Ultra-narrow pulse radar target attitude-insensitive feature extraction and cross-attitude recognition method

Abstract

The application discloses a kind of extremely narrow pulse radar target attitude insensitivity feature extraction and cross-attitude identification method, the method is first based on the automatic extraction of target category feature and attitude feature of depth network;Then successively the obtained feature is input into two modules of classification and decoupling, classification module is used to constrain the correctness of the above two types of features corresponding semantics respectively;Decoupling module is used to constrain the above two types of features semantics irrelevant, and no information loss occurs in the decorrelation process;Finally, based on category feature, target recognition is completed, the method of the application can be for the extremely narrow pulse echo sample under the attitude that does not appear in training set, with good recognition performance.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar target recognition, and particularly relates to a method for extracting attitude-insensitive features of an extremely narrow pulse radar target and cross-attitude recognition. BACKGROUND

[0002] An extremely narrow pulse radar refers to a type of radar whose single echo pulse width is much smaller than the size of a target after processing. For an extremely narrow pulse radar, the echo of a target contains multiple extremely narrow pulses, which correspond to different scattering points on the target. Therefore, the extremely narrow pulse echo of a target can represent the distribution of the scattering points on the target along the radar line-of-sight direction, and is usually referred to as the high resolution range profile (HRRP) of the target.

[0003] The extremely narrow pulse radar echo can reflect the radial position relationship between the scattering centers of a target, and embodies the partial structural features of the target, which is an important approach to radar target recognition. Compared with synthetic aperture radar imaging (SAR) and inverse synthetic aperture radar imaging (ISAR), the extremely narrow pulse echo is easier to obtain and process, and has important research value in the field of radar target recognition (RTR).

[0004] However, the extremely narrow pulse echo has serious attitude sensitivity. The attitude sensitivity refers to the fact that the echo data changes constantly as the target changes its relative angle to the radar line-of-sight. Therefore, the attitude sensitivity will cause the echo pattern of the same target under different attitudes to change significantly, thereby affecting the recognition performance. In actual applications, due to the huge resource consumption of collecting echo data under all attitudes, and more importantly, it is difficult to collect data of non-cooperative targets, the samples to be recognized are usually the echo samples of the target under an attitude that has not appeared in the training set. The problem of cross-attitude recognition of the extremely narrow pulse radar target seriously restricts the application performance of various recognition methods.

[0005] In view of the attitude sensitivity problem existing in cross-attitude recognition, the main solution at present is to manually extract attitude-insensitive features of the target. However, this method not only requires a large amount of expert knowledge, but also has a strong correlation between the features and the target, and the adaptability of the features to different application scenarios is poor. In addition, in many scenarios, the target class information and the attitude information are seriously coupled, and it is difficult to extract attitude-insensitive features in most cases only by relying on manual methods. SUMMARY

[0006] Therefore, the application provides a method for extracting attitude-insensitive features of an extremely narrow pulse radar target and cross-attitude recognition, which can have good recognition performance for the extremely narrow pulse echo samples under an attitude that has not appeared in the training set.

[0007] The technical solutions of the present application are as follows:

[0008] The method for extracting the attitude-insensitive feature of an ultra-narrow pulse radar target and cross-attitude recognition comprises the following steps:

[0009] Step 1: An ultra-narrow pulse echo data set is constructed, and the data is preprocessed; the data set comprises a full-attitude learning set and a training set and a test set in a cross-attitude recognition scenario, the full-attitude learning set is constructed by computer electromagnetic simulation or radar turntable measurement, and is used for supervised recognition algorithm learning and has feature extraction and decoupling capabilities; the training set and the test set in the cross-attitude recognition scenario are used for test verification;

[0010] Step 2: A feature extraction module is constructed, the feature extraction module comprises a deep feature extraction network and a cross-decomposition part, and is used for extracting the category feature and the attitude feature of the target;

[0011] Step 3: A classification module and a classification loss function are constructed, the classification module specifically comprises a category classifier and an attitude classifier, the classification loss function comprises a category classification loss and an attitude classification loss, and is used for constraining the correctness of the category feature and the attitude feature corresponding to the semantics;

