Tensor space constraint based heat map sequence down-sampling reconstruction method

Abstract

This application describes a method for reconstructing thermal image sequences based on tensor space constraints, relating to the fields of photothermal science, detection, and signal processing. The aim is to address the limitations of active infrared thermal imaging detection technology in meeting the engineering requirements for high spatiotemporal resolution, low data transmission volume, and real-time monitoring. This method obtains the core tensor of the infrared image sequence through Tucker decomposition and updates it until convergence is met. The updated core tensor then reconstructs the infrared image sequence. The update process involves: performing temporal modal expansion on the core tensor of the infrared image sequence to obtain the spatial reconstruction field for each temporal mode; applying thermal diffusion physical constraints to the spatial reconstruction field using the lattice Boltzmann method to obtain the physical evolution field; projecting the difference between the physical evolution field and the corresponding spatial reconstruction field onto the corresponding position of the core tensor; and updating the core tensor slices through Adam optimization, thereby updating the core tensor.

Description

Technical Field

[0001] This application belongs to the field of photothermal science and detection and signal processing, and in particular relates to the downsampling reconstruction of thermal image sequences. Background Technology

[0002] Active infrared thermal imaging (AIR) is a non-destructive testing technique that induces temperature field changes by inputting external stimuli (such as light pulses, sound waves, or electric currents) to the object under test and then captures the thermal radiation response using an infrared camera. This technology is widely used in composite material structural health monitoring, coating peeling and defect detection, thermal distribution assessment of electronic devices, and defect location and performance evaluation of aerospace components.

[0003] Due to their multi-layered and multi-phase structural characteristics, composite materials often exhibit minute defects such as interfacial debonding and interlaminar cracks, which are difficult to comprehensively cover using traditional optical or ultrasonic testing methods. Active infrared thermal imaging, through a highly sensitive infrared detector, can directly image under minute temperature differences, revealing thermal conduction anomalies in both depth and lateral dimensions, thus enabling efficient localization of internal defects in composite materials. However, active infrared thermal imaging still faces several bottlenecks. First, the spatial resolution and thermal sensitivity of infrared cameras are limited by detector materials and pixel size, making it difficult to achieve high frame rates while maintaining high resolution. Second, capturing rapid thermal diffusion processes requires high frame rate performance, but this generates massive amounts of data, placing stringent demands on the front-end transmission channel and back-end storage system. Finally, in actual testing environments, the uniformity and power stability of the excitation source are difficult to fully control, and the thermal boundary conditions of the tested component are often complex and variable. These factors significantly increase the noise of the thermal image sequence and reduce the signal-to-noise ratio. Due to these limitations, relying solely on frame-by-frame thermal image acquisition and manual analysis can no longer meet the engineering application requirements for high spatiotemporal resolution, low data volume transmission, and real-time monitoring. Therefore, there is an urgent need to use innovative algorithms to reconstruct continuous and high-precision heatmap sequences from small amounts of low-dimensional data in order to improve system integration and detection efficiency. Summary of the Invention

[0004] This application aims to address the problem that active infrared thermal imaging detection technology cannot meet the requirements of high spatiotemporal resolution, low data transmission, and real-time monitoring in engineering applications. It provides a method for downsampling and reconstructing heat map sequences based on core tensor space physical constraints. This method solves the problems of existing compressed sensing, low-rank completion, and deep learning algorithms, such as oversmoothing, ringing artifacts, structured noise, and high sensitivity to prior selection, loss weights, and data size under low sampling rate, high modulation, and complex / time-varying boundary conditions.

[0005] This application provides a method for downsampling and reconstructing heatmap sequences based on tensor space constraints, including:

[0006] The core tensor of the infrared image sequence is obtained by Tucker decomposition, and the core tensor is updated until the convergence condition is met. The infrared image sequence is then reconstructed using the updated core tensor.

[0007] The update of the core tensor includes:

[0008] The core tensor of the infrared image sequence is expanded in time modes, and the spatial reconstruction field of each time mode is obtained by slicing the core tensor in each time mode after expansion.

