Terahertz wave dispersion compensation method based on physical constraint sparse deconvolution network

Abstract

A terahertz wave dispersion compensation method based on a physical constraint sparse deconvolution network relates to the technical field of terahertz nondestructive testing and comprises the following steps: preparing single-layer and multi-layer composite material samples and acquiring terahertz reference signals and dispersion terahertz signals; establishing a signal propagation model considering the terahertz wave dispersion effect; constructing a sparse deconvolution network to realize mapping of dispersion signals and flight time; introducing a progressive curriculum weighted loss function and an amplitude-position joint error evaluation index; and establishing a terahertz wave dispersion compensation model to realize accurate compensation of dispersion signals. According to the method, the sparse deconvolution network is constructed and combined with the progressive course weighting loss function, so that the problems that a traditional method depends on prior information, the anti-noise capability is poor and the calculation is complicated are solved; the method has the advantages that dispersion compensation precision is improved, dependence on prior information of a sample structure is reduced, manual parameter adjustment is reduced, a ringing effect is suppressed, and anti-noise capability is enhanced.

Description

Technical Field

[0001] This invention relates to the field of terahertz nondestructive testing technology, and more specifically, to a terahertz wave dispersion compensation method based on physically constrained sparse deconvolution networks. Background Technology

[0002] Terahertz time-domain spectroscopy (THz-TDS), as a "sensing window" in the non-ionizing electromagnetic spectrum, has shown irreplaceable advantages in recent years in fields such as aerospace composite material inspection, biomedical imaging, and semiconductor packaging defect analysis. On the one hand, terahertz waves occupy a unique position in the electromagnetic spectrum, located between microwaves and infrared waves, with a frequency range typically from 100 GHz to 10 THz. This spectral position endows terahertz waves with the penetrating power of microwaves and the non-destructive nature of infrared light, overcoming the ionization hazards of X-rays and the contact measurement limitations of ultrasound. On the other hand, its sub-picosecond temporal resolution can achieve micrometer-level spatial resolution, providing a promising detection method for the non-destructive testing of internal defects in complex structures.

[0003] However, in reflection-mode terahertz time-domain spectroscopy systems, signal overlap and distortion caused by dispersion effects have long limited breakthroughs in detection accuracy. When terahertz waves propagate through multilayer media, different frequency components experience group velocity mismatch due to changes in frequency-dependent characteristics such as dielectric constant and propagation constant. This leads to waveform broadening, amplitude attenuation, and phase distortion in the echo signal, fundamentally limiting the accuracy of time-of-flight estimation, and consequently affecting the accuracy of material thickness and defect detection. Dispersion phenomena are particularly pronounced in multilayer heterogeneous composite materials (such as honeycomb sandwich structures), where the complex frequency dependence makes it difficult to accurately model using traditional dispersion models.

[0004] To address these challenges, deconvolution techniques based on physical models have been proposed. For example, wavelet transform combined with frequency-domain deconvolution can filter noise and construct an inverse model of the transfer function to solve the overlap and multiple reflection problems of terahertz signals. However, this requires prior knowledge of the structure of the sample under test, manual setting of hyperparameters, and its performance is affected by the "ringing effect." Furthermore, sparse representation methods have been used for terahertz signal dispersion compensation. These methods mainly utilize the sparsity of the impulse response, constructing an overcomplete dictionary to reduce model dependence while achieving time-of-flight estimation. However, in actual measurements, signal noise severely undermines the sparsity assumption, leading to erroneous detection of false peaks. Moreover, the solution process requires multiple iterations, resulting in high computational complexity, which is insufficient for processing large volumes of terahertz signals. Summary of the Invention

[0005] The purpose of this invention is to solve the problem of signal distortion and overlap caused by the terahertz dispersion effect mentioned in the background art, which limits the accuracy of terahertz detection. Based on the shortcomings of traditional methods, a terahertz wave dispersion compensation method based on physically constrained sparse deconvolution networks is proposed.

[0006] The technical solution adopted by this invention to solve its technical problem is: A terahertz wave dispersion compensation method based on physically constrained sparse deconvolutional networks includes the following steps: S1. Prepare single-layer composite laminates and multi-layer composite laminates respectively, and obtain terahertz reference signals and dispersive terahertz signals of different samples through a reflective terahertz time-domain spectroscopy system. S2. Analyze the propagation characteristics of terahertz waves in the medium under test, and establish a signal propagation model that considers the dispersion effect of terahertz waves. S3. Based on the constructed terahertz signal propagation model, a sparse deconvolution network is built using the powerful feature extraction capability of the convolutional autoencoder to obtain the mapping relationship between the dispersive signal and the time of flight. S4. Introduce a progressively weighted loss function and an amplitude-position joint error evaluation index to improve the learning ability of deconvolutional networks for sparse time-of-flight data; S5. By combining the time-of-flight estimation results output by the deconvolution network with the terahertz reference signal, a terahertz wave dispersion compensation model is established to achieve accurate compensation for the dispersion signal.