[0012] Step 4: A decoupling module and a decoupling loss function are constructed, the decoupling module comprises a feature decorrelation part and a reconstruction self-supervision part, the decoupling loss function comprises a decorrelation loss and a reconstruction loss, and is used for constraining the semantics of the category feature and the attitude feature to be irrelevant to each other, so that the category feature becomes an attitude-insensitive feature, and no information loss occurs in the decorrelation process; from this, the construction of the multi-module ultra-narrow pulse radar target attitude-insensitive feature extraction and cross-attitude recognition network model is completed;

[0013] Step 5: The multi-module ultra-narrow pulse radar target attitude-insensitive feature extraction and cross-attitude recognition network model is trained and parameter updated by using the full-attitude learning set and the training set; specifically, a cross-iteration training mode and a gradient descent optimization algorithm are adopted;

[0014] Step 6: The test set is subjected to category determination through the network model after training, and the recognition of the ultra-narrow pulse radar echo target in the cross-attitude recognition scenario is completed.

[0015] Further, the deep feature extraction network is constructed based on a classical deep neural network in the recognition field.

[0016] Further, step four specifically comprises:

[0017] 401: A feature decorrelation part and a decorrelation loss are constructed, the feature decorrelation part is composed of a discriminator D, and the correlation between the category feature and the attitude feature is reduced in the idea of feature confrontation, so as to achieve the decoupling effect of the features;

[0018] The decoupling effect of two features is constrained based on mutual information theory; for the class feature F T , pose feature F A obtained by the feature extraction module from the extremely narrow pulse echo data x(n) T should not contain the information in F A , and vice versa; the mutual information of the two is denoted as L MI , then L MI should be as small as possible; the formula of L MI is as follows, where H(·) represents the amount of information:

[0019] L MI = H(F T ) + H(F A ) - H(F T , F A )

[0020] The above formula is described by JS divergence, so:

[0021]

[0022] wherein, is the mutual information of F T and F A , is the joint distribution of F T and F A , is the independent distribution of F T and F A , is the difference between the joint distribution and the independent distribution ;

[0023] To achieve the above purpose, the discriminator D needs to be trained to have the ability to distinguish the samples sampled from F as false samples, and the samples sampled from F as true samples; the way to sample from F is to directly concatenate the features F A , F T obtained by the decoupling network from each sample x(n) in each batch; and the way to sample from F is to adjust the order of multiple F A in each batch by Shuffer, while F T maintains its order in the original batch unchanged, and on this basis, F T is concatenated with the Shuffer-adjusted F AThe concatenation is also performed through a concat layer; the original distribution of the two types of features obtained by the feature extraction module is The decoupling module aims to make the distribution Gradually close In this way, the two features are not related and independent, and the purpose of full decoupling is achieved.

[0024] The adversarial loss L adv is denoted as:

[0025]

[0026] wherein, denotes the mean value of the output of the discriminator D obtained by inputting the samples sampled from the independent distribution to the discriminator D, denotes the mean value of the output of the discriminator D obtained by inputting the samples sampled from the joint distribution to the discriminator D.

[0027] 402, construct a reconstruction self-supervision part and a reconstruction loss

[0028] The category feature and the posture feature are input into the reconstruction self-supervision part, and the sum of the two is input into the deconvolution network G to reconstruct the original extremely narrow pulse echo data. The deconvolution network and the network structure of the initial mixed feature part in the feature self-extraction module are symmetrical, mainly composed of five deconvolution layers. This structure will be helpful to restore the generated input extremely narrow pulse echo sample.

[0029] The L2 self-supervision loss between the original extremely narrow pulse echo data x(n) and the generated extremely narrow pulse echo data x(n)' is denoted as:

[0030] L resc =MSE(x(n)'-x(n))

[0031] The L2 loss function is also called mean square error, denoted as MSE(·).

[0032] Beneficial effects:

[0033] Compared with the prior art, the method has the following advantages:

[0034] (1) The application proposes a target posture-insensitive category feature extraction method based on a deep neural network model, which avoids the complex and tedious process of traditional posture-insensitive artificial feature search based on expert knowledge, and improves the feature extraction efficiency and target cross-posture recognition performance.

[0035] (2) The application proposes a decoupling module for class feature and posture feature decorrelation. The module realizes mutual irrelevance of the above two types of feature semantics through decorrelation loss, and realizes loss of information in the decorrelation process through reconstruction loss, so as to achieve the purpose of full decoupling of class and posture information, and make the class feature a posture-insensitive feature.

