Deep learning phase unwrapping method fused with Kalman filtering technology

Abstract

The invention discloses a deep learning phase unwrapping method fused with a Kalman filtering technology, and the method comprises the steps: constructing an absolute phase generation model which is constructed based on a conditional generative adversarial network, and is used for building a direct mapping relation from a wrapping phase to an unwrapping phase; inputting an interference image to be unwrapped into the absolute phase generation model for processing, and generating an initial unwrapping phase; re-winding the initial unwrapping phase to obtain a re-winding phase, and performing conjugate multiplication on the re-winding phase and the interference image to be unwrapped to obtain a residual winding phase; and unwrapping the residual wrapping phase through a Kalman filtering phase unwrapping method to obtain a residual unwrapping phase, and summing the initial unwrapping phase and the residual unwrapping phase to obtain a final unwrapping phase. According to the method, a high-precision unwrapping result can be obtained from a large-gradient region, and better unwrapping model robustness is achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of synthetic aperture radar interferometric data processing, and particularly relates to a deep learning phase unwrapping method fusing Kalman filtering technology. BACKGROUND

[0002] Synthetic aperture radar interferometry (InSAR) is an active microwave remote sensing method that combines advanced radar imaging and interferometric techniques. It has shown great potential in applications such as digital elevation model (DEM) construction and ground deformation monitoring due to its excellent penetration and all-weather working capabilities. The core of InSAR is to use at least two SAR images with different spatial baselines for interferometric processing to extract key information such as ground deformation.

[0003] However, the interferometric phase generated by the InSAR system is naturally wrapped in the interval [-π, π], so phase unwrapping must be performed to recover the continuous and true absolute phase. Phase unwrapping is not only a key step in the InSAR data processing flow, but also a major source of error and technical difficulty. Its accuracy directly determines the quality and application value of the final InSAR product.

[0004] Currently, according to the method and means, phase unwrapping can be mainly divided into three categories. The first category is the path tracking algorithm developed from the branch cut method. This algorithm mainly identifies residual points, sets branch cut lines reasonably, or uses quality maps to guide the unwrapping path to avoid areas with large errors and prevent error propagation. However, in areas with high noise and discontinuous phase, the branch cut lines may be arranged densely, forming loops and causing unwrapping gaps. Unlike the path tracking method, the least norm method is a global optimization algorithm that does not rely on the path. Instead, it converts the phase unwrapping problem into a problem of solving the optimal solution of a nonlinear equation system. This algorithm is more stable than the path tracking method and can avoid local error propagation. The least norm unwrapping algorithm has the characteristics of small calculation amount and stable numerical calculation, so it is the most widely used algorithm at present. However, this algorithm cannot prevent error propagation, and the quality of phase unwrapping cannot be guaranteed. Moreover, under high noise conditions, the computational efficiency will be greatly reduced. With the development of deep learning technology and multidisciplinary integration, deep learning technology has been widely applied in phase unwrapping. Deep learning technology can learn the nonlinear relationship between wrapped phase and absolute phase. After training, the network can quickly and accurately obtain high-precision unwrapping results from the wrapped phase. However, the accuracy of unwrapping in areas with dense stripes and low coherence still needs to be improved, and the unwrapping phase may be lost or downsampled. Moreover, the neural network is highly dependent on high-quality samples and sample diversity, which greatly limits the performance of deep learning phase unwrapping algorithms.

[0005] In view of the above challenges, improving the accuracy of phase unwrapping in high-noise and large-gradient regions has become a hot and difficult topic of current research. SUMMARY

[0006] The application proposes a deep learning phase unwrapping method combined with Kalman filtering technology, which combines the advantages of Kalman filtering technology and deep learning to achieve more efficient and accurate phase unwrapping, thereby solving the problem of difficult terrain acquisition in high-noise and large-gradient regions and effectively improving the accuracy of phase unwrapping.

