Phase unwrapping method, system and storage medium based on itoh constrained mixed graph
Patent Information
- Application Number
- CN202611290075.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-25
- Publication Date
- 2026-09-25
AI Technical Summary
[0005]针对现有深度学习相位解缠方法依赖密集像素级监督导致的泛化能力差、以及真实场景下难以获取密集真实值的问题，本发明的目的在于提供一种基于Itoh约束混合图的相位解缠方法、系统及存储介质，将相位解缠重新表述为稀疏观测下的边缘级梯度回归问题
1. 将相位解缠重新表述为稀疏观测下的边缘级梯度回归问题。通过在图的边上强制引入Itoh条件，确保相位差的物理一致性，从根本上缓解相位解缠的病态性。摒弃了导致“一到多”映射模糊的密集像素级绝对相位回归，改为在满足Itoh条件的边上进行相位差（梯度）回归。这种映射是单值的且定义明确，使得网络学习更加稳定。
Smart Images
Figure CN122821152A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of image processing technology. It relates to a phase unwrapping method, system and storage medium based on Itoh-constrained hybrid graphs. Background Technology
[0002] Synthetic Aperture Radar Interferometry (InSAR) is a powerful remote sensing technique for measuring terrain and surface deformation. Because the interferometric phase is wrapped around... Within the interval, phase unwrapping (PU) is necessary to recover the absolute phase. However, due to... The ambiguity of phase unwrapping means that a single entangled phase observation may correspond to multiple valid absolute phase solutions, making phase unwrapping essentially an ill-posed problem. Existing phase unwrapping methods mainly suffer from the following shortcomings: 1. Traditional two-dimensional phase unwrapping methods (such as path following and optimization methods) rely on the Itoh condition to determine the solution. However, under complex conditions such as strong noise, phase discontinuity, or aliasing, the Itoh condition is often violated, leading to unwrapping failure.
[0003] 2. Most existing deep learning phase unwrapping methods rely on dense pixel-level supervision of absolute phase. This approach, which describes the problem as pixel-level absolute phase regression, not only fails to address the inherent ambiguity of one-to-many mappings and is prone to causing the model to get trapped in local minima and overfit, but also makes it difficult to obtain highly matched dense real surface elevation or deformation data as labels in real interferograms.
[0004] 3. In practical applications, sparse observation data (such as GPS, PSInSAR or LiDAR point clouds) are easier to obtain and contain valuable terrain or deformation information, but existing end-to-end networks have difficulty directly and effectively utilizing these sparse points for stable training. Summary of the Invention
[0005] To address the issues of poor generalization ability and difficulty in obtaining dense ground truth values in real-world scenarios caused by the reliance on dense pixel-level supervision in existing deep learning phase unwrapping methods, this invention aims to provide a phase unwrapping method, system, and storage medium based on Itoh-constrained hybrid graphs. Phase unwrapping is reformulated as an edge-level gradient regression problem under sparse observations. By forcibly introducing Itoh conditions onto the edges of the graph, the physical consistency of the phase difference is ensured, fundamentally alleviating the ill-conditioned nature of phase unwrapping.
[0006] The technical solution to achieve the purpose of this invention is as follows: A phase unwrapping method based on Itoh-constrained hybrid graphs includes the following steps: S01: Obtain a sparse sampling point set from the entangled interference phase diagram, construct a minimum spanning tree based on the sampling point set to form a global skeleton edge set, and assign a weight to each edge in the global skeleton edge set according to the Itoh condition. S02: Search the local edge set of each sampling point to form a local gradient candidate pool; S03: In each training iteration of the deep learning network, a subset is selected from the local gradient candidate pool to generate a dynamic edge set; S04: In each iteration, the supervised edge set used for training includes the global skeleton edge set and the dynamic edge set. The deep learning network is trained end-to-end by gradient regression based on the constructed loss function. The trained deep learning network is used to output the absolute phase map.
[0007] In the preferred technical solution, step S01, which assigns information weights to each edge in the global skeleton edge set according to the Itoh condition, includes: Calculate the global skeleton edge set Each edge Corresponding true phase difference ; Calculate the weight of the edge as follows:
[0008] in, The attenuation rate, This indicates a round-down operation; Global skeleton edge set based on Itoh condition Each edge in Weighted Allocation .