[0007] Furthermore, in step S1, the reflective terahertz time-domain spectroscopy system includes a femtosecond laser, a terahertz transmitter, a terahertz receiver, an optical delay line, and a motion platform, with an effective frequency range of 10 GHz to 4.5 THz.

[0008] Furthermore, the single-layer composite material laminate is a glass fiber reinforced plastic laminate of different thicknesses, with a transverse dimension of 50 mm × 50 mm and thicknesses of 0.1 mm, 0.2 mm, 0.4 mm, 0.6 mm, 0.8 mm, and 1.0 mm, respectively, and a refractive index of 2.24.

[0009] Furthermore, the multilayer composite laminate has a three-layer sandwich structure with a transverse dimension of 100 mm × 100 mm. The top and bottom layers are 0.5 mm thick glass fiber reinforced polymers, and the middle layer is filled with 1 mm thick extruded polystyrene foam board with a density of 32 kg / m³. 3 The refractive index is calibrated to 1.05.

[0010] Furthermore, in step S2, the signal propagation model includes the following formula: In a reflective terahertz time-domain spectroscopy system, the measured echo signal can be regarded as a linear superposition of the terahertz signals reflected by each reflector interface. The terahertz echo signal model considering additive noise is as follows:

[0011] in, It is the total number of reflectors. It is the first The terahertz signal reflected by the reflector The weight parameters, It is additive noise from the system.

[0012] The signal propagation model considering the terahertz wave dispersion effect is as follows:

[0013] in, It is the time-domain variation of the terahertz reference signal caused by dispersion. It is a sparse impulse response related to the reflector. It is additive noise from the system. It is a dispersive terahertz echo signal.

[0014] Furthermore, the sparse deconvolutional network adopts a convolutional autoencoder architecture, including encoder and decoder modules. The encoder extracts the features of the input signal step by step through multiple convolution operations, and the decoder maps the features back to the input space through transpose convolution operations, thereby realizing the automatic mining of the mapping relationship between input and output from the data.

[0015] Furthermore, the encoder uses three convolutional blocks, each including a convolutional layer, batch normalization, ReLU activation function, and max pooling layer; the decoder uses three deconvolutional blocks, each including a transposed convolutional layer, batch normalization, and ReLU activation function, and a dropout layer is added between the encoder and decoder to prevent overfitting.

[0016] Furthermore, in step S4, the progressive course weighted loss function includes the following steps: S41. Divide the sparse pulse sequence into a pulse region and a background region; S42. Apply the L1 loss function to the pulse region and the MSE loss function to the background region. S43. Introduce a dynamic weighting factor to adjust the loss weights of the pulse region and the background region according to the number of iterations. In the initial stage, set a lower pulse weight and a higher background weight. In the middle transition stage, the pulse weight increases linearly and the background weight decreases linearly. In the later stage, the pulse weight reaches its maximum value and the background weight decreases to its minimum value.

[0017] Furthermore, the amplitude-position joint error evaluation index is:

[0018] in, It is the actual pulse position. It is the predicted pulse position. It is the actual pulse amplitude. It is the predicted pulse amplitude. This is the maximum allowed position offset. It refers to the dynamic range of the signal amplitude. These are the weighting coefficients for amplitude and position. This is the actual total number of pulses. It represents the number of pulses matched by the network.

[0019] Furthermore, in step S5, the method for establishing the dispersion compensation model is to convolve the sparse pulse sequence (time-of-flight) output by the network with the terahertz reference signal to recover the terahertz compensation signal, specifically described as follows:

[0020] in, Terahertz reference signal The sparse pulse sequence output by the network. This is a terahertz compensation signal.

[0021] Compared with the prior art, the beneficial effects of the present invention are: by constructing a sparse deconvolution network and combining it with an asymptotic course weighted loss function, the present invention solves the problems of traditional methods relying on prior information, poor noise resistance and computational complexity. It has the advantages of improving dispersion compensation accuracy, reducing dependence on prior information of sample structure, reducing manual parameter adjustment, suppressing ringing effect, enhancing noise resistance and reducing computational complexity. Attached Figure Description