[0007] To achieve the above-mentioned purpose, the application provides a deep learning phase unwrapping method combined with Kalman filtering technology, comprising:

[0008] An absolute phase generation model is constructed, wherein the absolute phase generation model is constructed based on a conditional generative adversarial network and is used to establish a direct mapping relationship between wrapped phase and unwrapped phase;

[0009] The interference image to be unwrapped is input into the absolute phase generation model for processing to generate an initial unwrapped phase;

[0010] The initial unwrapped phase is re-wrapped to obtain a re-wrapped phase, and the re-wrapped phase is conjugate multiplied with the interference image to be unwrapped to obtain a residual wrapped phase;

[0011] The residual wrapped phase is unwrapped by a Kalman filtering phase unwrapping method to obtain a residual unwrapped phase, and the initial unwrapped phase and the residual unwrapped phase are summed to obtain a final unwrapped phase.

[0012] Preferably, the absolute phase generation model is constructed, comprising:

[0013] Based on the CGAN network, a one-step unwrapping network about direct mapping of wrapped phase to unwrapped phase is constructed;

[0014] Based on the existing digital elevation model DEM, an unwrapping data set about direct mapping of wrapped phase to unwrapped phase is constructed;

[0015] The one-step unwrapping network about direct mapping of wrapped phase to unwrapped phase is trained by the unwrapping data set to obtain the absolute phase generation model.

[0016] Preferably, the one-step unwrapping network about direct mapping of wrapped phase to unwrapped phase comprises a generator, a discriminator and a loss function;

[0017] The generator is a U-shaped structure with an encoder-residual module-decoder, and contains several convolution layers, transpose convolution layers and residual connections; the discriminator is a binary classifier composed of multiple cascaded convolution layers; the loss function includes a conditional generative adversarial loss function and a feature matching loss function.

[0018] Preferably, the conditional generative adversarial loss function is:

[0019]

[0020] In the formula, L cGAN (G, D) is a conditional generative adversarial loss, is an input image, ψ is a real image, is a generated image, is a discriminant network loss, is a generative network loss;

[0021] The feature matching loss function is:

[0022]

[0023] In the formula, L FM (G, D) is a feature matching loss, i is the number of layers, t is the total number of layers, N i is the number of pixels in each layer output feature map, is the i-th layer discriminant network loss, is the i-th layer generative network loss.

[0024] Preferably, an unwrapping data set about direct mapping of wrapped phase to unwrapped phase is constructed, comprising:

[0025] The DEM in the geographic coordinate system is radar encoded and converted into DEM in the radar coordinate system;

[0026] Based on the imaging geometric parameters, the DEM in the radar coordinate system is simulated to obtain the real absolute phase;

[0027] The real absolute phase is unwrapped and noise-added to generate a noisy wrapped phase;

[0028] The real absolute phase and the noisy wrapped phase are cropped into image pairs of a preset pixel to form the unwrapping data set.

[0029] Preferably, the residual wrapped phase is obtained as:

[0030]

[0031] In the formula, is a residual wrapped phase, is an initial interference phase, The initial absolute phase unwrapped after re-wrapping of the initial interferogram to be unwrapped is obtained by inputting the trained model, angle(·) represents the phase acquisition operation, conj(·) represents the complex conjugate operation, and exp(j*(·)) represents the conversion to a complex number.

[0032] Preferably, the Kalman filtering phase unwrapping method converts the phase unwrapping problem into a state estimation problem, establishes a state equation and an observation equation for phase unwrapping, processes the nonlinear equation by using the sigma transformation-based nonlinear Kalman filtering, and predicts and updates the absolute phase of the interferogram to be unwrapped.

[0033] Preferably, the state equation and the observation equation are as follows:

[0034]

[0035] In the formula, ψ(s) and ψ(s-1) are the true phases at the pixels s and s-1, respectively; is an estimated value of the phase gradient at the pixel s-1; ω(s-1) is the corresponding phase gradient estimation error; is an observation value at the pixel s; sin[ψ(s)] is the imaginary part of the unwrapped phase at the pixel s; cos[ψ(s)] is the real part of the unwrapped phase at the pixel s; H[ψ(s)] is an observation model function; v1(s) and v2(s) are the observation error variances of the observation value imaginary part and the observation value real part, respectively; and v(s) is a matrix of v1(s) and v2(s).

[0036] Preferably, the final unwrapped phase is obtained as follows:

[0037] ψ(s) * = ψ1(s) * + ψ2(s) * ,

[0038] In the formula, ψ(s) * represents the final unwrapped phase, ψ1(s) * represents the initial unwrapped phase, and ψ2(s) * represents the residual unwrapped phase.