[0009] The lattice Boltzmann method is used to apply thermal diffusion physical constraints to the spatial reconstruction field under each time mode to obtain the physical evolution field under each time mode;

[0010] The difference between the physical evolution field and the corresponding spatial reconstruction field under each time mode is projected to the corresponding position of the core tensor, and the core tensor slice is updated by Adam optimization, thereby updating the core tensor.

[0011] In one possible design, obtaining the core tensor of the infrared image sequence through Tucker decomposition includes:

[0012] The infrared image sequence is represented as a third-order tensor, and the mean field is calculated using this third-order tensor;

[0013] The infrared image sequence is centered and normalized using the third-order tensor and the mean field to obtain a centered tensor;

[0014] The centered tensor is decomposed into a core tensor and three sets of factor matrices using Tucker decomposition. The core tensor is obtained by modular product.

[0015] In one possible design, obtaining the spatial reconstruction field for each time modality using core tensor slices after unfolding includes:

[0016] The spatial reconstruction field for each time mode is obtained by the following formula:

[0017] ,

[0018] in, For the first Spatial reconstruction field under a time mode For the first Core tensor slices in each time modality and All are factor matrices.

[0019] In one possible design, the application of the lattice Boltzmann method to apply thermal diffusion physical constraints to the spatial reconstruction field under each time mode to obtain the physical evolution field under each time mode includes:

[0020] The initial state distribution function is constructed using the spatial reconstruction field under each time mode;

[0021] The initial state distribution function is subjected to collision and migration using the lattice Boltzmann method to obtain the final state distribution function;

[0022] The physical evolution field is obtained based on the final state distribution function.

[0023] In one possible design, the construction of the initial state distribution function using the spatial reconstruction field under each time mode includes:

[0024] The initial state distribution function is constructed according to the following formula:

[0025] ,

[0026] in, For the lattice Boltzmann method, the first Initial state distribution function in discrete directions, For the first Spatial reconstruction field under a time mode For the first Weights for each discrete direction.

[0027] In one possible design, obtaining the physical evolution field based on the final state distribution function includes:

[0028] The physical evolution field is obtained according to the following formula:

[0029] ,

[0030] in, For physical evolution field, For the lattice Boltzmann method, the first Final state distribution function in discrete directions, This represents the number of collision and migration steps in the lattice Boltzmann method.

[0031] In one possible design, projecting the difference between the physical evolution field and the corresponding spatial reconstruction field under each time mode onto the corresponding position of the core tensor includes:

[0032] The difference between the physical evolution field and the corresponding spatial reconstruction field in each time mode is projected onto the corresponding position of the core tensor using the following formula:

[0033] ,

[0034] in, Let be the loss function, expressed as follows: , For the first Core tensor slices in each time modality Represents the core tensor Location index, and All are factor matrices. For the first The difference between the physical evolution field and the corresponding spatial reconstruction field in each time mode and These represent the pixel positions in the row and column directions of the infrared image sequence, respectively. , .

[0035] In one possible design, updating the core tensor slice via Adam optimization, and thus updating the core tensor, includes:

[0036] The projection results are written in matrix form, and the first-order moment accumulation and second-order moment accumulation are obtained through gradient accumulation.

[0037] The first-order moment accumulation and the second-order moment accumulation are biased and corrected, and the core tensor slice is updated using the correction results.

[0038] In one possible design, obtaining the first-order moment accumulation and the second-order moment accumulation through gradient accumulation includes:

[0039] The first-order moment accumulation and the second-order moment accumulation are obtained according to the following formula:

[0040] ,

[0041] ,

[0042] in, For the first Gradients of core tensor slices in each time modality and These are the first-order moment accumulation and the second-order moment accumulation, respectively. and These are the first-order moment decay factor and the second-order moment decay factor, respectively;

[0043] The bias correction for the first-order moment accumulation and the second-order moment accumulation is performed according to the following formula:

[0044] ,

[0045] ,

[0046] in, and These are the first-order moment accumulation and second-order moment accumulation after bias correction, respectively;

[0047] The core tensor slices are updated according to the following formula:

[0048] ,

[0049] in, For learning rate, To prevent constants from being divided by zero, and The first and Core tensor slices in each time modality.