[0022] Figure 1 This is the overall flowchart of the present invention; Figure 2 This is a schematic diagram of the reflective terahertz time-domain spectroscopy system of the present invention; Figure 3 These are sample images of single-layer glass fiber reinforced plastic laminates of different thicknesses according to the present invention. Figure 4 The dispersion compensation results of single-layer glass fiber reinforced plastic laminates of different thicknesses according to the present invention; Figure 5 This is a sample diagram of the three-layer sandwich composite panel of the present invention; Figure 6 The dispersion compensation result of the three-layer sandwich composite plate of the present invention; Figure 7 This is a schematic diagram of the sparse deconvolutional network architecture of the present invention; Figure 8 This is the dispersion compensation strategy of the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. The present invention will be further described with reference to the accompanying drawings and embodiments: In existing technologies, terahertz time-domain spectroscopy is widely used in materials detection due to its non-ionizing properties and high resolution. However, the dispersion effect in the reflection mode has long caused signal overlap and distortion problems. Traditional methods rely on wavelet transform combined with frequency domain deconvolution or sparse representation techniques. The former requires manual setting of hyperparameters and is susceptible to ringing effects, while the latter is sensitive to noise and has high computational complexity. When detecting multilayer heterogeneous composite materials, the group velocity mismatch caused by dispersion leads to waveform broadening and phase distortion, which severely limits the accuracy of time-of-flight estimation. To address the aforementioned issues and overcome the shortcomings of traditional methods, such as reliance on prior knowledge and insufficient noise resistance, this paper proposes combining physical propagation models with deep learning. By analyzing the propagation characteristics of terahertz waves in a medium, it is found that the dispersion effect can be modeled as a convolution process between a reference signal and a sparse impulse response. Based on this, a method is proposed that uses a convolutional autoencoder to automatically extract dispersive signal features and enhances the sparse impulse learning capability through a dynamic loss function, thereby avoiding manual intervention and improving noise robustness.

[0024] like Figures 1-8 As shown, the terahertz wave dispersion compensation method based on physically constrained sparse deconvolutional networks includes the following steps: S1. Prepare single-layer composite laminates and multi-layer composite laminates respectively, and obtain terahertz reference signals and dispersive terahertz signals of different samples through a reflective terahertz time-domain spectroscopy system. S2. Analyze the propagation characteristics of terahertz waves in the medium under test, and establish a signal propagation model that considers the dispersion effect of terahertz waves. S3. Based on the constructed terahertz signal propagation model, a sparse deconvolution network is built using the powerful feature extraction capability of the convolutional autoencoder to obtain the mapping relationship between the dispersive signal and the time of flight. S4. Introduce a progressively weighted loss function and an amplitude-position joint error evaluation index to improve the learning ability of deconvolutional networks for sparse time-of-flight data; S5. By combining the time-of-flight estimation results output by the deconvolution network with the terahertz reference signal, a terahertz wave dispersion compensation model is established to achieve accurate compensation for the dispersion signal.

[0025] Through the above technical solutions, this application effectively solves the problems of signal overlap and waveform distortion caused by dispersion effects, significantly improving the accuracy of time-of-flight estimation. By automatically extracting features and optimizing dynamic loss, it reduces noise interference in sparse pulse detection, achieving accurate separation of reflection signals from multilayer composite material interfaces. Combining physical model constraints with deep learning improves the reliability of dispersion compensation results while ensuring computational efficiency.

[0026] In at least one embodiment, in step S1, the reflective terahertz time-domain spectroscopy system includes a femtosecond laser, a terahertz transmitter, a terahertz receiver, an optical delay line, and a motion platform, with an effective frequency range of 10 GHz to 4.5 THz. Figure 2 The diagram illustrates its basic structure. A femtosecond laser generates a terahertz signal, which is split into a pump pulse and a probe pulse by a beam splitter. The pump pulse enters the terahertz generator to produce short-wave terahertz pulses, which are reflected off the sample and then enter the terahertz wave receiver. Adjusting the optical delay line ensures that the pump pulse and probe pulse arrive at the terahertz wave receiver simultaneously, while a moving platform obtains terahertz signals from different sampling points within the sample.

[0027] In this context, a femtosecond laser is a light source capable of generating ultrashort pulse lasers. Specifically, it can use a titanium sapphire crystal as the gain medium and employ mode-locking technology to achieve stable pulse widths in the femtosecond range, providing a precise time reference for terahertz wave excitation. A terahertz emitter is a device that converts femtosecond laser light into terahertz radiation. Specifically, it can use a photoconductive antenna or a nonlinear optical crystal to generate broadband terahertz pulses through photogenerated carrier acceleration or optical rectification. A terahertz receiver is a detection device that converts terahertz signals into electrical signals. Specifically, it can use electro-optic sampling or a photoconductive antenna, utilizing the coherent interaction between the probe laser and the terahertz wave to achieve time-domain waveform measurement. An optical delay line is a mechanical device that adjusts the time delay between the pump light and the probe light. Specifically, it can use a linear translation stage with a mirror assembly, achieving sub-femtosecond time resolution by changing the optical path length. A motion platform is a positioning device that carries the sample and performs spatial scanning. Specifically, it can use a stepper motor-driven three-dimensional translation stage, achieving millimeter-level precision sample area coverage through programmed control.