[0039] Compared with the prior art, the present application has the following advantages and technical effects:

[0040] (1) The application adopts a deep learning phase unwrapping method fused with Kalman filtering technology. Previous studies have shown that the accuracy of phase unwrapping can be effectively improved by reducing the fringe density. Therefore, the phase loss characteristic will occur when using the one-step unwrapping method based on deep learning, and the phase unwrapping of the large gradient area is divided into two stages, first, the initial unwrapping phase of the first step is obtained through the absolute phase generation model; the residual wrapped phase is obtained by multiplying the to-be-unwrapped interferogram and the initial unwrapping phase; due to the influence of noise in the to-be-unwrapped interferogram and the deep learning unwrapping error, the residual wrapped phase still contains a large amount of noise, therefore, the Kalman filtering phase unwrapping method with better denoising effect is used to unwrap the residual wrapped phase to obtain the residual unwrapping phase; finally, the final unwrapping phase is obtained by summing the initial unwrapping phase obtained by the first step unwrapping and the residual unwrapping phase obtained by the second step unwrapping. Compared with other conventional phase unwrapping methods, the application can obtain high-precision unwrapping results from the large gradient area, and the method has better unwrapping model robustness, effectively improving the accuracy of the final InSAR product.

[0041] (2) The application uses the advantages of deep learning to reduce the unwrapping difficulty of the large gradient change area, uses the UKF phase unwrapping algorithm to overcome the influence of noise, improves the noise robustness of the algorithm, and further improves the performance of the overall algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0042] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application. The embodiments of the application illustrated in the drawings and their descriptions serve to explain the application and do not limit the application in any way. In the drawings:

[0043] Figure 1 A Kalman filtering technology-fused deep learning phase unwrapping method flowchart of an embodiment of the application;

[0044] Figure 2 A CGAN network flowchart of an embodiment of the application;

[0045] Figure 3 A CGAN network structure schematic diagram of an embodiment of the application, wherein (a) is a generator, and (b) is a discriminator;

[0046] Figure 4 An unwrapping data set making schematic diagram of an embodiment of the application;

[0047] Figure 5Figures (a) to (f) are unwrapped phase and error maps of different noise content interferograms using different phase unwrapping methods of embodiments of the present application, wherein (a) is a sub-map with noise content of 0, (b) is a sub-map with noise content of 0.2, (c) is a sub-map with noise content of 0.4, (d) is a sub-map with noise content of 0.6, (e) is a sub-map with noise content of 0.8, and (f) is a sub-map with noise content of 1;

[0048] Figure 6 Figures (a) to (f) are RMSE maps of different noise content interferograms using different phase unwrapping methods of embodiments of the present application;

[0049] Figure 7 Figures (a) to (f) are unwrapped phase and error maps of different noise content interferograms using different phase unwrapping methods of embodiments of the present application, wherein (a) is a sub-map with noise content of 0, (b) is a sub-map with noise content of 0.2, (c) is a sub-map with noise content of 0.4, (d) is a sub-map with noise content of 0.6, (e) is a sub-map with noise content of 0.8, and (f) is a sub-map with noise content of 1;

[0050] Figure 8 Figures (a) to (f) are unwrapped phase and error maps of different noise content interferograms using different phase unwrapping methods of embodiments of the present application, wherein (a) is a sub-map with noise content of 0, (b) is a sub-map with noise content of 0.2, (c) is a sub-map with noise content of 0.4, (d) is a sub-map with noise content of 0.6, (e) is a sub-map with noise content of 0.8, and (f) is a sub-map with noise content of 1; DETAILED DESCRIPTION

[0051] It should be noted that the embodiments and features in the present application can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0052] It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and although a logical order is shown in the flowchart, in some cases, the steps shown or described herein can be executed in an order different from that shown herein.

[0053] The present embodiment proposes a deep learning phase unwrapping method fusing Kalman filtering technology, as shown in Figure 1 , comprising:

[0054] constructing an absolute phase generation model, wherein the absolute phase generation model is constructed based on a conditional generative adversarial network, and is used to establish a direct mapping relationship from the wrapped phase to the unwrapped phase;

[0055] inputting an interferogram image to be unwrapped into the absolute phase generation model for processing to generate an initial unwrapped phase;

[0056] re-wrapping the initial unwrapped phase to obtain a re-wrapped phase, and performing conjugate multiplication on the re-wrapped phase and the interferogram image to be unwrapped to obtain a residual wrapped phase;

[0057] The residual wrapped phase is unwrapped by a Kalman filter phase unwrapping method to obtain residual unwrapped phase, and the initial unwrapped phase and the residual unwrapped phase are summed to obtain final unwrapped phase.