[0009] In the preferred technical solution, forming a local gradient candidate pool includes: For each point The K-nearest neighbor algorithm in the spatial domain is used to search for local edges in the spatial domain, and the true phase difference on the local edges satisfies the Itoh condition, thus obtaining the set of local edges. ; Eliminate edge sets that already belong to the global skeleton by using set difference operations. The edges form a local gradient candidate pool. , denotes the difference between sets.
[0010] In the preferred technical solution, generating the dynamic edge set in step S03 includes: Through random sampling function From the local gradient candidate pool Select a subset to generate a dynamic edge set. :
[0011] in, For sampling size; The edge weights within the dynamic edge set are all fixedly assigned. .
[0012] In the preferred technical solution, step S04, which involves performing end-to-end gradient regression training on the deep learning network based on the constructed loss function, includes: Merging the first The supervision edge set for the next iteration:
[0013] The loss function is constructed as follows:
[0014] in, For the global skeleton edge set, For dynamic edge sets, As an edge, The weight of the edge. To predict the phase difference, For the true phase difference, for Norm; Perform end-to-end gradient regression training on the deep learning network to update the network parameters.
[0015] This invention also discloses a phase unwrapping system based on Itoh-constrained hybrid graphs, used to implement the phase unwrapping method based on Itoh-constrained hybrid graphs, comprising: The global skeleton edge set generation module obtains a sparse sampling point set from the entangled interference phase map, constructs a minimum spanning tree based on the sampling point set to form a global skeleton edge set, and assigns a weight to each edge in the global skeleton edge set according to the Itoh condition. The local gradient candidate pool generation module searches the local edge set of each sampling point to form a local gradient candidate pool. The dynamic edge set generation module selects a subset from the local gradient candidate pool to generate a dynamic edge set in each training iteration of the deep learning network. The network training prediction module uses a set of supervised edges, including a global skeleton edge set and a dynamic edge set, in each iteration. It performs end-to-end gradient regression training on the deep learning network based on the constructed loss function and outputs an absolute phase map using the trained deep learning network.
[0016] The present invention also discloses a computer storage medium storing a computer program, which, when executed, implements the aforementioned phase unwrapping method based on Itoh constraint hybrid graph.
[0017] Compared with the prior art, the significant advantages of this invention are: 1. Phase unwrapping is reformulated as an edge-level gradient regression problem under sparse observations. By forcibly introducing the Itoh condition on the edges of the graph, the physical consistency of the phase difference is ensured, fundamentally alleviating the ill-conditioning of phase unwrapping. Instead of dense pixel-level absolute phase regression that leads to blurred "one-to-many" mappings, phase difference (gradient) regression is performed on edges that satisfy the Itoh condition. This mapping is single-valued and well-defined, making network learning more stable.
[0018] 2. Global MST prevents error propagation and global phase drift; local dynamic KNN sampling captures high-frequency details and acts as a structure regularizer, preventing the network from geometrically overfitting to local noisy structures, thus exhibiting high robustness.
[0019] 3. By utilizing sparse supervisory signals (such as GPS and PSInSAR points), the method significantly improves the generalization ability and robustness of the model while solving the unwrapping problem in complex scenarios (noise, discontinuities). The method does not rely on dense real labels, which greatly reduces the data acquisition cost and is suitable for real-world scenarios where only sparse measurements (such as GPS and LiDAR) can be obtained. Attached Figure Description
[0020] Figure 1 This is a flowchart of the phase unwrapping method based on the Itoh constraint hybrid graph in this embodiment; Figure 2 This is a schematic diagram of the Itoh constraint hybrid graph learning mechanism in this embodiment; Figure 3 This is a schematic diagram of the weighted global topology skeleton in this embodiment; Figure 4 This is a schematic diagram of the local gradient candidate pool in this embodiment; Figure 5 This is a schematic diagram of the dynamic resampling and mixing graph in this embodiment; Figure 6 The figure shows the experimental results of this embodiment. Detailed Implementation
[0021] The principle of this invention is as follows: This invention reformulates phase unwrapping as an edge-level gradient regression problem under sparse observations. By forcibly introducing the Itoh condition on the edges of the graph, the physical consistency of the phase difference is ensured, fundamentally alleviating the ill-conditioned nature of phase unwrapping; at the same time, by utilizing sparse supervision signals (such as GPS and PSInSAR points), the unwrapping problem in complex scenarios (noise, discontinuities) is solved, while significantly improving the model's generalization ability and robustness.