[0036] (3) The multi-module extremely narrow pulse radar target posture-insensitive feature extraction and cross-posture recognition network model proposed in the application utilizes the characteristics of deep neural network "end-to-end" learning, has the advantages of simple development, no restriction of application scene and target type, and the realized cross-posture target recognition capability can greatly improve the practical application performance of radar target recognition.

[0037] Therefore, the application has high popularization and application value in the field of extremely narrow pulse radar echo target recognition. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 The figure is a multi-module extremely narrow pulse radar target posture-insensitive feature extraction and cross-posture recognition model block diagram.

[0039] Figure 2 The figure is a feature extraction module schematic diagram.

[0040] Figure 3 The figure is a classification module schematic diagram.

[0041] Figure 4 The figure is a decoupling module schematic diagram.

[0042] Figure 5 The figure is an experimental data set division situation schematic diagram.

[0043] Figure 6 The figure is a confusion matrix schematic diagram. DETAILED DESCRIPTION

[0044] The application will be described in detail below in combination with the drawings and examples.

[0045] The application provides a new idea for extremely narrow pulse echo cross-posture recognition, such as Figure 1As shown, the model of the application includes three modules: a feature extraction module, a classification module, and a decoupling module. The feature extraction module is used to automatically extract category features and posture features; the classification module is used to constrain the correctness of the semantic meaning corresponding to the category features and the posture features; the decoupling module is used to constrain the correlation between the category features and the posture features, so that the two are irrelevant and achieve decoupling effect; on the other hand, it is used to constrain the information loss brought by the decoupling decorrelation process, thereby avoiding the problem of performance degradation caused by the reduction of information amount. The above idea is used to achieve the purpose of separating the category features and the posture features in the extremely narrow pulse echo data, so that the category features extracted by the model of the application can be better applied to the cross-posture recognition scene.

[0046] The application specifically includes the following steps:

[0047] Step 1: Construct an extremely narrow pulse echo data set and complete preprocessing of the data. The data set specifically includes a full posture learning set and a training set and a test set under a cross-posture recognition scene. The full posture learning set can be constructed by computer electromagnetic simulation or radar turntable measurement, and is used to supervise the learning of the recognition algorithm and has feature extraction and decoupling capabilities; the training set and the test set under the cross-posture recognition scene are used to verify the effectiveness of the application.

[0048] 101, Obtain θ s ~ θ e The extremely narrow pulse echo data of the C-class targets within the posture range and the corresponding category labels and posture labels.

[0049] 102, Take L-class target echo data from the C-class targets as a full posture learning set, and the remaining (C-L) class target data is used to construct a training set and a test set under a cross-posture recognition scene. The specific method is as follows: for the (C-L) class targets, within the posture range θ s ~ θ e Extract part of the posture data as a training set, and the remaining posture data as a test set.

[0050] 103, Align all the data to alleviate the translation sensitivity.

[0051] 104, Perform amplitude normalization processing on all the data to avoid amplitude sensitivity. Let x(n) be a certain frame of original echo data, and its amplitude normalization is represented as:

[0052]

[0053] 105, At the same time, in order to ensure that the input of the deep network has the same length, a certain length of N extremely narrow pulse echo data is intercepted as input, where N=200 points.

[0054] Step 2: Construct a feature extraction module, such asFigure 2 As shown, the feature extraction module includes a deep feature extraction network and a cross-decomposition part, aiming to extract the class feature and the pose feature of the target. The deep feature extraction network can be constructed based on the classic deep neural network in the recognition field, and the present application adopts VGG-11 network.

[0055] VGG-11 contains eight convolutional layers for extracting features of different levels of input data. The present application takes the features after the fifth convolutional layer as the initial mixed features, which are coupled with the interference of the pose feature and affect the recognition performance. The feature is further abstracted and separated from the pose feature through the remaining three convolutional layers of VGG-11, denoted as F A , and the initial mixed feature is adaptively pooled to match the size of the pose feature, constructing a cross-decomposition model, and taking the difference between the two as the target class feature, denoted as F T .

[0056] Step 3: constructing a classification module and a classification loss function, as shown in Figure 3 The classification module specifically includes a class classifier and a pose classifier, and the classification loss function includes a class classification loss and a pose classification loss. The purpose is to constrain the correctness of the semantic meaning corresponding to the class feature and the pose feature.

