A deep learning-based central difference information filtering phase unwrapping method

Abstract

The present application aims to provide a kind of center difference information filtering phase unwrapping method based on deep learning, comprising the following steps: A, CDIF phase unwrapping recursive model and deep neural network are constructed, the deep neural network is based on LANET interferogram semantic segmentation network;B, after interferogram is input into deep neural network processing, the semantic segmentation image based on interferogram fringe distribution is obtained;C, the merging and optimization adjustment of interferogram semantic segmentation area are carried out, and the segmentation area with appropriate size is obtained, to constitute interferogram area segmentation graph D, each segmentation area in interferogram area segmentation graph is unwrapped using CDIF phase unwrapping recursive model;E, the unwrapping result of each segmentation area is merged, and the unwrapping phase of whole interferogram is obtained.The present application can obtain more robust results in interferogram phase unwrapping experiment, and its efficiency can be accepted, can effectively process interferogram phase unwrapping problem.

Description

Technical Field

[0001] This invention relates to the field of phase unfolding technology, and more specifically to a phase unwrapping method based on deep learning-based center difference information filtering. Background Technology

[0002] Phase unwrapping is the process of recovering the unwrapped phase reflecting the true physical quantity of the measured target from the wrapped phase space [-π,π) mapped from the interferogram modulus 2π. Phase unwrapping is an indispensable step in many interferometric techniques, such as digital holographic interferometry and fringe projection profilometry (DHM), interferometric synthetic aperture radar (InSAR), magnetic resonance imaging (MRI), interferometric synthetic aperture sonar (InSAS), adaptive optics, and speckle imaging. The accuracy of interferogram phase unwrapping directly affects the accuracy of the physical quantity estimation extracted by the above interferometric techniques.

[0003] Commonly used unwrapping methods in existing technologies include BUT, QGPU, ILS, and UKFPU. These methods are prone to problems such as a large amount of burr-like noise at the edges of the rewound phase map fringes, and a relatively large dynamic range of unwrapped phase error. Therefore, a more effective technical solution is needed to address the phase unwrapping problem of interferograms. Summary of the Invention

[0004] The present invention aims to provide a deep learning-based central difference information filtering phase unwrapping method, which can obtain more robust results in interferogram phase unwrapping experiments and has acceptable efficiency, and can effectively handle the interferogram phase unwrapping problem.

[0005] The technical solution of the present invention is as follows:

[0006] The deep learning-based center difference information filtering phase unwrapping method includes the following steps:

[0007] A. Construct a CDIF phase unwrapping recursive model and a deep neural network, wherein the deep neural network is an interferometric image semantic segmentation network based on LANET; the LANET neural network is described in the following document:

[0008] L.Ding, H.Tang, L.Bruzzone, "LANet: Local attention embedding to improve the semantic segmentation of remote sensing images," IEEE Trans Geosci RemoteSens.59(1), 426-435(2020).

[0009] B. The interferogram is cropped into several 256*256 sub-interferograms using an overlapping cropping method. During cropping, several rows or columns of overlapping pixels are left between adjacent sub-interferograms. These sub-interferograms are then sequentially input into a deep neural network to obtain several semantic segmentation maps of the sub-interferogram based on the fringe distribution of the interferogram and composed of different integer winding numbers K. Then, the semantic segmentation maps of each sub-interferogram are stitched together using the principle that the phase winding number of overlapping pixels in adjacent sub-blocks is the same, to obtain the semantic segmentation map of the entire interferogram.

[0010] C. Merge and optimize the semantic segmentation regions in the semantic segmentation map of the entire interferogram to obtain the interferogram region segmentation map;

[0011] D. Using the CDIF phase unwrapping recursive model, unwrap each segmented region in the interferogram region segmentation diagram to obtain the unwrapping results of each segmented region in the interferogram region segmentation diagram;

[0012] E. Using the unwrapping phase consistency criterion of adjacent regions of the interferogram, merge the unwrapping results of each segmented region to obtain the unwrapped phase map of the entire interferogram.

[0013] In step B, the process of stitching together the semantic segmentation maps of each sub-interferogram using the principle that the phase wrapping number of overlapping pixels in adjacent sub-blocks is the same is as follows:

[0014] a. The preceding sub-interferogram semantic segmentation image is spliced ​​with its adjacent sub-interferogram semantic segmentation image to its right or below. The difference between the overlapping pixels of the two sub-interferogram semantic segmentation images is calculated. This difference is then added to or subtracted from the right or below sub-interferogram semantic segmentation image to ensure that the phase entanglement number of the overlapping pixels in the two sub-interferogram semantic segmentation images is consistent. The overlapping pixel portion of the right or below sub-interferogram semantic segmentation image is then cropped to obtain the adjusted right or below sub-interferogram semantic segmentation image. The adjusted right or below sub-interferogram semantic segmentation image is then merged with the preceding sub-interferogram semantic segmentation image to obtain the spliced ​​sub-interferogram semantic segmentation image.

[0015] b. Starting from the semantic segmentation map of the sub-interference map located in the upper left corner, repeat step a in the following order: first from left to right, then move to the next row after reaching the end, and then from left to right again, until all the semantic segmentation maps of the sub-interference map are stitched together into one image, thus obtaining the semantic segmentation map of the entire interference map.

[0016] In step C, the process of merging and optimizing the semantic segmentation regions in the semantic segmentation map of the entire interferogram is as follows:

[0017] a. Set a threshold for the number of pixels in the segmented region. The threshold for the number of pixels in the segmented region is 1 / 6 of the total number of pixels in the entire interferogram.

