discontinuities like object edges. Code implementation typically involves DCT transformation of wrapped phase differences followed by inverse DCT of the solution.

Total Variation (TV) Model Incorporating variational regularization, this approach optimizes an energy function balancing data fidelity and phase gradient sparsity. Its strength lies in preserving phase jump edges, making it suitable for complex scenarios with discontinuous regions. The trade-off is higher computational complexity, often requiring iterative optimization algorithms like gradient descent.

Goldstein Branch-Cut Method This technique identifies residue points and places branch cuts to constrain integration paths, preventing "vortex error" propagation. While sensitive to noise and requiring residue correction strategies, it's widely used in localized unwrapping applications like interferometric SAR (InSAR). Implementation involves residue detection through closed-path integration and optimal branch-cut placement.

Algorithm selection requires balancing accuracy, noise resistance, and computational efficiency. For instance, DCT suits rapid global unwrapping, while the TV model excels at detail preservation in high-noise environments.