[0022] Example 1: like Figure 1As shown, a phase unwrapping method based on Itoh-constrained hybrid graphs includes the following steps: S01: Obtain a sparse sampling point set from the entangled interference phase diagram, construct a minimum spanning tree based on the sampling point set to form a global skeleton edge set, and assign a weight to each edge in the global skeleton edge set according to the Itoh condition. S02: Search the local edge set of each sampling point to form a local gradient candidate pool; S03: In each training iteration of the deep learning network, a subset is selected from the local gradient candidate pool to generate a dynamic edge set; S04: In each iteration, the supervised edge set used for training includes the global skeleton edge set and the dynamic edge set. The deep learning network is trained end-to-end by gradient regression based on the constructed loss function. The trained deep learning network is used to output the absolute phase map.
[0023] The core technical solution of this invention is to construct an Itoh-constrained hybrid graph (IC-HG) and use the edges extracted from this graph for gradient regression training. The specific solution is as follows: Step 1: Sparse Sampling and Global Topology Skeleton Construction Obtaining a sparse sampling point set from the interferogram , Let N be the number of sampling points. Based on these sampling points, Kruskal's algorithm is used to construct a minimum spanning tree (MST), forming a global skeleton edge set. To suppress unreliable long-distance connections traversing dense stripes or decorrelated regions, the Itoh condition is applied... Each edge in Weighted Allocation For intervals outside the main interval The phase difference, the weight of which decreases exponentially with its amplitude. For example... Figure 3 As shown, red dots represent sparsely sampled supervision points in the actual interferogram; blue solid lines represent normal short-distance connections in the minimum spanning tree (MST). They are responsible for connecting all isolated points to prevent global phase drift. Purple solid lines represent long-distance unreliable connections that cross multiple phase fringes or noise regions. These dangerous edges, which are highly likely to violate the Itoh condition, are identified by the network and penalized with a step-by-step exponential weighting strategy.
[0024] For interferograms with dense annotations, the algorithm uses Poisson random sampling to extract a very small number of pixels from the entire image as control points by pre-setting a specified number of target points (such as 500 to 2000 points).
[0025] The generation of the Poisson point process is controlled by the spatial density parameter. This invention strictly limits the absolute number of sampling points from a mathematical expectation perspective by setting an extremely small number of expected points (e.g., only 500 to 2000 points are generated in the entire image of 65536 pixels), thereby physically ensuring the sparsity property of the control point set.
[0026] It should be noted that, in addition to Kruskal's algorithm, Prim's algorithm can also be used to construct the global skeleton. They are mathematically equivalent, and the resulting globally connected skeleton features are consistent.
[0027] In practical engineering implementations, due to the excessive computational cost of fully connected graphs, Delaunay triangulation is first used to construct a sparse graph (with approximately three times the number of edges) from the sampled points. Kruskal's algorithm, based on edge sorting, has a time complexity of O(ElogE) (where E is the number of edges). When dealing with such extremely sparse graphs, its computational efficiency is significantly better than the vertex-based Prim algorithm.
[0028] Step 2: Constructing the Local Gradient Candidate Pool
[0029] While the global MST guarantees connectivity, its acyclic structure leads to sparse local connections. Therefore, for each sampling point... Search for its K nearest neighbors (KNN) in the spatial domain and construct a local edge set while satisfying the Itoh condition. Set difference operations are used to remove elements that already belong to the set. The edges form a local gradient candidate pool. , denotes the difference between sets. For example... Figure 4 As shown, the light green thin lines represent the set of local connections constructed through K-Nearest Neighbor (KNN) search (removing edges that overlap with the MST).
[0030] It should be noted that other search methods can also be used, such as Delaunay triangulation, fixed radius nearest neighbor search, etc.
[0031] Step 3: Dynamic Random Resampling Strategy
[0032] In each training iteration of the network, to prevent the model from overfitting to a fixed geometric structure, a pool of candidates is selected from the local candidate pool. A subset is randomly sampled to form a dynamic edge set. And assign it the largest constant weight ( ).like Figure 5 As shown, the blue solid line represents the weighted MST global skeleton that remains unchanged in each training iteration, and the orange dashed line represents a portion of the local connections randomly selected from the local gradient candidate pool in the current training iteration.