[0018] b. Number each segmented region in the semantic segmentation map of the entire interferogram. The number of each segmented region is marked by the phase winding number K of the integer of that region. Then, in order of ascending sequence of segmented region number K, determine whether the number of pixels in each semantic segmented region is greater than the segmented region pixel number threshold. If yes, keep the semantic segmented region unchanged; if no, merge adjacent semantic segmented regions until the number of pixels in the merged semantic segmented region is greater than the segmented region pixel number threshold.

[0019] c. Sort the semantic segmentation regions processed in step b according to the order of optimization and adjustment to obtain the interferogram region segmentation map.

[0020] In step D, the unwrapping process using the CDIF phase unwrapping recursive model is as follows:

[0021] According to the ascending order of the segmentation region numbers in the interferogram region segmentation diagram, the CDIF phase unwrapping recursive model is used to unwrap each segmentation region in the interferogram region segmentation diagram in turn; when unwrapping each segmentation region, a path tracking strategy based on heap sort is used to perform two-dimensional phase unwrapping on the pixels in the region along the path from high-quality pixels to low-quality pixels.

[0022] The CDIF phase unwrapping recursive model is as follows:

[0023] a. Construct CDIF Sigma points

[0024] Calculate the one-step state prediction for cell (m,n) and one-step state prediction error covariance

[0025]

[0026] In the formula, pixel (a,s) is the unwrapped pixel in the 8-neighborhood of pixel (m,n); ψ is the set of unwrapped pixels in the 8-neighborhood of pixel (m,n); and SNR(a,s) is the signal-to-noise ratio of pixel (a,s). Based on the L-dimensional state variables (L=1), the following 2L+1 Sigma points are further generated:

[0027]

[0028] In the formula, h represents the central difference half-step length, which is usually taken as... The corresponding weights are calculated as follows:

[0029]

[0030] b. State prediction

[0031] Calculate the state prediction value of cell (m,n) and state prediction error covariance

[0032]

[0033] In the formula, Q(m,n) represents the variance of the phase gradient estimation error; To utilize the Levenberg-Marquardt operator pair The optimized state prediction error covariance, where u represents the adjustment parameter (u = 0.21 in this paper), and I is the identity matrix;

[0034] c. State space transitions to information space.

[0035] Calculate the prediction information matrix for pixel (m,n) and the predicted information state vector

[0036]

[0037] d. Measurement update

[0038] Calculate the measurement prediction value of pixel (m,n) and mutual covariance p xz (m,n):

[0039]

[0040] Calculate the information matrix distribution I(m,n) and information state distribution i(m,n) for pixel (m,n):

[0041]

[0042] In the formula, z(m,n) and e(m,n) represent the observed value and residual of pixel (m,n), respectively; R(m,n) is the observation noise variance of pixel (m,n). Then, the information matrix Y(m,n) and information state vector y(m,n) of pixel (m,n) are calculated using the following formula:

[0043]

[0044] e. Information space shifts to state space

[0045] Update the state estimate of cell (m,n) and state estimation error covariance

[0046]

[0047] The system equations for CDIF-based phase unwrapping are as follows:

[0048]

[0049] In the formula, x(m,n) and z(m,n) represent the state variables (i.e., unwrapped phase) of the interferogram (m,n) pixels and the observation vector, respectively; w is the estimated phase gradient between pixels (m,n) and (a,s) in the interferogram. (m,n)|(a,s) The phase gradient estimation error of the interferogram is represented by v(m,n); v(m,n) represents the observation noise vector of the (m,n) pixel in the interferogram; v1(m,n) and v2(m,n) are the observation noise of the orthogonal component and the in-phase component of the state variable, respectively.

[0050] The deep neural network includes a ResNet50 module, a PAM module, and an AEM module;

[0051] The sub-interferograms are input into the ResNet50 module, and after compression by the ResNet50 module, high-level feature maps compressed to 1 / 32 and low-level feature maps compressed to 1 / 4 are obtained respectively.

[0052] The high-level feature map is processed by the PAM module and then added to and fused with the high-level feature map to obtain the enhanced high-level feature map;

[0053] After processing by the PAM module, the low-level feature map is added to and fused with the low-level feature map to obtain the low-level feature fusion map. The low-level feature fusion map and the enhanced high-level feature map are respectively input into the AEM module. The output of the AEM module is added to and fused with the low-level feature fusion map to obtain the enhanced low-level feature map.

[0054] After the enhanced high-level feature map and the enhanced low-level feature map are superimposed and fused, a sub-interferogram semantic segmentation map is obtained based on the interferogram fringe distribution and composed of different integer winding numbers K.

[0055] The ResNet50 module includes a convolutional layer, a max pooling layer, and blocks 1-4 connected in sequence. After the sub-interference map is processed by the convolutional layer and adjusted by the max pooling layer, it is compressed to 1 / 4 in the block 1 layer to obtain a low-level feature map.

[0056] The low-level feature maps are input into the block2 layer and the PAM module respectively. After being compressed to half its size by the block2 layer, the low-level feature maps are output to the block3 layer. After being compressed to half its size again in the block3 layer, they are output to the block4 layer. After being compressed to half its size again by the block4 layer, the high-level feature maps are obtained by being compressed to 1 / 32.

[0057] The convolutional layer is a 7×7-16 convolutional layer; the max pooling layer is a 3×3 max pooling layer.

[0058] The PAM module processing procedure is as follows: the input features are sequentially processed by adaptive average pooling, 1×1 convolution, and upsampling, then multiplied by trainable weights normalized by the sigmoid function, then multiplied and fused with the input features, and finally added and fused with the input features to obtain the PAM output features.

[0059] The AEM module processing procedure is as follows: after the enhanced high-level feature map undergoes adaptive average pooling, 1×1 convolution, and upsampling, it is multiplied by trainable weights normalized by the sigmoid function, then multiplied and fused with the low-level feature fusion map, and finally added and fused with the low-level feature fusion map to obtain the AEM output feature.