[0058] The embodiment utilizes the advantages of deep learning to reduce the unwrapping difficulty of large gradient change regions, utilizes the Kalman filter phase unwrapping method to overcome the influence of noise, improves the noise robustness of the algorithm, and further improves the performance of the overall algorithm.

[0059] Further, an absolute phase generation model is constructed, including:

[0060] Based on the CGAN network, a one-step unwrapping network for direct mapping of wrapped phase to unwrapped phase is constructed.

[0061] Based on the existing digital elevation model DEM, an unwrapping data set for direct mapping of wrapped phase to unwrapped phase is constructed.

[0062] The one-step unwrapping network for direct mapping of wrapped phase to unwrapped phase is trained by the unwrapping data set to obtain the absolute phase generation model.

[0063] Specifically, the embodiment takes the CGAN network as a basic model. The CGAN network is optimized by introducing conditional information on the basis of the original GAN. The core improvement is to add an additional conditional variable (such as a class label, a text description or other auxiliary information) in the generator and the discriminator, so as to realize precise control of the generation process. The model can directly generate high-precision absolute phase from wrapped phase, and the generated image quality is higher than that of CNN, U-Net and other networks.

[0064] Further, the one-step unwrapping network for direct mapping of wrapped phase to unwrapped phase includes a generator, a discriminator and a loss function.

[0065] The generator is a U-shaped structure using an encoder-residual module-decoder, including a plurality of convolution layers, transpose convolution layers and residual connections. The discriminator is a binary classifier composed of multiple cascaded convolution layers. The loss function includes a conditional generative adversarial loss function and a feature matching loss function.

[0066] Specifically, the generator is used to learn wrapped phase features and generate absolute phase. The discriminator is used to determine whether the image is a real absolute phase or an absolute phase generated by the generator. The specific process is as shown in Figure 2

[0067] ​When the model is trained, the two networks compete with each other, the generator generates absolute phase images that are closer and closer to the real absolute phase images to deceive the discriminator, and the discriminator learns the features of the real absolute phase images to improve the discrimination ability to identify the generated absolute phase images. In the continuous game, the absolute phase images generated by the generator will become more and more real, and the image quality is higher than that of CNN, U-Net and other networks.

[0068] Generator: The generator is designed based on the U-shaped structure of encoder-residual module-decoder, and the overall structure and detailed parameters of each layer are shown in Figure 3 (a) and Table 1. The encoder and decoder are respectively composed of multiple convolutional layers and transposed convolutional layers, the convolutional layers gradually extract the features of the input wrapped phase image in the encoding stage, the transposed convolutional layers try to reconstruct the output absolute phase image from the extracted features in the decoding stage, the residual module not only effectively alleviates the gradient vanishing and explosion problem in the deep network, but also accelerates the convergence to a better solution, promotes the learning of complex robust features, and improves the generalization ability of the model.

[0069] Table 1

[0070]

[0071] Discriminator: The discriminator is a classifier composed of multiple convolutional layers, and the overall structure and detailed parameters of each layer are shown in Figure 3 (b) and Table 2. The features transmitted by the convolutional layers are fed into a single sigmoid output to produce a probability value between 0 and 1, when the probability is closer to 1, the discriminator considers the input image as a real absolute phase image, on the contrary, when the probability is closer to 0, the discriminator considers the input image as an absolute phase image generated by the generator.

[0072] Table 2

[0073]

[0074] Loss function: The CGAN network constructs two loss functions, one is a conditional generative adversarial loss function, and the other is a feature matching loss function. The conditional generative adversarial loss function is used to make the generator and the discriminator compete with each other, the generator tries to generate real images to minimize the conditional generative adversarial loss, while the discriminator tries to enhance the discrimination ability of the false image to maximize the conditional generative adversarial loss function.

