Fringe-Enhanced Phase Unwrapping Method Based on an Iterative Bayes–Sard Quadrature Kalman Filter

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript innovatively introduces the Bayes-Sard quadrature transform into the phase unwrapping field for the first time and proposes an iterative Bayes-Sard quadrature Kalman filter unwrapping method. Meanwhile, a multi-level and multi-scale feature fusion network named PFTNet is constructed as the pre-filtering module. Experiments on simulated and real-world data verify that the proposed method can further suppress unwrapping errors and exhibits prominent advantages under low signal-to-noise ratio and blurred fringe conditions. Nevertheless, several issues still exist in this manuscript:

1. The manuscript provides a comprehensive overview of deep learning advances in phase unwrapping but omits a critical discussion of their fundamental limitations. The authors are advised to include an analysis of these methods' heavy reliance on labeled training data, limited out-of-distribution generalization, and lack of physical interpretability, and clearly demonstrate how the proposed framework mitigates these shortcomings to better justify the research rationale and highlight the novelty of this work.
2. This manuscript fails to strictly distinguish between real Gaussian distribution and circularly symmetric complex Gaussian distribution. In InSAR, the noise of complex interferometric observations follows complex Gaussian distribution, while the noise of real-valued phase state variables obeys real Gaussian distribution. Please check and revise the relevant statements throughout the full text to ensure consistent and accurate noise modeling.
3. The adjustment factor in Equation (7) is generally set to 0 or 3-d,while the physical implication and theoretical basis for such a setting are not explained. The authors are suggested to supplement the relevant rationales for this parameter configuration.
4. The manuscript only qualitatively states that convergence is achieved after three iterations, without providing quantitative criteria for convergence evaluation. As a core parameter, the iteration count affects experimental reliability. It is necessary to supplement quantitative index variations across iterations to clarify the rationality of setting three iterations.
5. Results only need to present experimental facts and indicator data without in-depth interpretation. The Discussion section is non-standard and insufficient. It is required to reasonably explain the internal mechanism of experimental phenomena and abnormal results, horizontally compare with existing mainstream InSAR phase unwrapping methods, and clarify the essential advantages of the proposed algorithm. Meanwhile, systematically analyze the synergistic effect of iteration strategy, PFTNet pre-filtering and key parameters, objectively summarize the application scope, limitations and applicable boundaries of the method. In addition, connect with related studies in this field to further highlight the scientificity and application value of this research.
6. Some headings do not have numbers before them.
7. Images and their captions should be centered.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper proposes a novel framework for InSAR phase unwrapping that integrates deep learning-based pre-filtering with an improved Kalman filter. The primary contribution lies in the first-time application of the Bayes-Sard Quadrature (BSQ) transform to the field of phase unwrapping. Compared to the traditional Unscented Kalman Filter (UKF), the proposed IBSQKF theoretically offers a more robust state estimation calibration mechanism by quantifying the additional uncertainty arising from integration errors. Furthermore, the proposed PFTNet employs a complex-domain filtering strategy, processing the real and imaginary parts separately. This design is superior to traditional real-domain filtering and better preserves the edge information of interferometric fringes. Experiments on both simulated and real data demonstrate that the proposed method outperforms traditional methods such as MCF, UKF, and the fundamental UNet in terms of unwrapping accuracy (RMSE) and residue elimination rate, particularly in low signal-to-noise ratio and fringe ambiguity scenarios, validating the effectiveness of the framework.

However, despite the introduction of an iterative strategy, the discussion on computational complexity is insufficient. The lack of comparison with state-of-the-art deep learning unwrapping networks (e.g., Transformer-based architectures or specialized phase gradient networks) somewhat weakens the argument for its novelty. Secondly, the selection of hyperparameters (e.g., kernel function parameter θ) relies mainly on experimental tuning, lacking theoretical derivation for adaptive adjustment. The following specific issues are provided for the authors' consideration:

1. The paper uses UNet as the representative deep learning model for comparison and notes its suboptimal performance. However, in recent years, networks specifically designed for InSAR phase unwrapping (such as PGNet, BCNet, or Transformer-based models) have demonstrated superior performance. Comparing only with the UNet is insufficient to prove the advantages of PFT-IBSQKF over current state-of-the-art deep learning methods. It is recommended that the authors add comparative experiments with at least one recent deep learning model specifically designed for phase unwrapping.
2. Although the paper mentions that the computational cost remains within an acceptable range after introducing the iterative strategy, Table 6 shows that the running time of IBSQKF (81.9s for Dataset 3) is significantly higher than that of MCF (8.2s) and UNet (0.4s). When processing large-scale InSAR data, this high computational cost may limit its application. The authors need to discuss in greater depth the feasibility of this method for large scenes or propose ideas for optimization strategies, such as parallel computing.
3. The paper states that the kernel function parameters θ_f and θ_h were determined through "extensive experimental tuning". This reliance on manual experience reduces the generality of the algorithm. Are fixed parameters still optimal under different terrain conditions and noise levels? It is suggested that the authors explore strategies for adaptive parameter adjustment or analyze the sensitivity of unwrapping accuracy to parameter variations.
4. PFTNet serves as a pre-filtering module, and its output is directly fed into the IBSQKF. However, the paper does not discuss in detail how the filtering error of PFTNet (i.e., the network prediction error) is modeled within the Bayesian framework of IBSQKF. Should the observation noise covariance matrix R(k) in IBSQKF be dynamically adjusted based on the output confidence of PFTNet? The current framework appears to treat PFTNet as a perfect black-box filter, which is theoretically not rigorous enough.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I have no further comments