[0028] The specific steps are as follows: First, a terahertz wave (1 THz frequency) is emitted onto the polished metal, and a reference terahertz signal is obtained after reflection. Then, the sample is placed on the metal plate, and the terahertz echo signal at a single sampling point is obtained after reflection from the sample. Finally, the terahertz echo signals at all sampling points are obtained by moving the motion platform. The received terahertz echo signal has a length of 2048 ohms and a sampling period of 0.02 ps.

[0029] Furthermore, in step S1, the single-layer composite material laminate is a glass fiber reinforced plastic laminate of varying thicknesses. The glass fiber reinforced plastic laminate refers to a composite material laminate structure prepared using glass fiber as the reinforcing material and thermosetting resin as the matrix. Specifically, it can be achieved using a molding process. Its uniform dielectric properties can reduce non-uniform scattering interference during signal propagation. The terahertz echo signal of the single-layer composite material laminate is obtained using a terahertz time-domain spectroscopy system.

[0030] like Figure 3 The image shows sample images of single-layer glass fiber reinforced plastic laminates of different thicknesses prepared according to the present invention. All laminates have a transverse dimension of 50 mm × 50 mm and thicknesses of 0.1 mm, 0.2 mm, 0.4 mm, 0.6 mm, 0.8 mm, and 1.0 mm, respectively, with a refractive index of 2.24. 3000 terahertz dispersion signals were obtained by randomly selecting 3000 sampling points from the single-layer laminates of different thicknesses. 2400 of these dispersion signals were selected as the training set for the convolutional autoencoder, and 600 dispersion signals were selected as the test set. The dispersion compensation signal was obtained by convolving the output of the neural network with the reference signal.

[0031] like Figure 4 As shown, the dispersion compensation results for single-layer glass fiber reinforced plastic laminates of different thicknesses are illustrated. Due to multiple reflections of terahertz waves at the material's upper and lower interfaces, wave packets overlap, increasing the difficulty of reconstructing sparse pulse sequences from the terahertz dispersive signal and even misleading the accurate thickness of the interface. Furthermore, as the thickness of the single-layer plate increases, the dispersion effect of the echo signal intensifies, leading to significant amplitude attenuation and signal elongation, hindering accurate time-of-flight positioning. As can be seen from the right-hand figure, the predicted time of flight corresponds closely to the actual time of flight. Dispersion compensation of the terahertz echo signal effectively suppresses the dispersion effect and solves the wave packet overlap problem caused by multiple reflections, improving the accuracy of the dispersion compensation results.

[0032] Furthermore, in step S1, the multilayer composite laminate is a three-layer sandwich structure. The three-layer sandwich structure refers to a composite laminate composed of two upper and lower layers of high-refractive-index material and a middle layer of low-refractive-index material. Specifically, it can be achieved using glass fiber reinforced polymer as the outer layer and extruded polystyrene foam as the middle layer, optimizing the reflection and transmission paths of terahertz waves through the differences in the electromagnetic properties of the different materials. The extruded polystyrene foam filling refers to the middle layer being a lightweight material with a closed-cell structure, specifically a material with a density of 32 kg / m³. 3 The extrusion process was used to form the sheet material, and its low refractive index characteristic reduced the propagation loss of terahertz waves in the intermediate layer. Terahertz echo signals of multilayer composite laminates were obtained using a terahertz time-domain spectroscopy system.

[0033] like Figure 5 The image shows a sample of the three-layer sandwich composite panel prepared according to the present invention. The transverse dimensions are 100 mm × 100 mm. The top and bottom layers are made of glass fiber reinforced polymer with a thickness of 0.5 mm and a refractive index of 2.24. The middle layer is filled with 1 mm thick extruded polystyrene foam board with a density of 32 kg / m³. 3 The refractive index is 1.05. Similar to a single-layer laminate, 3000 sampling points were randomly selected to obtain 3000 terahertz dispersion signals. 2400 of these dispersion signals were used as the training set in the input convolutional autoencoder, and 600 dispersion signals were used as the test set. The dispersion compensation signal was obtained by convolving the neural network output with the reference signal.

[0034] like Figure 6 As shown, the dispersion compensation results for the three-layer sandwich composite panel are displayed. From Figure 6 As can be observed in (a), due to the strong wave transmission characteristics of extruded polystyrene foam board, the amplitude attenuation of the second and third wave packets is not significant. However, the terahertz echo signals reflected from the top and bottom surfaces of the outer layer of the glass fiber reinforced plastic laminate exhibit severe dispersion. Furthermore, multiple reflections of the signal, along with noise, increase the difficulty of feature extraction. During the propagation of the terahertz wave from the glass fiber reinforced plastic laminate to the extruded polystyrene foam board, the refractive index at the material interface decreases sharply (while the refractive index at other interfaces increases). Compared to other interfaces, this manifests as a phase reversal, resulting in a negative amplitude value for the time of flight at this location. Moreover, the energy of the dispersive terahertz signal is mainly concentrated in the first and fourth wave packets. This phenomenon is caused by the high terahertz wave reflectivity of the top and bottom surfaces of the three-layer structure. Compensation signals are as follows: Figure 6As shown in (b), even for complex multilayer structures, the network still has a strong ability to extract the hidden time-of-flight in dispersive signals, where all dispersive wave packets are effectively compensated. Compared with dispersive signals, the compensated signals have better smoothness and eliminate interference from multiple reflections and noise.