[0075] The conditional generative adversarial loss function is:

[0076]

[0077] In the formula, L cGAN (G, D) is the conditional generative adversarial loss, is an input image, ψ is a real image, is a generated image, is a discriminative network loss, is a generative network loss.

[0078] The feature matching loss is used to solve the problem that the generator and the discriminator cannot effectively counter each other. The feature matching loss calculates the loss of the generator by comparing the feature outputs of the intermediate layers of the discriminator, thereby providing more data to guide the training of the generator.

[0079] The feature matching loss function is:

[0080]

[0081] In the formula, L FM (G, D) is the feature matching loss, i is the layer number, t is the total number of layers, N i is the number of pixels in each layer output feature map, is the i-th layer discriminative network loss, is the i-th layer generative network loss.

[0082] Based on the above two loss functions, the complete goal of optimizing G and D is:

[0083]

[0084] In the formula, L Total is the total loss, G is the generator loss, D1 is the loss of the first discriminator, D2 is the loss of the second discriminator, k is the discriminator, L cGAN (G, D k ) is the conditional generative adversarial loss, L FM (G, D k ) is the feature matching loss, and λ is the weight. Wherein, λ balances the adversarial loss and the feature matching loss.

[0085] Further, an unwrapping data set about direct mapping of wrapped phase to unwrapped phase is constructed, such as Figure 4 , comprising:

[0086] The DEM in the geographic coordinate system is radar encoded and converted into DEM in the radar coordinate system;

[0087] Based on the imaging geometric parameters, the DEM in the radar coordinate system is simulated to obtain the real absolute phase;

[0088] The real absolute phase is unwrapped and added with noise to generate a noisy wrapped phase;

[0089] The real absolute phase and the noisy wrapped phase are cropped into image pairs of a preset pixel to form the unwrapping data set.

[0090] Specifically, comprising:

[0091] The DEM in the geographic coordinate system is radar encoded to obtain a DEM in a radar coordinate system;

[0092] According to the imaging geometric parameters, the DEM converted to the radar coordinate system is simulated for absolute phase to obtain a real absolute phase;

[0093] The real absolute phase is re-wrapped to obtain a noise-free wrapped phase;

[0094] Noise is added to the noise-free wrapped phase to obtain a noisy wrapped phase;

[0095] The real absolute phase and the noisy wrapped phase are cropped to 256x256 to construct an unwrapping training data set;

[0096] The network is trained to obtain an absolute phase generation model. Wherein, during the network training, the input is the noisy wrapped phase, and the output is the real absolute phase.

[0097] Further, the interferogram to be unwrapped is input into the trained absolute phase generation model to generate an initial unwrapped phase. In this embodiment, the model is trained on an Intel(R) Xeon(R) Silver 4214R CPU and an NVIDIA RTX A4000 GPU computer. During model training, the epoch is set to 150, the Batch_Size is set to 8, the optimizer is selected as Adam, the initial learning rate is set to 0.0002, and the weight λ is set to 10.

[0098] Further, the residual wrapped phase is obtained, comprising:

[0099] The initial unwrapped phase is re-wrapped, and the interferogram to be unwrapped and the re-wrapped phase map are differentially processed by conjugate multiplication, so as to sparsify the interference fringes, and the expression is as follows:

[0100]

[0101] In the formula, is the residual wrapped phase, is the initial interference phase, is the re-wrapped phase after the initial absolute phase obtained by inputting the initial interferogram to be unwrapped into the trained model, angle(·) represents the phase acquisition operation, conj(·) represents the complex conjugate operation, and exp(j*(·)) represents the conversion into a complex number.

[0102] Further, the Kalman filtering phase unwrapping method converts the phase unwrapping problem into a state estimation problem, and by establishing a state equation and an observation equation of phase unwrapping, the absolute phase of the interferogram to be unwrapped is predicted and updated by using the sigma transformation-based nonlinear Kalman filter to process the nonlinear equation.