[0057] 301. Constructing a classification module

[0058] The classification module includes two classifiers, a class classifier C T and a pose classifier C A , which are used to constrain the correctness of the semantic meaning corresponding to the class feature and the pose feature, respectively. Both classifiers are stacked by fully connected layers and softmax classification layers, and the class and pose determination results are denoted as C T (F T ) and C A (F A ), respectively.

[0059] 302. Constructing a class and pose classification loss

[0060] The cross-entropy (Cross-Entropy) loss function is the most commonly used loss function in the classification task, also known as the softmax loss function, denoted as CE(·). Assuming that the training set of narrow pulse echo samples x(n) (n = 1, 2,..., N, where N is the total number of samples) has a real class label y T (n) and a real pose label y A (n), then the class classification loss L TCE and the pose classification loss L ACE are as follows:

[0061] LTCE = CE(C T (F T ), y T )

[0062] L ACE = CE(C A (F A ), y A )

[0063] Step 4: constructing a decoupling module and a decoupling loss function, as shown in the following formula, the decoupling module includes feature decorrelation and reconstruction self-supervision two parts, and the decoupling loss function includes decorrelation loss and reconstruction loss two parts. The purpose is to constrain the semantic independence of the category feature and the pose feature, so that the category feature becomes a pose-insensitive feature, and no information loss occurs in the decorrelation process. Figure 4

[0064] 401, constructing a feature decorrelation part and a decorrelation loss, the feature decorrelation part is mainly composed of a discriminator D, and the correlation between the category feature and the pose feature is reduced by the idea of feature confrontation, so as to achieve the decoupling effect of the feature.

[0065] The application constrains the decoupling effect of the two features based on the mutual information theory. For the category feature F T and the pose feature F A obtained by the feature extraction module from the extremely narrow pulse echo data x(n), the information in F T should not be contained in F A , and vice versa. The mutual information of the two is denoted as L MI , and L MI should be as small as possible. L MI is as follows, wherein H(·) represents the information amount:

[0066] L MI = H(F T ) + H(F A ) - H(F T , F A )

[0067] The above formula can be described by JS divergence, and there is:

[0068]

[0069] To achieve the above purpose, the discriminator D needs to be trained to have the ability to distinguish the samples sampled from F as false samples, and the samples sampled from F as true samples. The sample acquisition method of F is: directly passing each sample x(n) in each batch through the decoupling network to obtain the feature F​A F T This can be achieved by concatenating layers; and sampling is... The sample acquisition method is as follows: multiple F samples obtained in each batch A The order should be adjusted, that is, it should be allowed to proceed. Figure 4 The Shuffer operation in F, and F T Keeping their order in the original batch unchanged, and on this basis, F T With Shuffer adjusted F A Similarly, the concatenation can be performed using a concat layer. The original distributions of the two types of features obtained from the feature extraction module are as follows: The decoupling module aims to enable distributed... Approaching This method achieves the goal of making the two features unrelated and independent, thus fully decoupling them.

[0070] The countermeasure loss is denoted as:

[0071]

[0072] 402. Constructing the self-supervised reconstruction component and the reconstruction loss.

[0073] To reduce the information loss caused by the decoupling and decorrelation process, a self-supervised reconstruction component is constructed, which enables the original data to be recovered based on category features and pose features. This reduces the information loss caused by the decoupling process.

[0074] The specific implementation method is as follows: Category features and pose features are input into the self-supervised reconstruction part. The two are then summed and reconstructed using a deconvolutional network G to reconstruct the original extremely narrow pulse echo data. The deconvolutional network maintains symmetry with the network structure of the initial mixed feature part obtained in the feature extraction module, and mainly consists of five deconvolutional layers. This structural setting is beneficial for reconstructing the generated input extremely narrow pulse echo samples.

[0075] The sample generated based on the original data x(n) is denoted as x(n)'. The two are constrained by L2 loss. The L2 loss function is also called the mean squared error, denoted as MSE(·), which reflects the square of the difference between the generated sample and the real input sample.