[0035] In at least one embodiment, in step S2, in the reflective terahertz time-domain spectroscopy system, the measured echo signal can be considered as a linear superposition of the terahertz signals reflected by each reflector interface. Considering the presence of additive noise in reality, the terahertz echo signal can be modeled as: (1) in, It is the total number of reflectors. It is the first The terahertz signal reflected by the reflector The weight parameters, It is additive noise from the system.

[0036] Furthermore, the terahertz echo signal can be viewed as the convolution of the emitted terahertz reference signal and the system response. Assuming the terahertz detection process is a linear time-invariant system, i.e., without considering the dispersion effect of the terahertz wave, the above formula (1) can be described as: (2) in, It transmits a terahertz reference signal. It is the system response related to the reflector of the sample under test, corresponding to the time-of-flight (ToF) information of the sample. It is additive noise from the system.

[0037] Based on the Fourier transform, equation (2) can be expressed in the frequency domain as: (3) in, They are respectively Fourier transform.

[0038] In actual measurement processes, due to factors such as material electromagnetic parameters (e.g., plasma frequency, resonant frequency), signal bandwidth, propagation distance, and waveguide characteristics, terahertz waves produce wave velocity differences for different frequency components, leading to signal distortion or broadening. In this case, considering the dispersion effect of terahertz waves, the terahertz echo signal in formula (3) can be updated as follows: (4) in, The system's frequency domain response is caused by the dispersive medium. Let be the propagation constant. It is the transmission distance. This can be viewed as a frequency domain variation of the terahertz reference signal caused by dispersion. It is a dispersive terahertz echo frequency domain signal.

[0039] Based on the inverse Fourier transform, formula (4) is expressed in the time domain as: (5) in, It is the time-domain variation of the terahertz reference signal caused by dispersion. It is a sparse impulse response related to the reflector. It is additive noise from the system. It is a dispersive terahertz echo signal.

[0040] Comparing formulas (2) and (5), the sparse impulse response is accurately extracted during terahertz detection. The time-of-flight information of the signal is crucial for improving the accuracy of terahertz detection.

[0041] In at least one embodiment, in step S3, the sparse deconvolutional network adopts a convolutional autoencoder architecture, including an encoder and a decoder module. The encoder extracts the features of the input signal step by step through multiple convolution operations, and the decoder maps the features back to the input space through transpose convolution operations, thereby realizing the automatic mining of the mapping relationship between input and output from the data.

[0042] Furthermore, to solve for the sparse impulse response in equation (5), a sparse deconvolution network for sparse impulse prediction was constructed based on the terahertz signal propagation model, such as... Figure 7 As shown, this network employs a convolutional autoencoder architecture, comprising encoder and decoder modules. The network input is a dispersive terahertz signal, and the output is a sparse impulse response. Time-of-flight information can be extracted from the sparse impulse response for thickness estimation. In this process, due to the sparsity of the impulse response sequence, its effective time-of-flight information is typically concentrated in local regions. The sparse deconvolutional network uses convolution operations instead of traditional fully connected layers, and through a sliding window local perception mechanism, it can efficiently capture key local features in sparse data. This local perception mechanism makes the convolutional autoencoder more sensitive to local patterns in the signal. Simultaneously, the deep convolutional structure in the encoder progressively extracts high-order features through multi-level abstraction. Lower-level networks filter sparse noise, and higher-level networks integrate contextual information to map the input data to a low-dimensional latent space representation. Furthermore, the decoder uses a transposed convolution operation to map the high-order features of the latent space representation back to the input space, automatically mining the input-output mapping relationship from the data. This structure not only reduces the number of model parameters and the risk of overfitting but also better adapts to the complexity and diversity of signals.

[0043] Furthermore, the encoder uses three convolutional blocks, each including a convolutional layer, batch normalization, ReLU activation function, and max pooling layer; the decoder uses three deconvolutional blocks, each including a transposed convolutional layer, batch normalization, and ReLU activation function, and a dropout layer is added between the encoder and decoder to prevent overfitting.

