SURVEY ON PHASE UNWRAPPING ALGORITHMS: STRENGTHS, LIMITATIONS, AND FUTURE DIRECTIONS (Special Issue: 3rd Young Researches Conference 2025 )

Phase unwrapping is a fundamental task in many signal processing applications such as synthetic aperture radar,
magnetic resonance imaging, and optical interferometry. All these applications require accurate reconstruction of phase
information from wrapped signals. This paper evaluates phase unwrapping algorithms by studying the path-following, leastsquares-based, and singularity compensation methods. Efficient path-following methods such as Goldstein’s branch-cut and Flynn’s Minimum Weighted Discontinuity struggle when dealing with noise and dense singularities. The Least-Squares method using the Discrete Cosine Transform demonstrates strong noise resilience, yet may fail to preserve overall accuracy due to its reliance on global assumptions. On the other hand, singularity compensation methods like the Rotational Compensator and Localized Compensator provide precise results through localized correction operations; however, they require significant processing power and memory capacity. Among them, the Localized Compensator stands out for its superior precision, though at the cost of high computational expenses. This review emphasizes the strengths and limitations of each method while comparing their performance metrics in terms of accuracy, noise tolerance, and computational efficiency. Additionally, it suggests strategies for scalability, such as parallelization, GPU acceleration, and the use of sparse matrix representations, to improve performance when handling large datasets.