An inertial sensor overrange signal repair and signal quality enhancement system

Abstract

The application discloses an inertial sensor super-range signal repair and signal quality enhancement system, and relates to the technical field of sensors. H→L and generator GAN L→H for conversion between low-cost sensor signals and high-cost sensor signals; an MLE module, configured to inject Laplace energy into signals when converting low-cost sensor signals into high-cost sensor signals, and inject Laplace energy into signals when converting high-cost sensor signals into low-cost sensor signals; and an OTS module, configured to construct an optimal mapping between features of low-cost and high-cost sensor signals based on optimal transport theory. L→H H→L The application significantly improves the reconstruction accuracy and quality of low-cost accelerometer signals through multi-level detail enhancement.​

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of sensors, in particular to an inertial sensor super-range signal repair and signal quality enhancement system. BACKGROUND

[0002] Low-cost accelerometers have become key components in modern industries, medical and intelligent devices, etc. due to their affordability and wide application. However, these sensors are often limited by precision and measurement range, making it difficult to provide accurate signals in high dynamic environments, which may lead to data loss or measurement errors in some critical applications. Therefore, improving the signal quality of low-cost accelerometers and expanding their measurement range have significant practical value. Although traditional hardware upgrade methods can improve sensor performance to some extent, their high cost limits their promotion in large-scale applications. On the other hand, as an advanced generative model, generative adversarial network (GAN) can convert low-quality input into high-quality output by learning the distribution characteristics of data, providing an economical and efficient way for low-cost accelerometer signal enhancement.

[0003] However, due to the lack of frame-by-frame paired data between low-cost and high-cost sensor signals, traditional GAN architecture and fully supervised training methods are not applicable in this case. SUMMARY

[0004] The purpose of the application is to provide an inertial sensor super-range signal repair and signal quality enhancement system, which can significantly improve the reconstruction accuracy and quality of low-cost accelerometer signals through multi-level detail enhancement.

[0005] To achieve the above purpose, the application provides the following solutions:

[0006] In a first aspect, the application provides an inertial sensor super-range signal repair and signal quality enhancement system, comprising: a generator GAN L→H , a generator GAN H→L , an OTS module, an MLE module and a signal acquisition module.

[0007] The signal acquisition module is configured to acquire high-cost sensor signals and low-cost sensor signals; the correlation between the low-cost sensor signals and the high-cost sensor signals is unpaired or weakly paired;

[0008] The generator GAN H→L is configured to convert high-cost sensor signals into low-cost sensor signals.

[0009] The generator GAN L→H is configured to convert low-cost sensor signals into high-cost sensor signals.

[0010] the MLE module is configured to inject Laplacian energy into the low-cost sensor signal when converting the low-cost sensor signal into the high-cost sensor signal, and inject Laplacian energy into the high-cost sensor signal when converting the high-cost sensor signal into the low-cost sensor signal. L→H the MLE module is configured to inject Laplacian energy into the low-cost sensor signal when converting the low-cost sensor signal into the high-cost sensor signal, and inject Laplacian energy into the high-cost sensor signal when converting the high-cost sensor signal into the low-cost sensor signal. H→L the MLE module is configured to inject Laplacian energy into the low-cost sensor signal when converting the low-cost sensor signal into the high-cost sensor signal, and inject Laplacian energy into the high-cost sensor signal when converting the high-cost sensor signal into the low-cost sensor signal.

[0011] the OTS module is configured to mine potential correlations between unpaired and weakly paired data based on optimal transport theory, and construct an optimal mapping between features of the low-cost sensor signal and features of the high-cost sensor signal according to the potential correlations.