[0044] The scheme is refined by normalizing the acquired dispersive terahertz signals to ensure their amplitude range is between [0,1], thereby improving the training efficiency and stability of the model. Simultaneously, the corresponding time-of-flight labels are also normalized to allow learning on the same scale as the dispersive signals. Initially, the encoder extracts features from the input signal progressively through multiple convolutional operations. First, a convolutional block is defined: convolutional layers are used to extract features from the input signal, with a kernel size of 5 and padding of 2. After convolution, batch normalization (BN) and ReLU activation functions are applied to accelerate training and introduce non-linearity. This process is repeated twice, followed by a max pooling layer to further extract higher-level features. The above operations can be described as follows: (6) (7) in, Represents the input to the convolutional block. This represents the weights and biases of the first convolutional layer. This represents the weights and biases of the second convolutional layer. It is a batch normalization function. It is a non-linear activation ReLU function. It is a max pooling operation. This represents the entire convolutional block operation. The encoder uses three convolutional blocks to first extract local features, then gradually increases the number of channels to extract deeper global features. Therefore, the output feature signal of the input dispersive terahertz signal after encoder processing can be described as: (8) Represents the output characteristic signal of the encoder. Representing the Sub-convolution block operation.

[0045] Furthermore, after obtaining the output feature signal from the encoder, the reconstructed sparse impulse response can be obtained through the decoder. The goal of the decoder is to progressively restore the spatial dimension of the original signal from the features extracted by the encoder. To prevent overfitting, a dropout layer is added between the encoder and decoder. In the decoder part, a deconvolution block is defined: a transposed convolution operation is used to upsample the feature input, replacing the first convolution layer in the encoder convolution block, while removing max pooling; the rest remains consistent with the encoder convolution block. As the network upsamples, the number of channels gradually decreases, eventually restoring to the same number of channels as the input signal. The deconvolution block can be represented as: (9) (10) in The input signal representing the deconvolution block. This represents the weights and biases of the first deconvolution layer. This represents the weights and biases of the second convolutional layer. It is batch normalization. It is a non-linear activation ReLU function. This represents the deconvolution block operation. Similar to the encoder structure, three deconvolution blocks are first used for decompression. At the end of the decoder, a fully connected layer is added to map the decoded features to the final output space, i.e., the time-of-flight space. The output size of the fully connected layer is the same as the length of the input signal to ensure that the model can accurately reconstruct the original signal subsequently. The reconstructed signal can be represented as: (11) in, The sparse impulse response output by the encoder. For the first The deconvolution block operation. This represents a fully connected layer.

[0046] In at least one embodiment, in step S4, the progressive course weighted loss function (PCW-Loss) includes the following steps: S41. Divide the sparse pulse sequence into a pulse region and a background region; S42. Apply the L1 loss function to the pulse region and the MSE loss function to the background region. S43. Introduce a dynamic weighting factor to adjust the loss weights of the pulse region and the background region according to the number of iterations. In the initial stage, set a lower pulse weight and a higher background weight. In the middle transition stage, the pulse weight increases linearly and the background weight decreases linearly. In the later stage, the pulse weight reaches its maximum value and the background weight decreases to its minimum value.

[0047] In detail, the mean squared error (MSE) loss is a commonly used loss function in regression networks. However, MSE has inherent limitations when processing sparse time-of-flight series. First, it treats the small errors in the background region (a large number of zeros) and the errors in the impulse region (Time-of-Flight information) equally, leading to over-optimization of unimportant background regions and weakening the focus on key Time-of-Flight information. Second, MSE assumes a Gaussian distribution of errors, while the error distribution of sparse data is quite different.

[0048] To address this, a novel function called Progressive Curriculum Weighted Loss (PCW-Loss) is proposed. Curriculum Learning is a machine learning strategy inspired by human education, training models progressively from easy to difficult. By categorizing training data by difficulty, it initially focuses on simple samples and gradually introduces complex ones, mimicking the human learning path from basic to advanced levels. This method optimizes model training through a structured learning sequence, reducing ineffective exploration of complex patterns in the early stages, thereby accelerating convergence and improving generalization ability. Dynamic Loss Weighting adaptively allocates weights to balance the model's focus on multiple objectives by real-time sensing of the learning status of each task or sample (such as loss value, gradient distribution, task difficulty, etc.). Therefore, Progressive Curriculum Weighting combines the optimization strategies of Curriculum Learning and Dynamic Loss Weighting, simulating cognitive patterns in the human learning process by adjusting the loss weights in different regions in stages, thereby improving the model's ability to capture key features and training stability.