[0050] In one possible design, the convergence condition includes:

[0051] ,

[0052] in, The iteration threshold, To find the norm, and The first and Core tensor slices in each time modality.

[0053] The beneficial effects of this application are:

[0054] This application discloses a heat map sequence downsampling reconstruction method based on core tensor space physical constraints. This method, based on core tensor space physical constraints, embeds differentiable multi-relaxation time lattice Boltzmann thermal diffusion projection into Tucker decomposition optimization, achieving a closed-loop coupling of "reconstruction-physical evolution-residual backprojection" in the core tensor space. It can recover high-fidelity spatiotemporal temperature fields with only partial time-series frame observations, while maintaining consistency between the observed data and thermal diffusion dynamics. By progressively adopting adaptive updates of the core tensor gradient and repeated projection of physical constraints, it effectively suppresses non-physical oscillations and edge oversmoothing, reduces amplitude and phase deviations, and enables the acquisition of high peak signal-to-noise ratio / structural similarity and stable defect signal-to-noise ratio even at extremely low sampling rates (e.g., 5%–10%). It also maintains natural compatibility with downstream feature extraction algorithms such as phase-locked loop and fractional Fourier transform, thereby significantly reducing acquisition bandwidth and storage pressure and improving the real-time performance of online detection. These advantages enable the thermal image sequence downsampling reconstruction method based on core tensor space physical constraints to exhibit strong adaptability and accuracy when facing complex environments, non-uniform excitations (sine / chirp, etc.), diverse boundary conditions, and various materials. It overcomes the limitations of traditional methods in terms of cross-sampling rate generalization and boundary sensitivity, and can achieve rapid and high-precision active infrared thermal imaging detection of composite material delamination / debonding, coating defects, thermal anomalies of electronic devices, and aerospace components.

[0055] In summary, this application is applicable to fields such as composite material structural health monitoring, coating evaluation, electronic packaging thermal analysis, and non-destructive testing of aerospace components, and is particularly suitable for online NDT scenarios that require synchronization of high spatiotemporal resolution and low data volume transmission. Attached Figure Description

[0056] Figure 1 A schematic diagram of thermal diffusion simulation using the D2Q9 model of the lattice Boltzmann method;

[0057] Figure 2 The flowchart below shows the heatmap sequence downsampling reconstruction method based on core tensor space physical constraints as described in the embodiment.

[0058] Figure 3 This is a schematic diagram showing the comparison of reconstruction results of infrared image sequences of prefabricated defects in glass fiber boards under sinusoidal excitation at different sampling rates.

[0059] Figure 4 A schematic diagram showing the reconstruction results of infrared image sequences of prefabricated defects in glass fiber boards at different sampling rates under chirped excitation;

[0060] Figure 5 A schematic diagram showing the comparison of infrared feature images of prefabricated defects in fiberglass boards at different sampling rates;

[0061] Figure 6This is a flowchart of the heatmap sequence downsampling reconstruction method based on tensor space constraints described in this invention. Detailed Implementation

[0062] The technical solutions of the embodiments of this application 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 this application, and not all of them. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other.

[0063] Currently, in order to reconstruct thermal imaging sequences under undersampling conditions to improve defect detection and facilitate system integration, researchers have proposed a variety of numerical and signal processing schemes. At the application level, there are also several practical techniques under specific excitation protocols (such as synchronous undersampling phase-locked thickness measurement, linear frequency modulation excitation combined with frequency domain cross-correlation, and hierarchical edge detection after logarithmic domain polynomial fitting). However, these methods are difficult to form a universal reconstruction mechanism that can span sampling rates, materials, and boundary conditions. In general, common industrial approaches include: Compressed sensing, which can achieve high data efficiency and interpretability by leveraging sparse priors and matching pursuit / Bayesian frameworks, but its performance is highly sensitive to sparse bases and regularized weights. It is prone to oversmoothing and ringing artifacts under high modulation depths or complex / time-varying boundaries, especially at low sampling rates; Low-rank matrix / tensor completion, which relies on global low-rank priors to compactly characterize dominant thermal patterns and is suitable for smooth scenarios with simple boundaries, but its intrinsic rank increases under non-uniform excitations such as sinusoidal / chirped excitations. A single global low-rank can weaken data consistency, leading to structured noise and amplitude-phase bias near defect boundaries, especially at extremely low sampling rates; Deep learning, which is flexible and can perform rapid inference after training, but often requires large-scale multi-material and multi-excitation data to ensure generalization. Although physically constrained neural networks introduce partial differential residuals and boundary / initial conditions, they are applied in the form of soft penalties, and their performance is sensitive to boundary parameter calibration.