[0012] According to the specific embodiments provided in the present application, the following technical effects are disclosed:

[0013] The present application provides an inertial sensor ultra-range signal repair and signal quality enhancement system, wherein the generator GAN L→H , the generator GAN H→L , the OTS module, the MLE module and the signal acquisition module constitute the system; the signal acquisition module is responsible for collecting high-cost sensor signals and low-cost sensor signals; the generator GAN H→L is used to convert the high-cost sensor signals into low-cost sensor signals; the generator GAN L→H is responsible for converting the low-cost sensor signals into high-cost sensor signals; the function of the MLE module is to inject modulated Laplacian energy into the low-cost sensor signals during the conversion process of the generator GAN L→H , and inject modulated Laplacian energy into the high-cost sensor signals during the conversion process of the generator GAN H→L ; the OTS module establishes an optimal mapping relationship between the features of the low-cost sensor signals and the features of the high-cost sensor signals according to the optimal transport theory. The present application can effectively enhance the signal quality of the low-cost inertial sensor without relying on frame-by-frame paired data. BRIEF DESCRIPTION OF DRAWINGS

[0014] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0015] Figure 1 A schematic diagram of a HEROS-GAN framework is provided for an embodiment of the present application.

[0016] Figure 2 A schematic diagram of optimal transmission supervision is provided for an embodiment of the present application, where (a) is element-wise supervision and (b) is optimal transmission supervision.

[0017] Figure 3 A schematic diagram of modulated Laplacian energy (MLE) is provided for an embodiment of the present application. DETAILED DESCRIPTION

[0018] The technical solutions in the embodiments of the present application will be apparently and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0019] In order to make the above objectives, characteristics and advantages of the present application more apparent, comprehensible and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0020] Embodiment One

[0021] The present embodiment provides an inertial sensor over-range signal repair and signal quality enhancement system, comprising: a generator GAN L→H , a generator GAN H→L , an OTS module, an MLE module and a signal acquisition module.

[0022] The signal acquisition module is configured to acquire high-cost sensor signals and low-cost sensor signals; the correlation between the low-cost sensor signals and the high-cost sensor signals is unpaired or weakly paired.

[0023] The generator GAN H→L is configured to convert the high-cost sensor signals into the low-cost sensor signals.

[0024] The generator GAN L→H is configured to convert the low-cost sensor signals into the high-cost sensor signals.

[0025] The MLE module is configured to: inject Laplacian energy into the low-cost sensor signals when the generator GAN L→H converts the low-cost sensor signals into the high-cost sensor signals, and inject Laplacian energy into the high-cost sensor signals when the generator GAN H→LThe Laplace energy is injected into the high-cost sensor signal when converting the high-cost sensor signal into the low-cost sensor signal; the Laplace energy is a Laplace energy of a neural network; and the Laplace energy is used to adjust the Laplace energy of the model in the generative deep learning architecture.

[0026] The OTS module is configured to mine potential correlations between unpaired and weakly paired data based on the optimal transport theory, and construct an optimal mapping between the features of the low-cost sensor signal and the features of the high-cost sensor signal according to the potential correlations.

[0027] In some embodiments, the overall architecture of the HEROS-GAN is as shown in Figure 1 The HEROS-GAN mainly includes two generators. The generator GAN L→H is responsible for converting the low-cost sensor signal into the high-cost sensor signal, while the generator GAN H→L is responsible for mapping the high-cost sensor signal back to the low-cost sensor signal. The design inspiration of this bidirectional generative architecture comes from CycleGAN, but unlike the traditional CycleGAN, the HEROS-GAN introduces OTS and MLE modules in the generation and supervision process to enhance the learning ability and generation effect of the model.

[0028] In some embodiments, the high-cost sensor signal obtained by the signal acquisition module is an unpaired data signal in an inertial sensor, and the low-cost sensor signal obtained by the signal acquisition module is an unpaired data signal in an inertial sensor.

[0029] In some embodiments, the OTS module includes a transport cost sub-module, a feature alignment sub-module, and an optimal mapping calculation sub-module.

[0030] The transport cost sub-module is configured to calculate the transport cost between the features of the low-cost sensor signal and the features of the high-cost sensor signal; and the transport cost is determined according to the similarity between the features of the low-cost sensor signal and the features of the high-cost sensor signal.

[0031] The feature alignment sub-module is configured to align the features of the low-cost sensor signal and the features of the high-cost sensor signal.

[0032] The optimal mapping calculation sub-module is configured to determine the optimal mapping of the features of the low-cost sensor signal to the features of the high-cost sensor signal according to the minimum transport cost when the features of the low-cost sensor signal and the features of the high-cost sensor signal are aligned.