[0060] In step E, the process of merging the unwrapping results of each segmented region using the phase consistency criterion for unwrapping adjacent regions of the interferogram is as follows:

[0061] Let any two adjacent segmented regions be defined as interferogram segmentation region A and interferogram segmentation region B, respectively;

[0062] If the number of pixels in interferogram segment A is greater than or equal to the number of pixels in its adjacent segment B, then segment B is merged into its adjacent segment A, and its unwrapping phase is calculated as follows:

[0063]

[0064] In the formula, i and j are pixels in regions A and B, respectively, and i is located within the adjacency domain of j; Φ A (i) and Φ B (j) represents the unwrapping phase of pixels i and j, respectively; round[x] indicates that x is rounded down; Φ B For the unwrapping result of region B, Φ' B The untangled phase is the corrected phase for region B; A′ is the region formed by merging regions A and B, Φ A′ This is the untangling phase of the merged region A′.

[0065] If the number of pixels in interferogram segment B is greater than or equal to the number of pixels in its adjacent segment A, then segment A is merged into its adjacent segment B, and the unwrapping phase is calculated as follows:

[0066]

[0067] In the formula, Φ' A Φ represents the unwrapped phase after correction for region A; B′ represents the region formed by merging regions A and B. B′ This is the untangling phase of the merged region B′;

[0068] The merged unwrapped result is then combined with the unwrapped result of the next adjacent segmented region. This process is repeated for all segmented region unwrapped results until all segmented region unwrapped results are merged, thus obtaining the unwrapped phase map of the entire interferogram.

[0069] The unwrapping method of this invention is the result of organically combining deep learning-based region segmentation technology, the CDIF algorithm, an efficient local phase gradient estimation algorithm, and a path tracking strategy based on heap sorting. The effectiveness of the algorithm has been verified in simulated and experimental data. Compared with some commonly used algorithms, including branch cutting, iterative least squares, quality-guided methods, and UKFPU, the method of this invention achieves more robust results and acceptable efficiency in interferogram phase unwrapping experiments, effectively handling the interferogram phase unwrapping problem. Attached Figure Description

[0070] Figure 1 This is a schematic diagram of the overall structure of the deep neural network in Embodiment 1 of the present invention;

[0071] Figure 2 This is a schematic diagram of the ResNet50 module in Embodiment 1 of the present invention;

[0072] Figure 3 This is a schematic diagram of the PAM module in Embodiment 1 of the present invention;

[0073] Figure 4 This is a schematic diagram of the structure of the AEM module in Embodiment 1 of the present invention;

[0074] Figure 5 These are simulated interferograms of different fringe patterns in Embodiment 2 of the present invention;

[0075] Figure 6 This is an example of untangling using the BUT algorithm in Embodiment 2 of the present invention. Figure 5 The result of df;

[0076] Figure 7 This is the QGPU algorithm used for untangling in Embodiment 2 of the present invention. Figure 5 The result of df;

[0077] Figure 8 This is an example of untangling using the ILS algorithm in Embodiment 2 of the present invention. Figure 5 The result of df;

[0078] Figure 9 This is an example of untangling using the UKFPU algorithm in Embodiment 2 of the present invention. Figure 5 The result of df;

[0079] Figure 10 This is the algorithm for untangling in Embodiment 2 of the present invention using the algorithm from Embodiment 1. Figure 5The result of df;

[0080] Figure 11 This is a partial Enta volcano interferometry phase diagram and a BUT unwrapping result diagram of Embodiment 2 of the present invention;

[0081] Figure 12 The QGPU, ILS, and UKFPU methods are used to unwrap the local Enta volcano interferometric phase map in Embodiment 2 of the present invention.

[0082] Figure 13 This is a diagram showing the unwrapping result of the algorithm from Embodiment 1 of the present invention for the local Enta volcano interferometric phase map of Embodiment 2 of the present invention; Detailed Implementation

[0083] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0084] Example 1

[0085] This embodiment provides a deep learning-based center difference information filtering phase unwrapping method, which includes the following steps:

[0086] The deep learning-based center difference information filtering phase unwrapping method includes the following steps:

[0087] A. Construct a CDIF phase unwrapping recursive model and a deep neural network, wherein the deep neural network is an interferometric graph semantic segmentation network based on LANET;

[0088] like Figure 1 As shown, the deep neural network includes a ResNet50 module, a PAM module, and an AEM module;

[0089] like Figure 2 As shown, the ResNet50 module includes a 7×7-16 convolutional layer, a 3×3 max pooling layer, and block 1-4 layers connected in sequence; Figure 2 In this example, C represents the number of network layers and channels; C = 16.

[0090] The ResNet50 module includes a convolutional layer, a max pooling layer, and blocks 1-4 connected in sequence. After the sub-interference map is processed by the convolutional layer and adjusted by the max pooling layer, it is compressed to 1 / 4 in the block 1 layer to obtain a low-level feature map.

[0091] The low-level feature maps are input into the block2 layer and the PAM module respectively. After being compressed to half its size by the block2 layer, the low-level feature maps are output to the block3 layer. After being compressed to half its size again in the block3 layer, they are output to the block4 layer. After being compressed to half its size again by the block4 layer, the high-level feature maps are obtained by being compressed to 1 / 32.

[0092] The high-level feature map is processed by the PAM module and then added to and fused with the high-level feature map to obtain the enhanced high-level feature map;

[0093] After processing by the PAM module, the low-level feature map is added to and fused with the low-level feature map to obtain the low-level feature fusion map. The low-level feature fusion map and the enhanced high-level feature map are respectively input into the AEM module. The output of the AEM module is added to and fused with the low-level feature fusion map to obtain the enhanced low-level feature map.