[0064] In summary, existing methods generally face problems such as oversmoothing, artifacts, structural noise, and sensitivity to prior / data scale / weight tuning under low sampling rates, emphasis, and complex boundary conditions. There is an urgent need to deeply couple explicit physical models with efficient differentiable optimization strategies during the reconstruction process to ensure consistency between observation data and thermal diffusion dynamics, while maintaining compatibility with downstream defect feature extraction.

[0065] In existing research, patent CN111052173A discloses a method for reconstructing and synthesizing dense super-resolution images from low-information-content images. This method uses sparse localization images and / or low-resolution wide-field images as input, and directly outputs dense super-resolution (SR) results through a trained artificial neural network. Based on pairwise / triple training data and objective functions such as L2 or cGAN, it achieves undersampling reconstruction from few frames of data to high-resolution images. However, this method does not show modeling physical priors and boundary conditions, and its performance depends on the distribution of training data and loss design, resulting in limitations in cross-scene generalization. Patent CN112884644A discloses multi-scale coded aperture spectral temporal compression sensing imaging. It uses two complementary coding paths of DMD to achieve temporal compression (single frame → multi-frame sequence) and spectral aliasing (single frame → multi-spectral sequence) inversion reconstruction, and achieves spatiotemporal spectral joint compression and super-resolution based on spatiotemporal registration and maximum a posteriori (MAP) optimization. However, this method has high requirements for system calibration and registration, involves information trade-offs between dimensions, and has a large system complexity, limiting its robustness to non-ideal hardware and noisy conditions. Patent CN108010064A discloses a method for reconstructing and tracking motion cell sequences based on active contours and Kalman filtering. It utilizes Kalman preprocessing and SVD feature vector reconstruction from adjacent N+1 frames to obtain a "feature image sequence," then uses active contour segmentation combined with inter-frame / intra-frame position correction to achieve stable localization. However, this method is geared towards target tracking scenarios and lacks design for undersampled sequence reconstruction and cross-sampling rate generalization for physical fields. Furthermore, it is sensitive to initial boundaries and noise in complex environments.

[0066] In view of this, in order to address the difficulties in sequence reconstruction, noise, and oversmoothing caused by low sampling rates, limited bandwidth and storage, non-uniform excitation, and complex / time-varying boundary conditions in active infrared thermal imaging detection, this embodiment relates to a thermal image sequence downsampling reconstruction method based on core tensor space physical constraints. This method introduces an explicit thermal diffusion physical constraint reconstruction strategy in the core tensor space, which can recover a continuous and high-precision spatiotemporal temperature field from a small number of low-dimensional observations, and is compatible with subsequent defect feature extraction and automatic identification; thereby effectively reducing the data acquisition and transmission pressure and improving the real-time performance and robustness of online detection. The following will be combined with the appendix... Figures 1 to 6 The implementation scheme of this application will be described in detail.

[0067] Using the D2Q9 discrete velocity model, the two-dimensional heat diffusion equation is numerically solved using the multi-relaxation time lattice Boltzmann method with collisions and migrations (distribution functions moving along the velocity direction). In the two-dimensional case, the steady-state or transient heat diffusion / heat conduction equations can be written as:

[0068] ,

[0069] In the formula, For temperature field, For location, Indicates time, Where is the thermal diffusivity, This represents the Laplace operator.