[0033] Specifically, the OTS module is to extract as much supervision information as possible from unpaired data and feed it back to the generator. Specifically, the OTS module finds the optimal mapping between low-cost sensor signal features and high-cost sensor signal features through optimal transport theory to minimize the difference between the two. The introduction of this module effectively solves the lack of supervision problem in unpaired data and provides the generator with more abundant training signals. The MLE module enhances the local details of the generated signal by calculating the Laplace energy of the features and performing appropriate energy modulation. This module is particularly important in high dynamic signal generation, as it can ensure that the generator does not introduce too much noise when capturing subtle changes in the signal, thereby generating signals that are physically consistent and rich in detail.

[0034] Specifically, the core idea of the OTS mechanism is to construct an optimal mapping between low-cost sensor signal features and high-cost sensor signal features through optimal transport theory, thereby maximizing the supervision information in unpaired data. Let the feature representation of the low-cost sensor signal be and the feature representation of the high-cost sensor signal be At this time, the goal of the optimal transport problem is to find an optimal mapping to align the feature distribution of the low-cost sensor signal with the feature distribution of the high-cost sensor signal, so as to minimize the "transport cost" between the two feature distributions, as shown in Figure 2 This problem can be formalized as the following optimization problem:

[0035]

[0036] where Γ(F L ,F H ) represents the set of all joint distributions of the features F L of the low-cost sensor signal and the features F H of the high-cost sensor signal, and c(f Li ,f Hj ) is a cost function defined between features f Li and f Hj . To ensure the reasonableness of the optimal mapping, the calculation formula of the transport cost in the transport cost submodule in the embodiment is:

[0037]

[0038] where f Li is the feature of the low-cost sensor signal in the i-th dimension, f Hj is the feature of the high-cost sensor signal in the j-th dimension, and c(f Li ,f Hj ) is the transport cost.

[0039] The design of this transportation cost function takes into account the effect of the inner product (i.e. similarity) between features: the more similar the features, the lower the cost, thus guiding the optimal mapping to favor aligning similar features.

[0040] Due to the computational complexity of the optimal transport problem, the Sinkhorn algorithm is used to approximate the solution of the above optimization problem. By introducing entropy regularization, the Sinkhorn algorithm can obtain a relatively optimal approximate solution within a reasonable computation time. Through the Sinkhorn algorithm, the embodiment can obtain an optimal mapping T: X→Y from the features of the low-cost sensor signal to the features of the high-cost sensor signal. This mapping allows the embodiment to identify and align the most similar features in the feature space of the generative model, thereby providing effective supervision information for the unpaired data. Based on this mapping, the embodiment defines an OTS loss function to impose appropriate supervision and encourage the features of the low-cost sensor signal to align with certain features of the high-cost sensor signal.

[0041] Specifically, the feature alignment submodule has a specific supervision mechanism imposed; the OTS loss function after imposing the specific supervision mechanism specifically includes:

[0042]

[0043] where P L and P H represent the domain distribution of the low-cost sensor signal and the high-cost sensor signal respectively, F H (x H ) is the feature of the high-cost sensor signal, F L (x L ) is the feature of the low-cost sensor signal, is, is the virtual high-cost signal feature generated by the generator G L after the low-cost signal x L→H , which is compared with the real high-cost signal feature F H (x H ), and the potential consistency constraint between the two is established by means of the optimal transport mapping T. is the virtual low-cost signal feature generated by the generator G H after the high-cost signal x H→L , which is compared with the real low-cost signal feature F L (x L ), and the potential consistency constraint between the two is established by means of the optimal transport inverse mapping T -1 .

[0044] by minimizing The generated model is guided to generate low-cost sensor signal features that are as aligned as possible with high-cost sensor signal features, thereby achieving enhancement of the signal.

[0045] To ensure the effectiveness of the OTS mechanism, this embodiment provides a strict mathematical proof of the existence of optimal mapping and demonstrates its convergence in the training process. In addition, this embodiment also finds that in the traditional GAN architecture, the conflict between the generator and the discriminator often leads to oscillation and instability of gradient updates, while the OTS mechanism effectively reduces the oscillation in the training process by fine control of the feature space of the generated signal, ensuring that the generator optimizes to the optimal solution more stably. These properties of the OTS mechanism enable it to effectively improve the quality of the generated signal even in the case of unpaired data, and play a key role in low-cost accelerometer signal enhancement.