[0094] like Figure 3 As shown, the PAM module processing procedure is as follows: the input features are sequentially processed by adaptive average pooling, 1×1 convolution, and upsampling, then multiplied by trainable weights normalized by the sigmoid function, then multiplied and fused with the input features, and finally added and fused with the input features to obtain the PAM output features.

[0095] like Figure 4 As shown, the AEM module processing procedure is as follows: after the enhanced high-level feature map undergoes adaptive average pooling, 1×1 convolution, and upsampling, it is multiplied by trainable weights normalized by the sigmoid function, then multiplied and fused with the low-level feature fusion map, and then added and fused with the low-level feature fusion map to obtain the AEM output feature.

[0096] After the enhanced high-level feature map and the enhanced low-level feature map are superimposed and fused, several sub-interferogram semantic segmentation maps are obtained, which are based on the interferogram fringe distribution and are composed of different integer winding numbers K.

[0097] B. Training the neural network:

[0098] STEP 1, produced in the following two ways: (I) First, create 7000 random initial matrices with a size of 2×2-5×5. Then, use bicubic interpolation to expand the initial matrices to a size of 256×256, which is the true interferometric phase. Then, convert the generated true interferometric phase into noise-wrapped phases with different signal-to-noise ratios, thereby generating 7000 sets of data with an image size of 256×256 and a true unwrapped phase range of 0-60 radians. (II) Convert 10000 sets of InSAR interferometric phase data from terrain DEM data. That is, first, use the InSAR technology principle to convert the DEM data into true interferometric phases with an image size of 256×256 and a true interferometric phase range of 0-60 radians. Then, convert the generated true interferometric phases into noise-wrapped phases with different signal-to-noise ratios.

[0099] STEP 2, the true phase Φ(m,n) and the entangled phase Ψ(m,n) of the interferogram have the following relationship:

[0100] Φ(m,n)=Ψ(m,n)+2πκ(m,n) (13)

[0101] Wherein, κ(m,n) is the number of wraps around the integer number of pixels in the interferogram (m,n);

[0102] According to Formula 13 above, the integer winding numerical map is extracted from the real interferometric phase map generated by STEP 1 and used as the label image of the InSAR interferogram input to the network for training.

[0103] The LANET network was trained using the mainstream deep learning framework Keras 2.4.3. The computer hardware and software configuration is shown in Table 1 below. The adaptive moment estimation optimizer was used for network training, with the loss function being class cross-entropy, the initial learning rate being 0.001, the number of training epochs being 160, the minimum training batch size being 8, and the training time being approximately 32 hours.

[0104] Table 1 Computer Hardware and Software Configuration

[0105]

[0106] C. The interferogram is cropped into several 256*256 sub-interferograms using an overlapping cropping method. During cropping, several rows or columns of overlapping pixels are left between adjacent sub-interferograms. These sub-interferograms are then sequentially input into a deep neural network to obtain a semantic segmentation map of the sub-interferogram based on the fringe distribution of the interferogram and composed of different integer winding numbers K. Then, the semantic segmentation maps of each sub-interferogram are stitched together using the principle that the phase winding number of overlapping pixels in adjacent sub-blocks is the same, to obtain the semantic segmentation map of the entire interferogram.

[0107] The process of stitching together the semantic segmentation maps of each sub-interferogram using the principle that the phase wrapping number of overlapping pixels in adjacent sub-blocks is the following:

[0108] a. The preceding sub-interferogram semantic segmentation image is spliced ​​with its adjacent sub-interferogram semantic segmentation image to its right or below. The difference between the overlapping pixels of the two sub-interferogram semantic segmentation images is calculated. This difference is then added to or subtracted from the right or below sub-interferogram semantic segmentation image to ensure that the phase entanglement number of the overlapping pixels in the two sub-interferogram semantic segmentation images is consistent. The overlapping pixel portion of the right or below sub-interferogram semantic segmentation image is then cropped to obtain the adjusted right or below sub-interferogram semantic segmentation image. The adjusted right or below sub-interferogram semantic segmentation image is then merged with the preceding sub-interferogram semantic segmentation image to obtain the spliced ​​sub-interferogram semantic segmentation image.

[0109] b. Starting from the semantic segmentation map of the sub-interference map located in the upper left corner, repeat step a in the following order: first from left to right, then move to the next row after reaching the end, and then from left to right again, until all the semantic segmentation maps of the sub-interference map are stitched together into one image, thus obtaining the semantic segmentation map of the entire interference map.

[0110] D. Merge and optimize the semantic segmentation regions in the semantic segmentation map of the entire interferogram to obtain the interferogram region segmentation map;

[0111] The process of merging and optimizing the semantic segmentation regions in the semantic segmentation map of the entire interferogram is as follows:

[0112] a. Set a threshold for the number of pixels in the segmented region. The threshold for the number of pixels in the segmented region is 1 / 6 of the total number of pixels in the entire interferogram.

[0113] b. Number each segmented region in the semantic segmentation map of the entire interferogram. The number of each segmented region is marked by the phase winding number K of the integer of that region. Then, in order of ascending sequence of segmented region number K, determine whether the number of pixels in each semantic segmented region is greater than the segmented region pixel number threshold. If yes, keep the semantic segmented region unchanged; if no, merge adjacent semantic segmented regions until the number of pixels in the merged semantic segmented region is greater than the segmented region pixel number threshold.

[0114] c. Sort the semantic segmentation regions processed in step b according to the order of optimization and adjustment to obtain the interferogram region segmentation map.

[0115] E. Using the CDIF phase unwrapping recursive model, each segmented region in the interferogram region segmentation diagram is unwrapped to obtain the unwrapping results of each segmented region in the interferogram region segmentation diagram.