[0049] Since the signal flight time is sparse, theoretically, the non-zero values ​​in the sequence depend only on the number of reflectors, and the number of non-zero values ​​is much smaller than the number of zero values. Therefore, the sparse pulse sequence is divided into two regions: the pulse region (non-zero value region) and the background region (zero value region). The losses for each region are calculated separately, assigned different weights, and then summed to obtain a new loss function, enhancing the network's feature extraction capabilities for the pulse region. Simultaneously, a progressive learning mechanism is used to implement a phased optimization strategy, mimicking the human learning process from easy to difficult, improving the network's physical interpretability. For the pulse region, the L1 loss function is chosen. Compared to the MSE loss, the L1 loss penalizes amplitude prediction errors more linearly, enhancing robustness to pulse amplitude prediction and avoiding the oversensitivity of MSE to outliers, making it suitable for pulse spike characteristics. Furthermore, it provides smoother gradients even with slight pulse position shifts. For the background region, the MSE loss function is chosen. Its gradient decreases linearly with error, and its convex function characteristic ensures a clear optimization direction, driving the background prediction value to converge quickly to zero. Simultaneously, sparsity constraints are introduced to force the output in non-pulse regions to approach zero, enhancing the model's ability to suppress background noise. To force the network to focus on physically important impulse information, we designed a progressively weighted loss function. This loss function mimics the human learning pattern of progressing from easy to difficult, reducing the model's focus on background information and accelerating its convergence process. Furthermore, it can dynamically adjust the model's focus on different types of information, enhancing its ability to extract key features. The loss function is as follows: (12) in, Set the pulse mask (assign 1 to non-zero values ​​and 0 to zero values). Set as the background mask (assign 0 for non-zero values ​​and 1 for zero values). As a dynamic weighting factor, This represents the current iteration number. This refers to the number of preheating iterations. When the number of iterations exceeds the number of preheating iterations, Initial stage With lower impulse weights and higher background weights, the model primarily learns to suppress background noise, avoiding overfitting caused by premature focus on sparse impulses. Mid-term transition phase. As the pulse weights increase linearly and the background weights decrease linearly, the model begins to balance background suppression and pulse localization, gradually adapting to complex tasks. (Later Stage) With the pulse weights reaching a maximum of 25 and the background weights decreasing to 0.5, the model focuses on high-precision pulse sequence detection, leveraging previously learned background suppression capabilities to improve localization accuracy. PCW-Loss, through partitioning and dynamic weights, guides the network to first understand the "parts of the signal without ToF information," and then accurately locate the "key ToF pulses and their attributes in the signal," perfectly aligning with the sparse physical nature of time-of-flight.

[0050] Furthermore, existing evaluation metrics struggle to simultaneously and accurately measure the position and amplitude reconstruction accuracy of sparse time-of-flight pulses. Amplitude information is related to signal attenuation, while position information implicitly reflects the thickness between different material layers. To simultaneously ensure both position and amplitude accuracy, the Amplitude-Position Joint Error (APJE) is proposed: (13) in, It is the actual pulse position. It is the predicted pulse position. It is the actual pulse amplitude. It is the predicted pulse amplitude. This is the maximum allowed position offset. It refers to the dynamic range of the signal amplitude. These are the weighting coefficients for amplitude and position. This is the actual total number of pulses. This represents the number of pulses matched by the network. Since both the network's input and output are normalized, and amplitude and position are equally important for dispersion compensation, therefore, [the following is omitted as it is not directly related to the preceding sentence]. Set to 1, The value is set to 0.5. This method simultaneously constrains amplitude and position errors, avoiding the bias of evaluating a single metric. It only calculates errors of non-zero values ​​to prevent dilution by a large number of zero values ​​and includes a penalty for missed pulses. Theoretically, the smaller the APJE, the more the network focuses on the timing, position, and amplitude of the pulse, and the closer the output is to the true result.

[0051] Furthermore, in step S5, the terahertz compensation signal can be recovered by convolving the sparse pulse sequence output by the network with the terahertz reference signal, specifically described as follows: (14) in, Terahertz reference signal The sparse pulse sequence output by the network. This is a terahertz compensation signal.

[0052] Based on the above analysis, the time-of-flight pulse sequence output by the network contains the positional information and attenuation amplitude required for dispersion compensation. This paper proposes a series of methods to improve the network's deconvolution capability on sparse sequences, and finally obtains the dispersion-compensated signal by directly convolving the network's output onto the reference signal. Figure 8 The proposed dispersion compensation strategy is as follows.

[0053] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of protection claimed by the present invention. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A terahertz wave dispersion compensation method based on physically constrained sparse deconvolutional networks, characterized in that, Includes the following steps: S1. Prepare single-layer composite laminates and multi-layer composite laminates respectively, and obtain terahertz reference signals and dispersive terahertz signals of different samples through a reflective terahertz time-domain spectroscopy system. S2. Analyze the propagation characteristics of terahertz waves in the medium under test, and establish a signal propagation model that considers the dispersion effect of terahertz waves. S3. Based on the constructed terahertz signal propagation model, a sparse deconvolution network is built using the powerful feature extraction capability of the convolutional autoencoder to obtain the mapping relationship between the dispersive signal and the time of flight. S4. Introduce a progressively weighted loss function and an amplitude-position joint error evaluation index to improve the learning ability of deconvolutional networks for sparse time-of-flight data; S5. By combining the time-of-flight estimation results output by the deconvolution network with the terahertz reference signal, a terahertz wave dispersion compensation model is established to achieve accurate compensation for the dispersion signal.