[0046] In some embodiments, in the task of low-cost accelerometer signal enhancement, in addition to the limitation of signal range, the lack of signal details is also a problem that needs to be solved. Low-cost sensors usually have low sensitivity and are difficult to capture subtle signal changes, resulting in generated signals that are relatively smooth and lack necessary details. This phenomenon is particularly evident in high-dynamic environments, directly affecting the reliability and application performance of the signal.

[0047] Although traditional generative adversarial networks (GANs) perform well in generating signals, they often struggle to generate signals that contain rich details. This is because GAN-generated signals tend to be globally smooth, ignoring local subtle changes. To address this issue, this embodiment proposes an "energy modulation Laplacian regularization" (MLE) mechanism that aims to enhance the details of the generated signal by regulating the local energy of the signal features, thereby improving the overall quality of the signal, as shown in Figure 3 .

[0048] The core of the MLE mechanism is to use the Laplacian operator to measure the local changes in the feature layer and enhance these changes through appropriate energy modulation. The Laplacian operator is a second-order differential operator that can effectively capture subtle changes and local fluctuations in the signal. Specifically, given a feature h (n) (represented as the nth layer feature in the network, with dimension d), this embodiment designs a Laplacian energy of neural network features The calculation formula of the Laplacian energy in the MLE module is:

[0049]

[0050] where, is the second-order derivative of the feature in the ith dimension; d is the dimension, n is the layer number; h(n) denotes the n-th layer feature in the i-th dimension; is the Laplacian energy. is defined as:

[0051]

[0052] denotes the n-th layer feature in the i-th dimension; denotes the n-th layer feature in the i+1-th dimension; denotes the n-th layer feature in the i-1-th dimension.

[0053] The higher the Laplacian energy, the stronger the volatility and the more significant local changes of the feature; and the lower the Laplacian energy, the smoother and the less changes of the feature. Therefore, by regulating the Laplacian energy, the generation network can enhance the local details of the signal when necessary, and maintain the smoothness of the signal when unnecessary.

[0054] In some embodiments, the present application further comprises an energy modulation module for modulating the Laplacian energy based on an energy modulation regularization term.

[0055] Specifically, in order to reasonably regulate the Laplacian energy, the present embodiment designs an energy modulation regularization term R MLE for dynamically adjusting the Laplacian energy of the feature layer in the generation process, so as to avoid excessive energy leading to excessive signal noise, or low energy leading to loss of signal details.

[0056] The formula expression of the energy modulation regularization term in the energy modulation module is:

[0057] R MLE = -log(E Laplace )-κ·log(1-E Laplace ).

[0058] Wherein, σ is a Sigmoid function for normalizing the Laplacian energy to the interval (0, 1), and κ is a modulation parameter. The modulation formula of the modulation parameter κ is specifically:

[0059]

[0060] In the formula, d is the dimension, n is the layer number; h (n) denotes the n-th layer feature in the i-th dimension, is the mean value of h ,

[0061] The embodiment designs kurtosis of the feature as κ, to measure the volatility of the feature. The κ parameter determines the minimum value position of the regularization term and the injection degree of Laplacian energy. Specifically, when the volatility of the feature is strong (κ is large), less energy injection is needed, and the minimum value of R MLE will be located at a lower Laplacian energy value; on the contrary, when the volatility of the feature is weak (κ is small), more energy injection is needed, and the minimum value of R MLE will be located at a higher Laplacian energy value. This adaptive behavior ensures that the MLE mechanism can dynamically adjust the energy injection according to the volatility of the feature, so as to both enhance signal details in a high dynamic environment and reduce noise in a stable state.

[0062] In constructing the MLE mechanism, the embodiment pays special attention to the mathematical properties of its regularization term. First, R MLE tends to infinity when E Laplace is close to 0 or 1, thereby imposing a strong penalty on extremely low or high Laplacian energy, ensuring that the Laplacian energy remains within a moderate range. Second, the modulation parameter κ controls how much energy is injected, so that less energy is injected when the feature volatility is strong, and more energy is injected when the feature volatility is weak. This adaptive energy modulation mechanism enables the generated signal to exhibit sufficient local details without introducing additional noise due to excessive energy injection. By minimizing R MLE , the generation network can effectively improve the local detail performance of the signal while maintaining the overall smoothness of the signal, thereby generating a more accurate and realistic signal. This mechanism plays a crucial role in low-cost accelerometer signal enhancement, effectively addressing the shortcomings of traditional generative adversarial networks in signal detail enhancement.