[0116] The unwrapping process using the CDIF phase unwrapping recursive model is as follows:

[0117] According to the ascending order of the segmentation region numbers in the interferogram region segmentation diagram, the CDIF phase unwrapping recursive model is used to unwrap each segmentation region in the interferogram region segmentation diagram in turn; when unwrapping each segmentation region, a path tracking strategy based on heap sort is used to perform two-dimensional phase unwrapping on the pixels in the region along the path from high-quality pixels to low-quality pixels.

[0118] The CDIF phase unwrapping recursive model is as follows:

[0119] a. Construct CDIF Sigma points

[0120] Calculate the one-step state prediction for cell (m,n) and one-step state prediction error covariance

[0121]

[0122] In the formula, pixel (a,s) is the unwrapped pixel in the 8-neighborhood of pixel (m,n); ψ is the set of unwrapped pixels in the 8-neighborhood of pixel (m,n); and SNR(a,s) is the signal-to-noise ratio of pixel (a,s). Based on the L-dimensional state variables (L=1), the following 2L+1 Sigma points are further generated:

[0123]

[0124] In the formula, h represents the central difference half-step length, which is usually taken as... The corresponding weights are calculated as follows:

[0125]

[0126] b. State prediction

[0127] Calculate the state prediction value of cell (m,n) and state prediction error covariance

[0128]

[0129] In the formula, Q(m,n) represents the variance of the phase gradient estimation error; To utilize the Levenberg-Marquardt operator pair The optimized state prediction error covariance, where u represents the adjustment parameter (u = 0.21 in this paper), and I is the identity matrix;

[0130] c. State space transitions to information space.

[0131] Calculate the prediction information matrix for pixel (m,n) and the predicted information state vector

[0132]

[0133] d. Measurement update

[0134] Calculate the measurement prediction value of pixel (m,n) and mutual covariance p xz (m,n):

[0135]

[0136] Calculate the information matrix distribution I(m,n) and information state distribution i(m,n) for pixel (m,n):

[0137]

[0138] In the formula, z(m,n) and e(m,n) represent the observed value and residual of pixel (m,n), respectively; R(m,n) is the observation noise variance of pixel (m,n). Then, the information matrix Y(m,n) and information state vector y(m,n) of pixel (m,n) are calculated using the following formula:

[0139]

[0140] e. Information space shifts to state space

[0141] Update the state estimate of cell (m,n) and state estimation error covariance

[0142]

[0143] The system equations for CDIF-based phase unwrapping are as follows:

[0144]

[0145] In the formula, x(m,n) and z(m,n) represent the state variables (i.e., unwrapped phase) of the interferogram (m,n) pixels and the observation vector, respectively; w is the estimated phase gradient between pixels (m,n) and (a,s) in the interferogram. (m,n)|(a,s) The phase gradient estimation error of the interferogram is represented by v(m,n); v(m,n) represents the observation noise vector of the (m,n) pixel in the interferogram; v1(m,n) and v2(m,n) are the observation noise of the orthogonal component and the in-phase component of the state variable, respectively.

[0146] F. Using the unwrapping phase consistency criterion of adjacent regions of the interferogram, merge the unwrapping results of each segmented region to obtain the unwrapped phase map of the entire interferogram.

[0147] The process of merging the unwrapping results of each segmented region using the phase consistency criterion for unwrapping adjacent regions of the interferogram is as follows:

[0148] Let any two adjacent segmented regions be defined as interferogram segmentation region A and interferogram segmentation region B, respectively;

[0149] If the number of pixels in interferogram segment A is greater than or equal to the number of pixels in its adjacent segment B, then segment B is merged into its adjacent segment A, and its unwrapping phase is calculated as follows:

[0150]

[0151] In the formula, i and j are pixels in regions A and B, respectively, and i is located within the adjacency domain of j; Φ A(i) and Φ B (j) represents the unwrapping phase of pixels i and j, respectively; round[x] indicates that x is rounded down; Φ B For the unwrapping result of region B, Φ' B The untangled phase is the corrected phase for region B; A′ is the region formed by merging regions A and B, Φ A′ This is the untangling phase of the merged region A′.

[0152] If the number of pixels in interferogram segment B is greater than or equal to the number of pixels in its adjacent segment A, then segment A is merged into its adjacent segment B, and the unwrapping phase is calculated as follows:

[0153]

[0154] In the formula, Φ' A Φ represents the unwrapped phase after correction for region A; B′ represents the region formed by merging regions A and B. B′ This is the untangling phase of the merged region B′;

[0155] The merged unwrapped result is then combined with the unwrapped result of the next adjacent segmented region. This process is repeated for all segmented region unwrapped results until all segmented region unwrapped results are merged, thus obtaining the unwrapped phase map of the entire interferogram.

[0156] Example 2

[0157] To verify the effectiveness of the algorithm in Embodiment 1 of this invention, several commonly used phase unwrapping algorithms, including Branch Cutting (BUT), Quality Guided GPU (QGPU), Iterative Least Squares (ILS), and Tasteless Kalman Filter Phase Unwrapping Algorithm (UKFPU), were used in the same MATLAB software environment (Intel(R) Core(TM) i7-10700K CPU@3.80GHz 3.79GHz) to conduct phase unwrapping experiments on different types of simulated and measured data, and the experimental results were compared and analyzed.

[0158] I. Simulated Data Experiment

[0159] Figure 5 The middle and a represent the true interferometric phases of the peaks, pyramid, and mountain scenes, respectively, and their image resolutions are all 502×502. Figure 5 df are respectively Figure 5 The signal-to-noise ratios of the noisy, entangled phase diagrams corresponding to the actual interference phases shown in Figure ac are 6.10 dB, 4.94 dB, and 3.92 dB, respectively.