[0070] Traditional finite difference, finite element, or finite volume methods directly discretize this partial differential equation. The multi-relaxation time lattice Boltzmann method, however, constructs an equivalent discrete velocity Boltzmann equation and uses a "collision + migration" approach for numerical solution. To simulate thermal diffusion, only the "scalar field," i.e., the distribution function of the temperature field, is needed; therefore, as... Figure 1 As shown, the velocity space can be discretized using the D2Q9 model of the lattice Boltzmann method:

[0071] The D2Q9 model discretizes the distribution function into nine velocity directions on a planar mesh. ,in , , , , , , , , , The first direction represents the stationary direction, and the other eight directions cover the eight adjacent grid points. The velocity direction... The distribution function is denoted as , representing the amount of temperature carried at discrete velocities, the macroscopic temperature field of the D2Q9 model can be obtained by the following equation:

[0072] .

[0073] When calculating the equilibrium distribution, it corresponds to each velocity direction. Weighting coefficients In the D2Q9 model , , By employing the triple discretization of velocity direction, grid, and time step, the lattice Boltzmann method can store only a finite number of distribution functions at each grid point. Updates can be made without integrating over a continuous velocity space. By using multi-relaxation time lattice Boltzmann to assign different relaxation rates to different modes in the moment / mode space, numerical stability and physical accuracy can be improved.

[0074] First, through the linear transformation matrix velocity space distribution vector Projecting onto the modal space yields the modal space distribution vector. , where the transformation matrix Represented as:

[0075] .

[0076] Then, relax the matrix diagonally in the modal space. Relax each mode separately.

[0077] The diagonal relaxation matrix is ​​expressed as: .

[0078] The core process of solving heat diffusion using the lattice Boltzmann algorithm includes two processes: collision and streaming. The collision process is represented as follows:

[0079] ,

[0080] in, Modal space distribution vector after collision, equilibrium mode Weighted by D2Q9 coefficients The distribution of temperature in each discrete direction is determined by the temperature field, meaning it is proportional to the macroscopic temperature at that point. , by weighting coefficient To be assigned to different directions.

[0081] Finally, through the velocity space distribution vector after migration The post-collision distribution is transformed back to velocity space and the migration is completed:

[0082] ,

[0083] in, For time intervals.

[0084] Thermal diffusivity at dimensionless or specific lattice scales There is generally an approximate relationship:

[0085] ,

[0086] In the formula, For the speed of sound in the lattice model, most D2Q9 models take... =1 / 3 (dimensionless), when the relaxation rate is related to thermal diffusion. When the relationship in the equation is satisfied, the resulting macroscopic temperature evolution equation is precisely the heat diffusion equation.

[0087] A new distribution function is obtained after migration. To allow for further collisions in the next moment.

[0088] In summary, the lattice Boltzmann method, which iteratively simulates the temperature field from the initial moment through collisions and migrations, is used. until the specified time The evolution process of the steps. To ensure that the numerical simulation conforms to the actual physical background, appropriate boundary conditions need to be set. In this embodiment, for the convenience of calculation and observation, only the heat map of the hot spot is extracted for calculation, so a periodic boundary is used for processing.

[0089] Pure data-driven approaches can efficiently extract the main thermal field modes from a small amount of sampled data, but they neglect the physical evolution of thermal diffusion. Pure physics-driven approaches can guarantee physical consistency, but they are computationally intensive and lack sufficient representation of full-frame details. The approach of this implementation is as follows: First, the 3D thermal field is reduced to a low rank using Tucker decomposition, and then optimization is performed on the low-dimensional core tensor, saving significant computation. Then, thermal diffusion physical constraints are applied to each time mode using a multi-relaxation time-lattice Boltzmann operator, ensuring that the reconstruction result not only matches the sampled data but also follows thermal diffusion dynamics. Finally, the Adam optimizer is used to gradually approximate the solution satisfying the physical laws within a controllable number of iterations and convergence criteria. The algorithm flowchart is as follows... Figure 2 As shown.

[0090] according to Figure 2 The aforementioned thermal image sequence downsampling reconstruction method based on core tensor space physical constraints obtains the original infrared image sequence by detecting prefabricated defects in glass fiberboard using active infrared thermal imaging. Then, the method described in this embodiment is used to reconstruct the original infrared image sequence at different sampling rates. The reconstructed image sequence is then processed by phase-locked loop and fractional Fourier transform to obtain infrared feature maps.