[0103] Specifically, the residual wrapped phase is unwrapped by the Kalman filter unwrapping method to obtain a residual unwrapped phase. In theory, the wrapped phase difference between adjacent pixels is equal to the absolute phase difference, but due to the influence of noise and other factors, the wrapped phase difference is often not equal to the absolute phase difference. The Kalman filter phase unwrapping method converts the phase unwrapping problem into a state estimation problem, and by establishing a state equation and an observation equation of phase unwrapping, the absolute phase of the pixel to be unwrapped is predicted and updated by using the sigma transformation-based nonlinear Kalman filter to process the nonlinear equation, and the state equation and the observation equation are as follows:

[0104]

[0105] In the formula, ψ(s) and ψ(s-1) are the true phases at pixels s and s-1, respectively; is the phase gradient estimation value at pixel s-1; ω(s-1) is the corresponding phase gradient estimation error; is the observation value at pixel s; sin[ψ(s)] is the imaginary part of the wrapped phase at pixel s; cos[ψ(s)] is the real part of the wrapped phase at pixel s; H[ψ(s)] is an observation model function; v1(s) and v2(s) are the observation error variances of the imaginary part and the real part of the observation value, respectively; and v(s) is a matrix of v1(s) and v2(s).

[0106] Further, the final unwrapped phase is obtained by summing the initial unwrapped phase and the residual unwrapped phase, and the expression is as follows:

[0107] ψ(s) * = ψ1(s) * + ψ2(s) * ,

[0108] In the formula, ψ(s) * represents the final unwrapped phase, ψ1(s) * represents the initial unwrapped phase, and ψ2(s) * represents the residual unwrapped phase.

[0109] This embodiment leverages the phase loss inherent in one-step unwrapping methods based on deep learning. It divides the phase unwrapping in high-gradient regions into two stages. First, an initial unwrapped phase is obtained using an absolute phase generation model. Then, the residual wrapped phase is obtained by conjugate multiplication of the interferogram to be unwrapped and the initial unwrapped phase. Due to noise in the interferogram itself and the influence of deep learning unwrapping errors, the residual wrapped phase still contains significant noise. Therefore, a Kalman filtering phase unwrapping method with better denoising performance is used to unwrap the residual wrapped phase. Finally, the unwrapped phase is obtained by summing the initial unwrapped phase obtained in the first step and the residual unwrapped phase obtained in the second step. Compared to other existing conventional phase unwrapping methods, this embodiment can obtain high-precision unwrapping results from high-gradient regions, and the method has better robustness of the unwrapping model, effectively improving the accuracy of the final InSAR product.

[0110] To verify the technical effectiveness of this solution, interferograms and simulation data with varying levels of noise were processed using MCF, SNAPHU, UKF, U-Net, VUR-Net models, and the method proposed in this solution. To quantitatively describe the quality of the unwrapping results from different phase unwrapping algorithms, the root mean square error (RMSE) of the unwrapped phase and the Pearson correlation coefficient (PCCs) were calculated to measure the accuracy of the unwrapping results. RMSE measures the deviation between the predicted and true values ​​and is sensitive to outliers in the data; a smaller RMSE indicates that the unwrapped phase is closer to the true absolute phase. PCCs are typically used to measure the linear correlation between two continuous variables; a smaller error between the predicted and true values ​​indicates a stronger correlation between them.

[0111] 1. Noise robustness test

[0112] Figure 5 (a)- Figure 5 (f) represents the winding phase and its corresponding absolute phase with different noise levels. The diagrams show the unwrapped phases and corresponding error maps obtained by processing the winding phase using MCF, SNAPHU, UKF, U-Net, VUR-Net models, and the method proposed in this paper. To quantitatively describe the unwrapping accuracy of each method, the RMSE of each method is calculated, and the results are shown in [the diagram]. Figure 6From the unwrapping results, it can be seen that as the amount of noise increases, the error propagation phenomenon of the traditional phase unwrapping algorithm becomes more and more serious, especially the SNAPHU algorithm, the unwrapping performance under high noise conditions decreases obviously, and the RMSE is much higher than that of other algorithms. The MCF algorithm is most affected by large gradient changes, and the unwrapping result under the noise-free condition has a significant phase jump, and the RMSE is also the highest, showing a lower precision. Fortunately, MCF shows high noise robustness, and the RMSE does not fluctuate significantly as the noise increases. The UKF algorithm has better filtering effect than MCF and SNAPHU, and the RMSE is even lower under high noise conditions. However, from the error map, it can be found that UKF still has unwrapping patches in the area with large gradient changes. Compared with traditional phase unwrapping algorithms, the advantage of deep learning phase unwrapping algorithm is that it can still obtain good unwrapping results in areas with large gradient changes, and has the function of filtering while unwrapping. From the error map, it can be found that the unwrapping results of the U-Net model and the VUR-Net model are relatively stable and less affected by noise, and still maintain good filtering effect under high noise conditions. In addition, the RMSE does not fluctuate too much as the noise content increases. However, in the area with dense fringes, there are still unwrapping errors. The method proposed in this technical solution, combined with the deep learning phase unwrapping algorithm, can get rid of the restriction of the phase continuity assumption and the advantage of the UKF algorithm with stronger filtering function. In the area with large gradient changes and high noise, it can obtain better unwrapping results than other algorithms, and the RMSE is also lower, and does not change sharply as the noise content increases. This experiment verifies that the method proposed in this technical solution has higher unwrapping precision and noise robustness.