[0160] Figure 6 For the BUT algorithm Figure 5The image shows the results of unwrapping the phase diagram shown in df. The rows from top to bottom are the unwrapping results of the "peaks" interferogram, the "pyramid" interferogram, and the "mountain scene" interferogram. The columns from left to right are: unwrapped phase, unwrapping error, and unwrapping error histogram.

[0161] Figure 7 Untangling for QGPU algorithm Figure 5 The results of the df interferogram are shown in the figure. The rows from top to bottom are the unwrapping results of the "peaks" interferogram, the "pyramid" interferogram, and the "mountain scene" interferogram; the columns from left to right are the unwrapping phase, the unwrapping error, and the unwrapping error histogram.

[0162] Figure 8 Untangling for the ILS algorithm Figure 5 The results of the df interferogram are shown in the figure. The rows from top to bottom are the unwrapping results of the "peaks" interferogram, the "pyramid" interferogram, and the "mountain scene" interferogram; the columns from left to right are the unwrapping phase, the unwrapping error, and the unwrapping error histogram.

[0163] Figure 9 Untangling the UKFPU algorithm Figure 5 The results of the df interferogram are shown in the figure. The rows from top to bottom are the unwrapping results of the "peaks" interferogram, the "pyramid" interferogram, and the "mountain scene" interferogram; the columns from left to right are the unwrapping phase, the unwrapping error, and the unwrapping error histogram.

[0164] Figure 10 Untangling algorithm in Example 1 Figure 5 The results of the df graph are shown below. The rows from top to bottom are the unwrapped results of the "peaks" interferogram, the "pyramid" interferogram, and the "mountain scene" interferogram. The columns from left to right are: semantic segmentation graph, region segmentation graph, unwrapped phase, unwrapping error, and unwrapping error histogram.

[0165] Table 2 Root Mean Square Error of Each Algorithm

[0166]

[0167]

[0168] Table 3 Running time of each algorithm

[0169]

[0170] Figures 6-9 The left, middle, and right columns represent the untangling algorithms BUT, QGPU, ILS, and UKFPU, respectively. Figure 5The unwrapped phase, unwrapped phase error, and error histogram obtained from the noise entanglement phase diagram shown in df;

[0171] Figure 10 The algorithm for untangling in Embodiment 1 of the present invention Figure 5 The results of the noise-wrapped phase diagram shown in df are as follows: columns 1 and 2 are the semantic segmentation diagram and the region segmentation diagram of the interferogram generated by the algorithm in Example 1, respectively; columns 3 to 5 are the unwrapped phase, unwrapped phase error and error histogram of the algorithm in Example 1, respectively.

[0172] Depend on Figures 6-10 The unwrapping phase errors and error histograms of each algorithm shown intuitively demonstrate that BUT, QGPU, and ILS have relatively large dynamic ranges of unwrapping phase errors; UKFPU and the algorithm of Embodiment 1 of this invention have higher unwrapping accuracy, with their unwrapping phase errors concentrated in the [-1,1] interval, meaning their dynamic range of unwrapping phase errors is much smaller than the aforementioned three algorithms. Table 2 lists the unwrapping phase errors of each algorithm. Figure 5 The root mean square error (RMSE) of the interferograms with different signal-to-noise ratios corresponding to the actual interferometric phases is shown in Table 2 (average of 30 experiments). Table 2 shows that as the interferogram SNR decreases, the unwrapping phase accuracy of BUT, QGPU, and ILS decreases significantly. Meanwhile, UKFPU and the algorithm of Embodiment 1 of this invention obtain relatively robust results from the interferogram phase unwrapping experiments with different SNRs. Their unwrapping phase error increases slowly with decreasing interferogram SNR, and the unwrapping phase error of the algorithm of Embodiment 1 of this invention is significantly smaller than that of the UKFPU method. The running time of the above algorithms depends almost entirely on the size of the interferogram. Table 3 lists the average running time of each algorithm when unwrapping the above interferogram phases. It can be seen that the running time of the algorithm of Embodiment 1 of this invention is slightly longer than that of the BUT and ILS methods, but much shorter than that of the QGPU and UKFPU methods. Therefore, the algorithm of Embodiment 1 of this invention obtains robust results in the above interferogram phase unwrapping experiments while also having acceptable unwrapping efficiency.

[0173] II. Experimental Data

[0174] Figure 11 In the image, 'a' represents the local Enta volcanic interferometry phase map and the BUT unwrapping result. Figure 11 In the middle b, the phase residual point diagram of the interferogram is shown. Figure 11 In the diagram, 'c' represents the unwrapping phase of the BUT method. It can be seen that the BUT method exhibits significant phase inconsistencies in regions with densely packed phase residuals, as well as isolated regions that cannot be unwrapped. (See...) Figure 11 The region within the black rectangle in the unwrapped phase diagram shown in Figure c.

[0175] The untangling results of the QGPU, ILS, and UKFPU methods are shown below. Figure 12 ,in Figure 12The 'ac' values ​​represent the unwrapping phases of the QGPU, ILS, and UKFPU methods, respectively. Figure 12 The df values ​​represent the unwrapping and phase rewinding results for the QGPU, ILS, and UKFPU methods, respectively.