[0076] The L2 self-supervised loss between the original extremely narrow pulse echo data x(n) and the generated extremely narrow pulse echo data x(n)' is denoted as:

[0077] L resc =MSE(x(n)'-x(n))

[0078] Step 5: The invented cross-pose target recognition network model of the extremely narrow pulse radar echo is trained and the parameters are updated based on the full-pose learning set and the training set. Specifically, a cross-iteration training method and a gradient descent optimization algorithm are adopted.

[0079] 501, The feature extraction module and the decoupling module are jointly trained.

[0080] The loss function used is:

[0081]

[0082] wherein φ represents the parameters of the feature extraction module, and ρ and respectively represent the parameters of the discriminator D and the deconvolution network G in the decoupling module.

[0083] 502, The classification module is trained alone.

[0084] The loss function used is:

[0085]

[0086] wherein w1 and w2 respectively represent the parameters of the class classifier C T and the pose classifier C A in the classification module.

[0087] 503, The gradient descent method is used to update the weights. The steps 501 and 502 are repeated until the network converges.

[0088] Step 6: The test set is subjected to the class determination by the trained multi-module extremely narrow pulse radar target pose-insensitive feature extraction and cross-pose recognition network model, and the recognition task of the extremely narrow pulse radar echo target in the cross-pose recognition scene is completed.

[0089] 601, The preprocessed test sample is input into the trained feature extraction module as shown in Figure 2 , to obtain the class features of the test sample.

[0090] 602, The above class features are input into the trained classification module as shown in Figure 3 , to obtain the class determination result of the test sample, and complete the recognition task of the extremely narrow pulse radar echo target in the cross-pose recognition scene.

[0091] Embodiment

[0092] This embodiment is based on the CVdomes simulation data set publicly disclosed by the U.S. Air Force Laboratory, and the effect of the present application is illustrated by the cross-pose recognition performance within a range of 90°.

[0093] CVdomes contains 10 types of civilian vehicle targets, which are Honda Civic 4dr, Mitsubishi, Toyota Tacoma, Camry, Jeep 93, Jeep 99, Maxima, Mazda MPV, Sentra and Toyota Avalon, which are numbered 0-9 respectively. The first three targets: Honda Civic 4dr, Mitsubishi and Toyota Tacoma are in the cross-pose identification scene. Some pose echo samples are extracted as the training set, and the remaining pose samples are used as the test set. The remaining 7 types of targets containing all poses are the full-pose learning set, which is used to learn the decoupled representation of class features and pose features. The experimental index will focus on the improvement effect of the recognition accuracy of the first three types of targets.

[0094] Two groups of experiments are designed to correspond to two cross-pose identification scenes. As shown in Figure 5 The 0-90° pose range is evenly divided into 9 intervals. For experiment group 1: 6 pose intervals are extracted as the training set, and the remaining 3 pose intervals are used as the test set, so the missing rate of the training set in the 0-90° pose interval is: 3 / 9=33%; for experiment group 2: 3 pose intervals are extracted as the training set, and the remaining 6 pose intervals are used as the test set, so the pose missing rate of the training set is: 6 / 9=67%. The specific sample size is shown in Table 1.

[0095] Table 1 dataset setting

[0096]

[0097] The hyperparameter setting is shown in Table 2:

[0098] Table 2 network hyperparameter setting

[0099]

[0100] The recognition effect of the present application and the classic model VGG11 in the deep network under the cross-pose condition is shown in Table 3:

[0101] Table 3 performance improvement effect

[0102]

[0103] From Table 3 and Figure 6It can be seen from the confusion matrix that when the proportion of missing poses in the training set is 33%, the three-classification accuracy is only 48.89%, while under the model of the present application, the three-classification accuracy can reach 72.22%; when the missing pose situation of the training set is worse, the missing proportion reaches 67%, and the three-classification accuracy can still be improved from 41.3% to 54.6%. It can be seen that the present application can well decouple the class features and the pose features, greatly reduce the adverse effects of pose sensitivity on the recognition performance, so as to obviously improve the recognition accuracy of the test samples under the poses that do not appear in the training data.