[0033] Step 4: Training a gradient regression network based on a weighted mixture graph
[0034] In the In this iteration, the final edge set used for supervised training It consists of a fixed weighted global skeleton and dynamically sampled local edges. A loss function is constructed, and the difference between the predicted and true phase gradients on the selected edge set is calculated. Norm error is used for end-to-end gradient regression training of deep learning networks (such as the Res-UNet-Inception architecture).
[0035] It should be noted that deep learning networks can also be replaced with U-Net, Attention U-Net, etc., and the network structure is not limited here.
[0036] Step 5: Output of Gradient Regression Network Based on Weighted Mixture Graph
[0037] After being trained with sparse constraints, the network has learned global phase integral and physical consistency, and can directly input unknown entangled phase maps to output dense absolute phase maps in an end-to-end manner.
[0038] Another embodiment, a phase unwrapping system based on an Itoh-constrained hybrid graph, includes: The global skeleton edge set generation module obtains a sparse sampling point set from the entangled interference phase map, constructs a minimum spanning tree based on the sampling point set to form a global skeleton edge set, and assigns a weight to each edge in the global skeleton edge set according to the Itoh condition. The local gradient candidate pool generation module searches the local edge set of each sampling point to form a local gradient candidate pool. The dynamic edge set generation module selects a subset from the local gradient candidate pool to generate a dynamic edge set in each training iteration of the deep learning network. The network training prediction module uses a set of supervised edges, including a global skeleton edge set and a dynamic edge set, in each iteration. It performs end-to-end gradient regression training on the deep learning network based on the constructed loss function and outputs an absolute phase map using the trained deep learning network.
[0039] This embodiment uses Res-UNet-Inception as the backbone network, employs the Adam optimizer, and sets the initial learning rate to [value missing]. The specific implementation steps are as follows: Step 1: Define network input and observation points like Figure 2 As shown, the entanglement interference phase diagram is obtained. Assume the available set of real surface observation points is as follows: (For example (A GPS observation point). Let any two points... The absolute phase gradient between them is ,in, It is an absolute phase.
[0040] Step 2: Construct the Weighted Global Topology Skeleton (MST)
[0041] In the sampling point set The minimum spanning tree is constructed using Kruskal's algorithm. Calculate based on Itoh's condition. The true phase difference corresponding to each edge To penalize unreliable long-distance connections that span multiple dense stripes and do not satisfy the Itoh condition, edge weights are defined. as follows:
[0042] Among them, attenuation rate Set it to 0.1. This indicates a floor operation. This weighting strategy results in edges that violate the Itoh condition having smaller weights.
[0043] Step 3: Construct a local gradient candidate pool (KNN)
[0044] Traverse the sampling points and find each point using the spatial domain K-nearest neighbor algorithm. local edge set (The true phase difference on this edge must strictly satisfy the Itoh condition, i.e., it must not span multiple winding cycles.) Edges already existing in the global skeleton are removed, forming a candidate pool that provides local details.
[0045] Step 4: Dynamic random resampling during training
[0046] In the first deep learning network In the next iteration of training, a random sampling function is applied. From the local gradient candidate pool Select a subset to generate a dynamic edge set. :
[0047] Sampling scale The selection is set to an average of 2-4 edges per point. To ensure reliable local connectivity, the edge weights within the dynamic edge set are all fixed. .
[0048] Step 5: Calculation of weighted mixed plot gradient regression loss
[0049] Merging the first The supervision edge set for the next iteration:
[0050] Let the predicted unwrapping phase output by the network be denoted as The loss is constrained using the constructed weighted mixture graph. Update network parameters:
[0051] in, This represents the predicted phase difference output by the deep learning network at edge (i, j) of the graph. It is calculated as follows: using the unwrapped absolute phase predicted by the deep learning network at node i. absolute phase of unentanglement with node j Subtracting the two, we get the formula: = - .
[0052] Because this loss function constrains the physical consistency of the gradient, it can guide the network to implicitly learn the global phase integral.
[0053] Step 6: Real-world application and generalization capability verification
[0054] To further verify the generalization ability and practicality of the present invention (IC-HG) in real complex scenarios, the model trained on simulated and real data will be applied to the real TanDEM-X interferogram dataset and compared with the dense supervision (DS) method and the traditional minimum cost flow (MCF) algorithm.