[0176] Figure 13 This is a diagram showing the untangling result of the algorithm in Embodiment 1 of the present invention, wherein... Figure 13 The diagrams in the image above represent the semantic segmentation diagram of the unwrapping algorithm in Embodiment 1 of the present invention, the region segmentation diagram of the unwrapping algorithm in Embodiment 1 of the present invention, the unwrapping phase of the unwrapping algorithm in Embodiment 1 of the present invention, and the rewrapping result of its unwrapping phase. Figure 12 It can be seen that QGPU, ILS, and UKFPU unwrapping phases are continuous, but both QGPU and ILS rewrapping phase maps exhibit significant spiculation noise at the edges of the fringes, which may reduce the reliability of these two algorithms. Meanwhile, Figure 13 The unwrapping phase of the algorithm in this embodiment is continuous and consistent. Its rewound phase pattern fringes are consistent with the original interferogram fringes, and there is almost no obvious phase noise in the rewound phase pattern. This shows that the algorithm has achieved good results in the above-mentioned interferogram phase unwrapping experiment.

[0177] 4. Conclusion

[0178] Compared with some commonly used algorithms, including branch cutting, iterative least squares, quality-guided method and UKFPU, the algorithm of Embodiment 1 of this invention can obtain more robust results and acceptable efficiency in interferogram phase unwrapping experiments, and can effectively handle the interferogram phase unwrapping problem.

Claims

1. A deep learning based center difference information filtering phase unwrapping method, characterized in that It comprises the following steps: A. Constructing a CDIF phase unwrapping recursive model and a deep neural network, wherein the deep neural network is an interferogram semantic segmentation network based on LANET; B. Cropping the interferogram into a plurality of 256*256-sized sub-interferograms in an overlapping cropping manner, leaving a plurality of rows or columns of overlapping pixels between adjacent sub-interferograms, inputting the sub-interferograms into the deep neural network in sequence to obtain a plurality of sub-interferogram semantic segmentation graphs based on interferogram fringe distribution and composed of different integer winding numbers K; then splicing the sub-interferogram semantic segmentation graphs according to the principle that the phase winding numbers of adjacent sub-block overlapping pixels are the same to obtain a semantic segmentation graph of the entire interferogram; C. Merging and optimizing the semantic segmentation regions in the semantic segmentation graph of the entire interferogram to obtain an interferogram region segmentation graph; D. Unwrapping each segmentation region in the interferogram region segmentation graph by using the CDIF phase unwrapping recursive model to obtain unwrapping results of each segmentation region in the interferogram region segmentation graph; E. Merging the unwrapping results of each segmentation region according to the consistency criterion of unwrapping phases of adjacent regions of the interferogram to obtain an unwrapping phase graph of the entire interferogram; In step E, the process of merging the unwrapping results of each segmentation region according to the consistency criterion of unwrapping phases of adjacent regions of the interferogram is as follows: Suppose that any two adjacent segmentation regions are interferogram segmentation region A and interferogram segmentation region B; If the number of pixels of the interferogram segmentation region A is greater than or equal to that of the adjacent segmentation region B, then the interferogram segmentation region B is merged into the adjacent segmentation region A, and the unwrapping phase is calculated as follows: Φ B = Φ B + 2πΔ AB A' = A U B Φ A′ = Φ A ∪ Φ' B where i and j are the image elements in regions A and B, respectively, and i is in the adjacent domain of j; Φ A (i) and Φ B (j) are the unwrapped phases of i and j, respectively; round[x] means rounding x; Φ B is the unwrapped result of region B, Φ B is the corrected unwrapped phase of region B; A' is the region formed by merging regions A and B, Φ A′ is the unwrapped phase of merged region A'. If the number of pixels of the interferogram segmentation region B is greater than or equal to that of the adjacent segmentation region A, then the interferogram segmentation region A is merged into the adjacent segmentation region B, and the unwrapping phase is calculated as follows: Φ A = Φ A + 2πΔ BA B' = B U A Φ B′ = Φ B ∪ Φ A′ Φ A is the unwrapped phase of the region A; Φ B′ is the unwrapped phase of the combined region B'; The merged unwrapping results and the unwrapping results of the next adjacent segmentation region are merged, and all the segmentation region unwrapping results are merged in this way until the unwrapping results of all the segmentation regions are merged, and an unwrapping phase graph of the entire interferogram is obtained.

2. The deep learning-based center difference information filtering phase unwrapping method according to claim 1, wherein In step B, the process of splicing each sub-interferogram semantic segmentation graph according to the principle that the phase winding numbers of adjacent sub-block overlapping pixels are the same is as follows: a. Splicing the previous sub-interferogram semantic segmentation graph with the adjacent sub-interferogram semantic segmentation graph on the right or below, obtaining a difference value by subtracting the overlapping pixels of the previous sub-interferogram semantic segmentation graph from the adjacent sub-interferogram semantic segmentation graph on the right or below, adding or subtracting the difference value from the adjacent sub-interferogram semantic segmentation graph on the right or below so that the phase winding numbers of the overlapping pixels of the two sub-interferogram semantic segmentation graphs are consistent, cropping the overlapping pixel part in the adjacent sub-interferogram semantic segmentation graph on the right or below to obtain an adjusted sub-interferogram semantic segmentation graph on the right or below, and merging the adjusted sub-interferogram semantic segmentation graph on the right or below with the previous sub-interferogram semantic segmentation graph to obtain a spliced sub-interferogram semantic segmentation graph; b. Take the semantic segmentation map of the top-left sub-interferogram as the starting point, and repeat step a in the order of first from left to right, then to the end of the line and turn to the next line, and then from left to right, until all the semantic segmentation maps of the sub-interferograms are spliced into one image to obtain the semantic segmentation map of the whole interferogram.

3. The deep learning-based center difference information filter (CDIF) phase unwrapping method of claim 2, wherein: In step C, the process of merging and optimizing the semantic segmentation regions in the semantic segmentation map of the whole interferogram is: a. Set a segmentation region pixel number threshold, which is 1 / 6 of the total number of pixels in the whole interferogram; b. Assign a serial number to each segmentation region in the semantic segmentation map of the whole interferogram, and mark each segmentation region with the integer phase wrapping number K of the region. Then, in the order of increasing segmentation region serial number K, determine whether the pixel number of each semantic segmentation region is greater than the segmentation region pixel number threshold. If yes, keep the semantic segmentation region unchanged. If no, merge adjacent semantic segmentation regions until the pixel number of the merged semantic segmentation region is greater than the segmentation region pixel number threshold; c. Sort the semantic segmentation regions processed in step b in the order of optimization adjustment to obtain an interferogram region segmentation map.

