phase unwrapping

本文提出了一种基于平移不变的分块相位解缠方法，通过DCT和最小二乘法在频域内解缠，并结合残差加权多路径平均来解决噪声、不连续性等问题。

This paper investigates the stability of the PhaseLift algorithm for phase retrieval from coded diffraction patterns (CDPs) under additive noise. Addressing the limitation of existing error bounds—namely, their dependence on the ℓ²-norm of the noise vector (|mathbf{w}|_2) without reflecting average noise intensity—the work provides the first rigorous proof of Soltanolkotabi’s conjecture: the optimal error bound scales with the *average* noise magnitude, i.e., (|mathbf{w}|_2 / sqrt{m}). Leveraging tools from convex optimization, random matrix theory, and high-dimensional statistics, the authors derive an upper bound of (O(log n cdot |mathbf{w}|_2 / sqrt{m})) under adversarial noise and (O(sigma sqrt{n log^4 n / m})) under sub-Gaussian noise. Matching minimax lower bounds are established in both settings, differing only by logarithmic factors. These results close a fundamental theoretical gap in the stability analysis of PhaseLift for CDP-based phase retrieval.

This work addresses the limitations of conventional Fourier-based methods in single-shot fringe projection profilometry, which suffer from limited accuracy, and circumvents the need for costly phase or depth labels required by supervised learning approaches. It introduces, for the first time, a self-supervised learning framework for dual-frequency phase unwrapping that operates without ground-truth labels. The method models the scale and directional relationships between high- and low-frequency phase gradients and incorporates a soft edge-consistency loss to preserve object boundaries and fine geometric details. Experimental results demonstrate that, under fully unsupervised conditions, the proposed approach outperforms state-of-the-art transform-domain methods, achieving a mean absolute error (MAE_z) of 0.367 mm and a root mean square error (RMSE_z) of 1.804 mm, while increasing the ratio of valid pixels to 95.07%.

This study addresses the challenge of stability analysis in phase retrieval arising from dependencies among Fourier measurements in coded diffraction patterns by establishing a unified lower isometry property framework. Methodologically, it introduces a row-subset operator norm bounding technique that preserves tangent injectivity while adaptively removing dependent rows. By integrating random masks with PhaseLift convex programming and non-convex factorization losses, the theoretical analysis is completed via matrix concentration inequalities. The primary contribution demonstrates that merely O(log n) masks suffice to achieve Gaussian-type stable recovery through convex optimization and to certify benign geometry for the non-convex landscape. These results rigorously guarantee noise robustness as well as global optimal convergence in the noiseless setting.

This paper addresses the affine phase retrieval problem—reconstructing an unknown signal from the magnitudes of affine measurements. To tackle this nonconvex, nonsmooth inverse problem, we propose a second-order optimization framework integrating Newton’s method and the Gauss–Newton method. Under signal priors (e.g., sparsity or structural constraints) and measurement models (e.g., Gaussian random or coded diffraction patterns), we establish, for the first time, a global quadratic convergence theory: we prove strong convexity of the objective function in a neighborhood of the solution and provide a unified convergence analysis for both second-order methods. The theoretical guarantees are initialization-free and hold in the noiseless setting. Numerical experiments demonstrate that our approach outperforms state-of-the-art first-order algorithms in reconstruction accuracy, convergence speed, and sampling efficiency—achieving exact recovery with measurements nearly attaining the information-theoretic lower bound, thus offering both computational efficiency and robustness.

This work addresses severe phase artifacts in fringe projection profilometry caused by nonlinear projection and limited pattern control in miniature diffractive optical element (DOE) projectors. To overcome these challenges, the authors propose a ray-based phase error correction framework that directly models phase errors along projection rays, incorporating geometric information without relying on image-domain post-processing or neighboring pixel dependencies. A key innovation is the use of unidirectional hyperbolic fringe patterns to estimate the projector’s pinhole location, enabling recovery of projection geometry without stereo calibration. An efficient correction model is then constructed from a single calibration pose. Experimental results demonstrate that the proposed method significantly improves 3D reconstruction accuracy under nonlinear conditions in miniature DOE-FPP systems, while maintaining robustness and physical consistency.

This work resolves a long-standing open problem in structured phase retrieval by establishing the optimal sampling rate required for exact reconstruction of complex-valued signals from coded diffraction patterns. Under the standard random mask model, the authors prove for the first time that PhaseLift recovers any n-dimensional complex signal—up to a global phase—with only O(log n) random masks, achieving the information-theoretic lower bound Ω(log n). This yields a total sampling complexity of O(n log n). The analysis hinges on several key technical innovations: an approximate dual certificate constructed via an enhanced golfing scheme, adaptive mask allocation, and a dimension-independent truncation threshold. The proposed method attains this optimal sampling efficiency with a failure probability that decays polynomially in the signal dimension.

This study investigates whether adaptive tiling can enhance both efficiency and accuracy in large-scale image phase unwrapping. By systematically comparing grid, quadtree, and KD-tree partitioning strategies, it quantitatively evaluates the trade-offs between runtime and reconstruction accuracy across nine subdivision criteria. The analysis reveals a counterintuitive mechanism: reducing the number of tiles does not necessarily accelerate computation. Specifically, the overhead of constructing adaptive structures and the increased solving time for larger tiles offset the benefits of reduced boundary length, resulting in single-threaded performance inferior to optimized grid methods alongside partial accuracy degradation. Based on these findings, this work proposes adopting the total time required to achieve a specified accuracy as a more appropriate evaluation metric for this task.

研究了周期性传感器环上任意观测掩模对高斯过程重建后验协方差、傅里叶模式耦合和归一化后验迹的影响，通过分析不同掩模几何形状导致的不同效果。

本文提出了一种新的全息图表示方法CVQPG，通过使用二次相位函数替代传统的2D高斯表示，并增加可学习参数控制基底曲率，提高了全息重建的视觉质量。