[0091] Step 1: Before starting the method, it is necessary to set the material's thermal diffusivity. , number of thermal diffusion evolution steps in the lattice Boltzmann method, and TV regularization coefficient Parameters such as the overall number of optimization iterations, initial learning rate, and learning rate decay coefficient.

[0092] In this embodiment, the thermal diffusivity of the glass fiber board material Set to 1.15 × 10⁻⁷ m² / s, LBM thermal diffusion evolution steps Set to 10, TV regularization coefficient The learning rate is set to 1×10⁻⁴, the total number of optimization iterations is set to 200, the initial learning rate is 0.5, and the learning rate decay coefficient is 0.98.

[0093] Step 2: The original infrared image sequence contains all the spatiotemporal temperature data, therefore the original infrared image sequence can be... Represented as a third-order tensor And calculate the mean field .

[0094] set up Given the sampled frame index set, we have:

[0095] ,

[0096] ,

[0097] in, , Indicates the position of a pixel in an image. For the number of image frames, , The pixel corresponds to its position in the tensor. No. The time corresponding to the frame and These represent the rows and columns of the original infrared image sequence, respectively. This represents the time dimension of the original infrared image sequence.

[0098] Step 3: Standardize each pixel to zero mean and unit scale to unify the dynamic dimensions of different pixels and prevent certain high-energy pixels from dominating the decomposition. Center and normalize the infrared image sequence data to generate a centered tensor. :

[0099] ,

[0100] Among them, intermediate variables , It represents the standard deviation.

[0101] Step 4: Tucker decomposition can be used to... Represented as a core tensor and three sets of factor matrices Modulus:

[0102] ,

[0103] in, For the core tensor, , , These represent the ranks of the core tensor in the row direction, column direction, and frame sequence direction, respectively. Factor matrix , , These are orthogonal bases corresponding to the row, column, and time sequence directions, respectively. and These represent the pixel positions in the row and column directions of the infrared image sequence, respectively. Indicates the number of frames in the infrared image sequence.

[0104] Step 5: To implement Boltzmann constraints based on multi-relaxation time lattice, The modulus is decomposed into several interpretable blocks of "temporal modes + spatial shape," facilitating the application of physical constraints and gradient backpropagation modally. And for the core tensor... Perform time mode expansion, given the first... Core tensor slices of each time modality Corresponding spatial reconstruction field It can be represented as:

[0105] .

[0106] Step Six: After normalization, it is regarded as the initial temperature field to match the numerical stability region of LBM; the spatial slices of tensor reconstruction are transformed into LBM initial state distribution functions that can be used for diffusion evolution. :

[0107] ,

[0108] in, These are the weights for the D2Q9 model.

[0109] Step 7: Use the lattice Boltzmann method to process the above... Do The final state distribution function is obtained by step-by-step collision and migration. Physical Evolution Field Represented as:

[0110] .

[0111] Step 8: Calculate the difference between the spatial reconstruction field and the physical evolution field to obtain the residual that violates the heat diffusion equation. ,

[0112] .

[0113] If the reconstructed field perfectly conforms to diffusion physics, then .therefore, It can be used as a measure of hard physical constraints to penalize components that do not conform to the laws of thermal diffusion (such as oversmoothing or non-physical oscillations).

[0114] Step 9: To optimize the core tensor gradient, the residuals... Projected onto the core tensor At the location, the loss function Defined as:

[0115] ,

[0116] Represents the core tensor Location index, , Core tensor slices The gradient is expressed as:

[0117] ,

[0118] The above expression can be written in matrix form as follows:

[0119] ,

[0120] in, For core tensor The gradient.

[0121] Step 10: Optimize the core tensor using Adam to gradually approximate a solution that conforms to physical laws, and obtain the result through gradient accumulation:

[0122] ,

[0123] ,

[0124] in, For first-order moment accumulation, For the accumulation of second-order moments, =0.9 is the first-order moment decay factor. =0.999 is the second-order moment decay factor.