4. The deep learning-based CDIF phase unwrapping method of claim 1, wherein: In step D, the process of unwrapping using the CDIF phase unwrapping recursive model is: In the order of increasing segmentation region serial number in the interferogram region segmentation map, unwrap each segmentation region in the interferogram region segmentation map using the CDIF phase unwrapping recursive model. When unwrapping each segmentation region, use a path tracking strategy based on heap sorting to perform two-dimensional phase unwrapping along the path from high-quality pixels to low-quality pixels in the region. The CDIF phase unwrapping recursive model is as follows: a. Construct CDIF Sigma points one-step state prediction value for the pixel (m, n) and one-step state prediction error covariance where (a, s) is an unwrapped pixel in the 8-neighborhood of pixel (m, n); ψ is the set of unwrapped pixels in the 8-neighborhood of pixel (m, n); SNR(a, s) is the signal-to-noise ratio of pixel (a, s); and based on the L-dimensional state variable, further generate the following 2L+1 Sigma points: In the formula, h represents the center difference half-step length, and h = 0.5 The corresponding weight value is calculated as follows: b. State prediction calculating a state prediction for the pixel (m, n) and a state prediction error covariance In the formula, Q(m, n) represents a phase gradient estimation error variance; For using Levenberg-Marquardt operator to optimize The optimized state prediction error covariance, wherein u represents an adjustment parameter, and I is a unit matrix; c. State space steering information space, a matrix of prediction information for the pixel (m, n) and a prediction information state vector d. Measurement update Calculating the measurement prediction value for pixel (m, n) and cross-covariance p xz (m, n): Calculate the information matrix distribution I(m, n) and the information state distribution i(m, n) of pixel (m, n): where z(m, n) and e(m, n) represent the observation value and residual error of pixel (m, n), respectively; R(m, n) is the observation noise variance of pixel (m, n); then the information matrix Y(m, n) and the information state vector y(m, n) of pixel (m, n) are calculated as follows: e. Information space steering state space updating the state estimate value of the pixel (m, n) and the state estimation error covariance 5. The deep learning-based CDIF phase unwrapping method of claim 4, wherein: The system equation of the CDIF-based phase unwrapping is: where x(m, n) and z(m, n) represent the state variable and the observation vector of the interferogram (m, n) pixel, respectively; is the phase gradient estimate between the interferogram (m, n) pixel and the (a, s) pixel, and w (m,n)|(a,s) is the interferogram phase gradient estimate error; v(m, n) represents the observation noise vector of the interferogram (m, n) pixel, and v1(m, n) and v2(m, n) are the observation noise of the state variable quadrature component and the in-phase component, respectively.

6. The deep learning-based center difference information filtering phase unwrapping method according to claim 1, wherein: the deep neural network comprises a ResNet50 module, a PAM module, and an AEM module; the sub-interferogram is input into the ResNet50 module, and after compression by the ResNet50 module, high-level feature maps compressed to 1 / 32 and low-level feature maps compressed to 1 / 4 are obtained; the high-level feature maps are processed by the PAM module, and then added and fused with the high-level feature maps to obtain enhanced high-level feature maps; the low-level feature maps are processed by the PAM module, and then added and fused with the low-level feature maps to obtain low-level feature fusion maps; the low-level feature fusion maps and the enhanced high-level feature maps are input into the AEM module, and the output of the AEM module is added and fused with the low-level feature fusion maps to obtain enhanced low-level feature maps; and the enhanced high-level feature maps and the enhanced low-level feature maps are superimposed and fused to obtain sub-interferogram semantic segmentation maps based on interferogram fringe distribution and composed of different integer wrapping numbers K.

7. The deep learning-based center difference information filtering phase unwrapping method according to claim 6, wherein: the ResNet50 module comprises convolution layers, maximum pooling layers, and block1-4 layers connected in sequence; after the sub-interferogram is processed by the convolution layers and adjusted by the maximum pooling layers, the sub-interferogram is compressed to 1 / 4 in the block1 layer to obtain low-level feature maps; the low-level feature maps are input into the block2 layer and the PAM module; after the low-level feature maps are compressed to 1 / 2 in the block2 layer, the low-level feature maps are output to the block3 layer, and then compressed to 1 / 2 in the block3 layer to be output to the block4 layer, and then compressed to 1 / 32 in the block4 layer to obtain high-level feature maps; and the convolution layers are 7x7-16 convolution layers, and the maximum pooling layers are 3x3 maximum pooling layers.

9. The deep learning-based center difference information filtering phase unwrapping method according to claim 6, wherein: the PAM module comprises the following processing process: input features are sequentially subjected to adaptive average pooling, 1x1 convolution, and up-sampling processing, multiplied by trainable weights normalized by a sigmoid function, then multiplied and fused with the input features, and then added and fused with the input features to obtain PAM output features; and the AEM module comprises the following processing process: the enhanced high-level feature maps are subjected to adaptive average pooling, 1x1 convolution, and up-sampling processing, multiplied by trainable weights normalized by a sigmoid function, then multiplied and fused with the low-level feature fusion maps, and then added and fused with the low-level feature fusion maps to obtain AEM output features. ​ ​ ​ ​ ​ 8. The deep learning based central-difference information filtering phase unwrapping method of claim 7, wherein: ​ ​ ​ ​

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