[0113] 2. Simulation data experiment

[0114] This embodiment uses a set of simulation data as shown in Figure 7 , the data size is 256x256 pixels, Figure 7 (a) is the reference absolute phase, Figure 7 (b) is the wrapped phase after adding Gaussian noise, from the figure, it can be seen that the interferogram contains a large amount of noise and has dense fringes, Figure 7 (c) is the coherence coefficient map of the wrapped phase with noise, from the figure, it can be seen that the coherence of the interferogram is low, and the coherence coefficient in most areas is less than 0.3. This creates good conditions for testing the unwrapping performance of different unwrapping algorithms in high noise and large gradient change areas.

[0115] Figure 8The unwrapping results and error distribution diagrams of different methods are shown, and the percentage of unwrapping errors of different methods in different ranges is also shown. Table 3 shows the quantitative evaluation results of different algorithms, including RMSE and PCCs. From the unwrapping images, it can be seen that the unwrapping result of MCF has a large difference from the reference absolute phase, and still contains a large amount of noise. From the error diagram, it can be found that the result of MCF has obvious error transmission along the dense stripe area, resulting in the highest RMSE of MCF, reaching 13.94 rad, and the PCCs is only 0.8391, the quality of unwrapping is much lower than the rest of the methods. The unwrapping results of SNAPHU and UKF are relatively close, both appear small area discontinuity, and there are unwrapping holes in the red rectangular area. However, UKF has better filtering effect than SNAPHU, and the unwrapping result is smoother, so the RMSE of UKF is also lower than that of SNAPHU, only 3.06 rad, and the PCCs is also higher, reaching 0.9939. The unwrapping results of U-Net model and VUR-Net model are the most smooth, and the denoising effect is obvious, only the red rectangular area has unwrapping error, and the unwrapping accuracy is higher than that of traditional algorithm. Compared with the VUR-Net model, the unwrapping accuracy of the U-Net model is higher, the RMSE is only 2.32 rad, and the PCCs reaches 0.9962. The unwrapping result of the method is closest to the reference absolute phase, only a small area of unwrapping error appears, because the deep learning phase unwrapping algorithm uses the characteristics of phase loss to reduce the phase gradient, so the unwrapping accuracy in the dense stripe area is improved, in addition, the Kalman filter phase unwrapping algorithm with filtering effect is used in the second step, so the unwrapping accuracy in the high noise area is also improved. Combining the above advantages, the RMSE of the method is only 1.5 rad, and the PCCs is 0.9976, which are the best among all methods. From the distribution range of the error, the improved algorithm has 92.01% of the error absolute value within 2 rad, which is much higher than other algorithms. It can also be found that the proportion of the absolute value of the unwrapping error of the deep learning phase unwrapping algorithm within 2 rad is higher than that of the traditional algorithm, which reflects the advantage of the deep learning phase unwrapping algorithm in the large gradient and high noise area. The experiment in the simulation data fully verifies that the method proposed in the technical scheme can obtain better unwrapping result in the high noise and large gradient change area than the existing method.