[0063] In actual experiments, the embodiment verifies the effectiveness of the MLE mechanism through multiple data sets and evaluation indicators. The experimental results show that the HEROS-GAN model applying the MLE mechanism not only significantly outperforms other methods in signal details, but also exhibits high reliability in signal physical consistency. These experimental results prove the effectiveness of the MLE mechanism in low-cost accelerometer signal enhancement and further establish the leading position of HEROS-GAN in this field.

[0064] In summary, the present application has the following technical effects:

[0065] 1) This application proposes an innovative "Optimal Transport Supervision" (OTS) mechanism to address the signal enhancement problem of low-cost inertial sensor signals in unpaired data scenarios. OTS utilizes optimal transport theory to construct an optimal mapping between low-cost and high-cost sensor signal features, maximizing the potential supervision information in unpaired data. Specifically, the OTS module guides the generator to achieve the best alignment of signal features in the feature space by calculating the transport cost between features. This mechanism effectively overcomes the challenge of insufficient supervision in traditional GAN architectures in unpaired data scenarios, significantly improving the learning ability and signal enhancement effect of the generated model.

[0066] 2) The "Modulated Laplacian Energy" (MLE) mechanism in this application is a novel feature layer energy regulation method aimed at enhancing the local detail performance of generated signals. MLE calculates the Laplacian energy of the neural network feature layer to capture subtle changes in the signal, and dynamically adjusts the energy input by combining the volatility of the features (such as kurtosis). This adaptive adjustment mechanism not only effectively enhances signal details in high dynamic environments, but also avoids noise introduction caused by excessive adjustment. MLE ensures the reasonableness and stability of the Laplacian energy through rigorous mathematical derivation, further improving the physical consistency and realism of the generated signal.

[0067] 3) This application proposes a bidirectional generation architecture (HEROS-GAN) that combines OTS and MLE mechanisms. This architecture achieves bidirectional mapping between low-cost and high-cost sensor signals through the collaborative work of two generators (G L→H and G H→L ). Unlike traditional CycleGAN, HEROS-GAN introduces OTS modules to enhance the supervision information of unpaired data during the generation process, and utilizes MLE modules to optimize the local details of the generated signal. This bidirectional architecture design not only ensures the global consistency of the generated signal, but also significantly improves the reconstruction accuracy and quality of low-cost accelerometer signals through multi-level detail enhancement.

[0068] 4) The HEROS-GAN architecture proposed in this application first combines the optimal transport theory with OTS and MLE mechanisms, innovatively solving the problems of insufficient supervision information and missing details in traditional GAN models for low-cost sensor signal enhancement. This solution maximizes the potential supervision information through the OTS mechanism and achieves precise energy regulation in the feature layer through the MLE mechanism, ensuring the consistency and accuracy of the generated signal in global and local details. The uniqueness of this solution lies in its ability to effectively enhance the signal quality of low-cost inertial sensors without relying on frame-by-frame paired data, providing an economical and efficient solution for a wide range of industrial, medical, and intelligent device applications.

[0069] 5) The application first realizes the reconstruction of the inertial sensor over-range signal.

[0070] The technical features of the above embodiments can be combined in any manner. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described, however, as long as the combinations of the technical features do not exist contradictions, they should be considered as the scope of the present disclosure.

[0071] The principles and implementation modes of the present application are described by using specific examples herein, and the above embodiments are only used to help understand the method and core idea of the present application; meanwhile, for those skilled in the art, the specific implementation modes and application ranges will be changed according to the idea of the present application. In conclusion, the content of the present description should not be understood as a limitation of the present application.