[0125] By performing bias correction, we can obtain:

[0126] ,

[0127] ,

[0128] in, The first moment after bias correction. This is the second moment after bias correction.

[0129] Updating the tensor yields:

[0130] ,

[0131] in, For learning rate, To prevent the constant from being divided by zero, this embodiment uses 10⁻⁸.

[0132] Step 11: Repeat steps 7 through 10 above until the following convergence condition is met:

[0133] ,

[0134] in, The iteration threshold, This indicates a search for the norm.

[0135] The algorithm terminates if the maximum number of iterations has been reached or the convergence criterion has been met.

[0136] Step 12: Visualize and output the reconstruction results The modulus is used to save the final reconstructed heatmap sequence and then uses a downstream feature extraction algorithm to display the feature map of the defect region. The result is compared with the original image sequence to evaluate the effectiveness of the downsampling reconstruction and confirm the accuracy of defect detection and localization.

[0137] Figure 3 and Figure 4 The results show the reconstruction of prefabricated defects in glass fiber boards at different sampling rates under sinusoidal and chirped excitation, respectively. Figure 5 Comparison of infrared feature images of prefabricated defects in fiberglass boards at different sampling rates.

[0138] This implementation introduces a reconstruction strategy with explicit thermal diffusion physical constraints in the core tensor space, which can recover a continuous and high-precision spatiotemporal temperature field from a small number of low-dimensional observations, and is compatible with subsequent defect feature extraction and automatic identification; thereby effectively reducing the data acquisition and transmission pressure and improving the real-time performance and robustness of online detection.

[0139] In summary, the heat map sequence downsampling reconstruction method based on core tensor space physical constraints of this application achieves closed-loop coupling of "reconstruction-physical evolution-residual backprojection" in the core tensor space by embedding differentiable multi-relaxation time lattice Boltzmann thermal diffusion projection into Tucker decomposition optimization. This enables the recovery of high-fidelity spatiotemporal temperature fields with only partial time-series frame observations, while maintaining consistency between the observed data and thermal diffusion dynamics. By progressively adopting adaptive updates of the core tensor gradient and repeated projection of physical constraints, non-physical oscillations and edge oversmoothing are effectively suppressed, and amplitude and phase deviations are reduced. This allows for the acquisition of high peak signal-to-noise ratio / structural similarity and stable defect signal-to-noise ratio even at extremely low sampling rates (e.g., 5%–10%). Furthermore, it maintains natural compatibility with downstream feature extraction algorithms such as phase-locked loop and fractional Fourier transform, thereby significantly reducing acquisition bandwidth and storage pressure and improving the real-time performance of online detection. These advantages enable the thermal image sequence downsampling reconstruction method based on core tensor space physical constraints to exhibit strong adaptability and accuracy in complex environments, non-uniform excitations (sine / chirp, etc.), diverse boundary conditions, and various materials. It overcomes the limitations of traditional methods in generalization across sampling rates and boundary sensitivity, enabling rapid and high-precision active infrared thermal imaging detection of composite material delamination / debonding, coating defects, thermal anomalies in electronic devices, and aerospace components. This application is applicable to accurate non-destructive testing and condition assessment of defects / damage in aerospace composite materials, microelectronic devices, and other fields.