[0116] Table 3

[0117]

[0118] The above merely provides the preferred embodiments of the present application, and the protection scope of the present application is not limited thereto, and any changes or substitutions within the technical scope disclosed by the present application should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A deep learning phase-unwrapping method fused Kalman filtering technique, characterized in that, The application relates to a method for constructing an absolute phase generation model, wherein the absolute phase generation model is constructed based on a conditional generative adversarial network and is used to establish a direct mapping relationship between wrapped phase and unwrapped phase. The method comprises the following steps: constructing the absolute phase generation model comprises: constructing a one-step unwrapping network for direct mapping between wrapped phase and unwrapped phase based on a CGAN network; constructing an unwrapping data set for direct mapping between wrapped phase and unwrapped phase based on an existing digital elevation model (DEM); 2. The deep learning phase un-wrapping method fused Kalman filtering technique according to claim 1, characterized in that, training the one-step unwrapping network for direct mapping between wrapped phase and unwrapped phase based on the unwrapping data set to obtain the absolute phase generation model. The one-step unwrapping network for direct mapping between wrapped phase and unwrapped phase comprises a generator, a discriminator and a loss function; wherein the generator is a U-shaped structure adopting an encoder-residual module-decoder, contains a plurality of convolution layers, a transposed convolution layer and residual connection, the discriminator is a binary classifier composed of a plurality of cascaded convolution layers, and the loss function comprises a conditional generative adversarial loss function and a feature matching loss function. The conditional generative adversarial loss function is:

3. The deep learning phase un-wrapping method fused Kalman filtering technique according to claim 2, characterized in that, The feature matching loss function is: constructing the unwrapping data set for direct mapping between wrapped phase and unwrapped phase comprises:

4. The deep learning phase un-wrapping method fused Kalman filtering technique according to claim 3, characterized in that, radar encoding the DEM in a geographic coordinate system to convert the DEM into a DEM in a radar coordinate system; In the formula, L cGAN (G,D) is the conditional generative adversarial loss, is the input image, and ψ is the real image, is the generated image, is the discriminant network loss, is the generated network loss; simulating absolute phase based on imaging geometric parameters to obtain real absolute phase; In the formula, L FM (G, D) is a feature matching loss, i is a layer number, t is a total layer number, N i is the number of pixels in each layer output feature map, is the i-th layer discriminant network loss, is the i-th layer generation network loss.

5. The deep learning phase un-wrapping method fused Kalman filtering technique according to claim 2, wherein, anti-wrapping and noise adding are performed on the real absolute phase to generate a noisy wrapped phase; the real absolute phase and the noisy wrapped phase are cropped into image pairs of a preset pixel to constitute the unwrapping data set. The residual wrapped phase is obtained by: The Kalman filter phase unwrapping method converts the phase unwrapping problem into a state estimation problem, establishes a state equation and an observation equation of phase unwrapping, processes a nonlinear equation by using a sigma transformation-based nonlinear Kalman filter, and predicts and updates the absolute phase of the interferogram to be unwrapped. The state equation and the observation equation are:

6. The deep learning phase un-wrapping method with fused Kalman filtering technique according to claim 1, wherein, The final unwrapped phase is obtained by: wherein, is the residual wrapping phase, is the initial interference phase, is the re-wrapped phase obtained by inputting the initial interferogram to be unwrapped into the trained model, angle(·) denotes the phase acquisition operation, conj(·) denotes the complex conjugate operation, and exp(j*(·)) denotes the conversion to a complex number.

7. The deep learning phase un-wrapping method fused Kalman filtering technique according to claim 1, wherein, ​ 8. The deep learning phase un-wrapping method fused Kalman filtering technique according to claim 7, characterized in that, ​ where ψ(s) and ψ(s-1) are the true phases at pixels s and s-1, respectively; is the phase gradient estimate at pixel s-1; ω(s-1) is the corresponding phase gradient estimation error; is the observation at pixel s; sin[ψ(s)] is the imaginary part of the wrapped phase at pixel s; cos[ψ(s)] is the real part of the wrapped phase at pixel s; H[ψ(s)] is the observation model function; υ1(s) and υ2(s) are the observation error variances of the imaginary and real parts of the observation, respectively; and υ(s) is the matrix of υ1(s) and υ2(s).

9. The deep learning phase un-wrapping method fused Kalman filtering technique according to claim 1, wherein, ​ ψ(s) * = ψ1(s) * + ψ2(s) * , In the formula, ψ(s) * Let ψ1(s) represent the final untangling phase. * Let ψ2(s) represent the initial untangling phase. * This indicates the residual untangling phase.

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