Claims

1. An inertial sensor overrange signal repair and signal quality enhancement system, characterized by, The method comprises the following steps: Generator GAN L→H , Generator GAN H→L , OTS module, MLE module, and signal acquisition module The signal acquisition module is configured to acquire high-cost sensor signals and low-cost sensor signals; the correlation between the low-cost sensor signals and the high-cost sensor signals is unpaired or weakly paired; The generator GAN H→L for converting high-cost sensor signals into low-cost sensor signals; The generator GAN L→H for converting low-cost sensor signals into high-cost sensor signals; The MLE module is configured to inject Laplacian energy into the low-cost sensor signal when converting the low-cost sensor signal into the high-cost sensor signal, and to inject Laplacian energy into the high-cost sensor signal when converting the high-cost sensor signal into the low-cost sensor signal. L→H The MLE module is configured to inject Laplacian energy into the low-cost sensor signal when converting the low-cost sensor signal into the high-cost sensor signal, and to inject Laplacian energy into the high-cost sensor signal when converting the high-cost sensor signal into the low-cost sensor signal. H→L The MLE module is configured to inject Laplacian energy into the low-cost sensor signal when converting the low-cost sensor signal into the high-cost sensor signal, and to inject Laplacian energy into the high-cost sensor signal when converting the high-cost sensor signal into the low-cost sensor signal. The OTS module is configured to mine potential correlation between unpaired or weakly paired data based on optimal transport theory, and construct optimal mapping between features of the low-cost sensor signals and features of the high-cost sensor signals according to the potential correlation.

2. An inertial sensor overrange signal recovery and signal quality enhancement system according to claim 1, wherein, The calculation formula of the Laplace energy in the MLE module is: wherein, is a feature Second-order derivative in the i-th dimension; d is the dimension, n is the number of layers; h (n) is represented as the n-th layer feature in the network; is the Laplacian energy.

3. An inertial sensor overrange signal recovery and signal quality enhancement system according to claim 1, wherein, The energy modulation module is further configured to modulate the Laplace energy based on an energy modulation regularization term.

4. An inertial sensor overrange signal recovery and signal quality enhancement system according to claim 3, wherein, The formula expression of the energy modulation regularization term in the energy modulation module is: R MLE = -log(E Laplace ) - κ · log(l - E Laplace ); wherein, σ is a sigmoid function for normalizing the Laplacian energy to the interval (0, 1), and k is a modulation parameter.

5. An inertial sensor overrange signal recovery and signal quality enhancement system according to claim 4, wherein, The modulation formula of the modulation parameter κ is specifically: where d is the dimensionality, n is the number of layers; h (n) denotes the n-th layer feature in the network, is the mean.

6. An inertial sensor overrange signal recovery and signal quality enhancement system according to claim 1, wherein, The OTS module comprises a transport cost submodule, a feature alignment submodule and an optimal mapping calculation submodule; The transport cost submodule is configured to calculate the transport cost between features of the low-cost sensor signals and features of the high-cost sensor signals; the transport cost is determined according to the similarity between the features of the low-cost sensor signals and the features of the high-cost sensor signals; The feature alignment submodule is configured to align the features of the low-cost sensor signals and the features of the high-cost sensor signals; The optimal mapping calculation submodule is configured to determine the optimal mapping from the features of the low-cost sensor signals to the features of the high-cost sensor signals according to the minimum transport cost in the state of alignment between the features of the low-cost sensor signals and the features of the high-cost sensor signals.

7. An inertial sensor overrange signal recovery and signal quality enhancement system according to claim 6, wherein, The calculation formula of the transport cost in the transport cost submodule is: where f Li is a feature of the low-cost sensor signal in the i-th dimension, f Hj is a feature of the high-cost sensor signal in the j-th dimension, c(f Li ,f Hj ) is the transportation cost.

8. An inertial sensor overrange signal recovery and signal quality enhancement system according to claim 7, wherein, The feature alignment submodule is subjected to a specific supervision mechanism; the OTS loss function after the specific supervision mechanism is applied specifically comprises: where P L and P H denote the domain distribution of low-cost sensor signals and high-cost sensor signals, respectively, F H (x H ) is a feature of the high-cost sensor signal, F L (x L ) is a feature of the low-cost sensor signal, is a virtual high-cost signal feature generated from the low-cost signal x L by a generator G L→H , is a virtual low-cost signal feature generated from the high-cost signal x H by a generator G H→L , and T is an optimal transport mapping.

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