[0104] To sum up, the above is only a preferred embodiment of the present application, not for limiting the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for extracting pose-insensitive features of a radar target of very narrow pulses and cross-pose recognition, characterized in that, The method comprises the following steps: Step 1, constructing an ultra-narrow pulse echo dataset and preprocessing the data; The dataset comprises a full-pose learning set and a training set and a test set in a cross-pose recognition scenario, the full-pose learning set is constructed by computer electromagnetic simulation or radar turntable measurement, is used for supervised recognition algorithm learning and has feature extraction and decoupling capabilities; the training set and the test set in the cross-pose recognition scenario are used for test verification; Step 2, constructing a feature extraction module, the feature extraction module comprises a deep feature extraction network and a cross-decomposition part, and is used for extracting category features and pose features of a target; Step 3, constructing a classification module and a classification loss function, the classification module specifically comprises a category classifier and a pose classifier, the classification loss function comprises a category classification loss and a pose classification loss, and is used for restricting the correctness of the category features and the pose features corresponding to the semantics; Step 4, constructing a decoupling module and a decoupling loss function, the decoupling module comprises a feature decorrelation part and a reconstruction self-supervision part, the decoupling loss function comprises a decorrelation loss and a reconstruction loss; the decoupling module is used for restricting the semantic independence of the category features and the pose features, so that the category features become pose-insensitive features, and no information loss occurs in the decorrelation process; from this, the construction of the multi-module ultra-narrow pulse radar target pose-insensitive feature extraction and cross-pose recognition network model is completed; Step 5, training and parameter updating of the multi-module ultra-narrow pulse radar target pose-insensitive feature extraction and cross-pose recognition network model are performed by using the full-pose learning set and the training set; specifically, a cross-iteration training mode and a gradient descent optimization algorithm are adopted; Step 6, performing category determination on the test set by using the network model after training, and completing the recognition of the ultra-narrow pulse radar echo target in the cross-pose recognition scenario.

2. The method of claim 1, wherein the method comprises: The deep feature extraction network is constructed based on a classical deep neural network in the recognition field.

3. The method of claim 1, wherein the method comprises: Step four specifically comprises: 401, constructing a feature decorrelation part and a decorrelation loss, the feature decorrelation part is composed of a discriminator D, and the correlation between the category features and the pose features is reduced in the thought of feature confrontation, so that the decoupling effect of the features is achieved; The decoupling effect of the two features is constrained based on mutual information theory; for extremely narrow pulse echo data x(n), the category feature F obtained by the feature extraction module is... T Posture characteristics F A F T F should not be included. A The information in one part is the same as the information in the other part; let the mutual information between the two be denoted as L. MI Then L should be made as much as possible MI Very small; L MI The formula is as follows, where H(·) represents the amount of information: L MI = H(F T ) + H(F A ) - H(F T , F A ) The above formula is described by JS divergence, and there is: wherein, is F T the mutual information, A is F T the joint distribution, A is F T the independent distribution, A is the difference between the joint distribution and the independent distribution ;​​​ To achieve the above purpose, the discriminator D needs to be trained to have the ability to distinguish the samples sampled from as false samples, and the samples sampled from as true samples; the samples sampled from are obtained by directly concatenating the features F A , F T obtained by the decoupling network for each sample x(n) in each batch; and the samples sampled from are obtained by adjusting the order of the multiple F A obtained for each batch by Shuffer, while F T maintains the order in the original batch unchanged, and then concatenating F T and the Shuffer-adjusted F A by the concat layer; the original distributions of the two types of features obtained by the feature extraction module are The decoupling module aims to gradually approach to in this way, so that the two features are not related and independent of each other, and are fully decoupled. Adversarial loss L adv Noted: wherein, denotes the mean of the outputs of discriminator D for samples sampled from the joint distribution denotes the mean of the outputs of discriminator D for samples sampled from the joint distribution denotes the mean of the outputs of discriminator D for samples sampled from the joint distribution​ 402, constructing a reconstruction self-supervision part and a reconstruction loss The category features and the pose features are input into the reconstruction self-supervision part, the sum of the two is input into a deconvolution network G to reconstruct the original ultra-narrow pulse echo data, the deconvolution network and the network structure of the initial mixed feature part in the feature self-extraction module are kept symmetrical, and mainly comprise five deconvolution layers, and this kind of structure setting will be conducive to restoring the generated input ultra-narrow pulse echo sample; The L2 self-supervision loss between the original ultra-narrow pulse echo data x(n) and the generated ultra-narrow pulse echo data x(n)' is denoted as: L resc = MSE(x(n)' - x(n)) The L2 loss function is also called mean square error, denoted as MSE(·).

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