[0055] The experimental results are shown in Table 1: Table 1 Experimental Results
[0056] Figure 6 (a)-(b) are the wrapping plot and truth plot of the selected image, respectively. Figure 6 (c)-(g) represent the five untangling methods in Table 1 above. Figure 6 The untangling diagram of (a) Figure 6 (h)-(l) represent the five untangling methods in Table 1 above. Figure 6 (a) Error diagram of untangling.
[0057] This embodiment fully demonstrates that the method based on Itoh-constrained hybrid graph (IC-HG) not only significantly reduces the dependence on label density, but also extracts robust and accurate physical representations under extremely sparse supervision, and has extremely high stability and engineering application value when facing complex deformations and noise in real-world scenarios.
[0058] In another embodiment, a computer storage medium stores a computer program that, when executed, implements the phase unwrapping method based on the Itoh constraint hybrid graph described above.
[0059] The above implementation method will not be elaborated further here.
[0060] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.
Claims
1. A phase unwrapping method based on Itoh-constrained hybrid graphs, characterized in that, Includes the following steps: S01: Obtain a sparse sampling point set from the entangled interference phase diagram, construct a minimum spanning tree based on the sampling point set to form a global skeleton edge set, and assign a weight to each edge in the global skeleton edge set according to the Itoh condition. S02: Search the local edge set of each sampling point to form a local gradient candidate pool; S03: In each training iteration of the deep learning network, a subset is selected from the local gradient candidate pool to generate a dynamic edge set; S04: In each iteration, the supervised edge set used for training includes the global skeleton edge set and the dynamic edge set. The deep learning network is trained end-to-end by gradient regression based on the constructed loss function. The trained deep learning network is used to output the absolute phase map.
2. The phase unwrapping method based on Itoh-constrained hybrid graphs according to claim 1, characterized in that, In step S01, the information weights are assigned to each edge in the global skeleton edge set according to the Itoh condition, including: Calculate the global skeleton edge set Each edge Corresponding true phase difference ; Calculate the weight of the edge as follows: in, The attenuation rate, This indicates a round-down operation; Global skeleton edge set based on Itoh condition Each edge in Weighted Allocation .
3. The phase unwrapping method based on Itoh-constrained hybrid graphs according to claim 1, characterized in that, Forming a local gradient candidate pool includes: For each point The K-nearest neighbor algorithm in the spatial domain is used to search for local edges in the spatial domain, and the true phase difference on the local edges satisfies the Itoh condition, thus obtaining the set of local edges. ; Eliminate edge sets that already belong to the global skeleton by using set difference operations. The edges form a local gradient candidate pool. , denotes the difference between sets.
4. The phase unwrapping method based on Itoh-constrained hybrid graphs according to claim 1, characterized in that, Step S03, generating the dynamic edge set, includes: Through random sampling function From the local gradient candidate pool Select a subset to generate a dynamic edge set. : in, For sampling size; The edge weights within the dynamic edge set are all fixedly assigned. .
5. The phase unwrapping method based on Itoh-constrained hybrid graphs according to claim 1, characterized in that, Step S04, which involves end-to-end gradient regression training of the deep learning network based on the constructed loss function, includes: Merging the first The supervision edge set for the next iteration: The loss function is constructed as follows: in, For the global skeleton edge set, For dynamic edge sets, As an edge, The weight of the edge. To predict the phase difference, For the true phase difference, for Norm; Perform end-to-end gradient regression training on the deep learning network to update the network parameters.
6. A phase unwrapping system based on an Itoh-constrained hybrid graph, used to implement the phase unwrapping method based on an Itoh-constrained hybrid graph as described in any one of claims 1-5, characterized in that, include: The global skeleton edge set generation module obtains a sparse sampling point set from the entangled interference phase map, constructs a minimum spanning tree based on the sampling point set to form a global skeleton edge set, and assigns a weight to each edge in the global skeleton edge set according to the Itoh condition. The local gradient candidate pool generation module searches the local edge set of each sampling point to form a local gradient candidate pool. The dynamic edge set generation module selects a subset from the local gradient candidate pool to generate a dynamic edge set in each training iteration of the deep learning network. The network training prediction module uses a set of supervised edges, including a global skeleton edge set and a dynamic edge set, in each iteration. It performs end-to-end gradient regression training on the deep learning network based on the constructed loss function and outputs an absolute phase map using the trained deep learning network.
7. A computer storage medium having a computer program stored thereon, characterized in that, When the computer program is executed, it implements the phase unwrapping method based on the Itoh constraint hybrid graph as described in any one of claims 1-5.