Fast phase unwrapping via nonconvex regularization and tail-minimization

In the forefront of imaging technology, the limitations of modulo-$2\pi$ phase measurement significantly hinder the in-depth understanding and analysis of the underlying characteristics of images. As one of most typical phase unwrapping methods, variational regularization methods aremore interpretable and stable. This paper proposes a novel variational phase unwrapping model, that incorporates a non-convex anisotropic and isotropic total variation regularization and balances phase data compatibility constraints with box constraints to ensure the rationality and physical consistency of the solution space. It is solved using primal-dual hybrid gradient algorithm, which is theoretically proven to possess global convergence and demonstrates low computational cost in practice. To optimize algorithm performance and efficiency, we introduce tail-minimization mechanism, which precisely identifies and corrects cumulative errors in phase estimation during iterations while automatically excluding pixels that have already converged from subsequent computations, thereby significantly reducing computational load and accelerating the overall convergence process. Through a series of simulations, we comprehensively compared the proposed method with existing iterative phase unwrapping algorithms. Numerical results indicate that, particularly in handling highly complex and high-wrapping-phase data, the proposed algorithm exhibits superior recovery performance and stability. Especially, the signal-to-noise ratio (SNR) of the unwrapping results is dramatically improved, with our method achieving up to double the SNR values of competing methods.