[0140] While specific embodiments of this application have been described herein with reference to them, it should be understood that these embodiments are merely examples of the principles and applications of this application. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of this application as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for heat map sequence down-sampling reconstruction based on tensor space constraints, characterized in that, include: The core tensor of the infrared image sequence is obtained by Tucker decomposition, and the core tensor is updated until the convergence condition is met. The infrared image sequence is then reconstructed using the updated core tensor. The update of the core tensor includes: The core tensor of the infrared image sequence is expanded in time modes, and the spatial reconstruction field of each time mode is obtained by slicing the core tensor in each time mode after expansion. The lattice Boltzmann method is used to apply thermal diffusion physical constraints to the spatial reconstruction field under each time mode to obtain the physical evolution field under each time mode; The difference between the physical evolution field and the corresponding spatial reconstruction field under each time mode is projected to the corresponding position of the core tensor, and the core tensor slice is updated by Adam optimization, thereby updating the core tensor; The method employs the lattice Boltzmann method to apply thermal diffusion physical constraints to the spatial reconstruction field under each time mode, thereby obtaining the physical evolution field under each time mode, including: The initial state distribution function is constructed using the spatial reconstruction field under each time mode; The initial state distribution function is subjected to collision and migration using the lattice Boltzmann method to obtain the final state distribution function; The physical evolution field is obtained based on the final state distribution function; The construction of the initial state distribution function using the spatial reconstruction field under each time mode includes: The initial state distribution function is constructed according to the following formula: ， in, For the lattice Boltzmann method, the first Initial state distribution function in discrete directions, For the first Spatial reconstruction field under a time mode For the first Weights for each discrete direction; The process of obtaining the physical evolution field based on the final state distribution function includes: The physical evolution field is obtained according to the following formula: ， in, For physical evolution field, For the lattice Boltzmann method, the first Final state distribution function in discrete directions, This represents the number of collision and migration steps in the lattice Boltzmann method; The step of projecting the difference between the physical evolution field and the corresponding spatial reconstruction field under each time mode onto the corresponding position of the core tensor includes: The difference between the physical evolution field and the corresponding spatial reconstruction field in each time mode is projected onto the corresponding position of the core tensor using the following formula: ， in, Let be the loss function, expressed as follows: , For the first Core tensor slices in each time modality Represents a core tensor slice Location index, and All are factor matrices. For the first The difference between the physical evolution field and the corresponding spatial reconstruction field in each time mode and These represent the number of pixels in the row and column directions of the infrared image sequence, respectively. , .

2. The heatmap sequence downsampling reconstruction method based on tensor space constraints according to claim 1, characterized in that, The process of obtaining the core tensor of the infrared image sequence through Tucker decomposition includes: The infrared image sequence is represented as a third-order tensor, and the mean field is calculated using this third-order tensor; The infrared image sequence is centered and normalized using the third-order tensor and the mean field to obtain a centered tensor; The centered tensor is decomposed into a core tensor and three sets of factor matrices using Tucker decomposition. The core tensor is obtained by modular product.

3. The heatmap sequence downsampling reconstruction method based on tensor space constraints according to claim 1, characterized in that, The method of obtaining the spatial reconstruction field of each time mode by utilizing the core tensor slices of each time mode after expansion includes: The spatial reconstruction field for each time mode is obtained by the following formula: ， in, For the first Spatial reconstruction field under a time mode For the first Core tensor slices in each time modality and All are factor matrices.

4. The heatmap sequence downsampling reconstruction method based on tensor space constraints according to claim 1, characterized in that, The step of updating the core tensor slice through Adam optimization, and then updating the core tensor, includes: The projection results are written in matrix form, and the first-order moment accumulation and second-order moment accumulation are obtained through gradient accumulation. The first-order moment accumulation and the second-order moment accumulation are biased and corrected, and the core tensor slice is updated using the correction results.

5. The heatmap sequence downsampling reconstruction method based on tensor space constraints according to claim 4, characterized in that, The method of obtaining first-order moment accumulation and second-order moment accumulation through gradient accumulation includes: The first-order moment accumulation and the second-order moment accumulation are obtained according to the following formula: ， ， in, For the first Gradients of core tensor slices in each time modality and These are the first-order moment accumulation and the second-order moment accumulation, respectively. and These are the first-order moment decay factor and the second-order moment decay factor, respectively; The bias correction for the first-order moment accumulation and the second-order moment accumulation is performed according to the following formula: ， ， in, and These are the first-order moment accumulation and second-order moment accumulation after bias correction, respectively; The core tensor slices are updated according to the following formula: ， in, For learning rate, To prevent constants from being divided by zero, and The first and Core tensor slices in each time modality.

6. The heatmap sequence downsampling reconstruction method based on tensor space constraints according to claim 1, characterized in that, The convergence conditions include: ， in, The iteration threshold, To find the norm, and The first and Core tensor slices in each time modality.

Images