2. The terahertz wave dispersion compensation method based on physically constrained sparse deconvolutional networks according to claim 1, characterized in that, In step S1, the reflective terahertz time-domain spectroscopy system includes a femtosecond laser, a terahertz transmitter, a terahertz receiver, an optical delay line, and a motion platform, with an effective frequency range of 10 GHz to 4.5 THz.

3. The terahertz wave dispersion compensation method based on physically constrained sparse deconvolutional networks according to claim 1, characterized in that, The single-layer composite material laminate is a glass fiber reinforced plastic laminate of different thicknesses, with a transverse dimension of 50 mm × 50 mm and thicknesses of 0.1 mm, 0.2 mm, 0.4 mm, 0.6 mm, 0.8 mm, and 1.0 mm, respectively, and a refractive index of 2.

24.

4. The terahertz wave dispersion compensation method based on physically constrained sparse deconvolutional networks according to claim 1, characterized in that, The multilayer composite laminate has a three-layer sandwich structure with a transverse dimension of 100 mm × 100 mm. The top and bottom layers are 0.5 mm thick glass fiber reinforced polymers, and the middle layer is filled with 1 mm thick extruded polystyrene foam board with a density of 32 kg / m³. 3 The refractive index is calibrated to 1.

05.

5. The terahertz wave dispersion compensation method based on physically constrained sparse deconvolutional networks according to claim 1, characterized in that, In step S2, the signal propagation model includes the following formula: In a reflective terahertz time-domain spectroscopy system, the measured echo signal can be regarded as a linear superposition of the terahertz signals reflected by each reflector interface. The terahertz echo signal model considering additive noise is as follows: in, It is the total number of reflectors. It is the first The terahertz signal reflected by the reflector The weight parameters, It is additive noise from the system; The signal propagation model considering the terahertz wave dispersion effect is as follows: in, It is the time-domain variation of the terahertz reference signal caused by dispersion. It is a sparse impulse response related to the reflector. It is additive noise from the system. It is a dispersive terahertz echo signal.

6. The terahertz wave dispersion compensation method based on physically constrained sparse deconvolutional networks according to claim 1, characterized in that, The sparse deconvolutional network adopts a convolutional autoencoder architecture, including encoder and decoder modules. The encoder extracts the features of the input signal step by step through multiple convolution operations, and the decoder maps the features back to the input space through transpose convolution operations, thereby realizing the automatic mining of the mapping relationship between input and output from the data.

7. The terahertz wave dispersion compensation method based on physically constrained sparse deconvolutional networks according to claim 6, characterized in that, The encoder uses three convolutional blocks, each including a convolutional layer, batch normalization, ReLU activation function, and max pooling layer; the decoder uses three deconvolutional blocks, each including a transposed convolutional layer, batch normalization, and ReLU activation function, and a dropout layer is added between the encoder and decoder to prevent overfitting.

8. The terahertz wave dispersion compensation method based on physically constrained sparse deconvolutional networks according to claim 1, characterized in that, In step S4, the progressive course weighted loss function includes the following steps: S41. Divide the sparse pulse sequence into a pulse region and a background region; S42. Apply the L1 loss function to the pulse region and the MSE loss function to the background region. S43. Introduce a dynamic weighting factor to adjust the loss weights of the pulse region and the background region according to the number of iterations. In the initial stage, set a lower pulse weight and a higher background weight. In the middle transition stage, the pulse weight increases linearly and the background weight decreases linearly. In the later stage, the pulse weight reaches its maximum value and the background weight decreases to its minimum value.

9. The terahertz wave dispersion compensation method based on physically constrained sparse deconvolutional networks according to claim 1, characterized in that, The magnitude-position joint error evaluation index is: in, It is the actual pulse position. It is the predicted pulse position. It is the actual pulse amplitude. It is the predicted pulse amplitude. This is the maximum allowed position offset. It refers to the dynamic range of the signal amplitude. These are the weighting coefficients for amplitude and position. This is the actual total number of pulses. It represents the number of pulses matched by the network.

10. The terahertz wave dispersion compensation method based on physically constrained sparse deconvolutional networks according to claim 1, characterized in that, In step S5, the method for establishing the dispersion compensation model is to convolve the sparse pulse sequence output by the network with the terahertz reference signal to recover the terahertz compensation signal, specifically described as follows: in, Terahertz reference signal The sparse pulse sequence output by the network. This is a terahertz compensation signal.

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