Heat map sequence downsampling reconstruction method based on tensor space constraint

Abstract

The invention discloses a heat map sequence downsampling reconstruction method based on tensor space constraint, and relates to the field of photo-thermal science and detection and signal processing. The invention aims to solve the problem that an active infrared thermal wave imaging detection technology cannot meet the requirements of high temporal-spatial resolution, low data volume transmission and real-time monitoring in engineering application. According to the method, the core tensor of the infrared image sequence is obtained through Tucker decomposition and is updated until the convergence condition is met, and the infrared image sequence is reconstructed through the updated core tensor; the updating process comprises the following steps of: performing time mode expansion on a core tensor of an infrared image sequence, and obtaining a spatial reconstruction field under each time mode; applying thermal diffusion physical constraint on the spatial reconstruction field by adopting a lattice Boltzmann method to obtain a physical evolution field; and projecting the difference between the physical evolution field and the corresponding space reconstruction field to the corresponding position of the core tensor, and updating the core tensor slice through Adam optimization so as to update the core tensor.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of photothermal science and detection and signal processing, and particularly relates to down-sampling reconstruction of thermal image sequences. BACKGROUND

[0002] Active infrared thermal wave imaging detection technology is a non-destructive testing technology that induces temperature field changes by inputting external excitation (such as light pulses, sound waves or electric current) to the measured object, and captures thermal radiation response using an infrared camera. This technology is widely used in composite structure health monitoring, coating peeling and defect detection, electronic device thermal distribution evaluation, and defect positioning and performance evaluation of aerospace components.

[0003] Due to the multi-level and multi-phase structural characteristics of composite materials, there are often small defects such as interface debonding and interlaminar cracks, which are difficult to fully cover by traditional optical or ultrasonic detection methods. Active infrared thermal wave imaging can directly image small temperature differences through high-sensitivity infrared detectors, revealing thermal conduction abnormalities in both depth and lateral dimensions, thereby efficiently positioning internal defects of composite materials. However, active infrared thermal wave imaging detection still faces multiple bottlenecks. First, the spatial resolution and thermal sensitivity of the infrared camera are limited by the detector material and pixel size, making it difficult to achieve high resolution while ensuring high frame rate. Second, to capture rapid thermal diffusion processes, high frame rate performance is required, but this generates massive data, posing strict requirements on front-end transmission channels and back-end storage systems. Finally, in actual detection environments, the uniformity and power stability of the excitation source are difficult to completely control, and the thermal boundary conditions of the measured object are often complex and variable, which significantly increases the noise of the thermal image sequence and reduces the signal-to-noise ratio. Due to the above limitations, relying solely on frame-by-frame thermal image acquisition and manual analysis cannot meet the demand for high spatiotemporal resolution, low data transmission, and real-time monitoring in engineering applications. Therefore, it is urgent to use innovative algorithms to reconstruct continuous and high-precision thermal image sequences from a small amount of low-dimensional data to improve system integration and detection efficiency. SUMMARY

[0004] The present application is to solve the problem that active infrared thermal wave imaging detection technology cannot meet the demand for high spatiotemporal resolution, low data transmission, and real-time monitoring in engineering applications. A thermal image sequence down-sampling reconstruction method based on core tensor space physical constraints is provided to solve 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 weight, and data size under low sampling rate, high modulation, and complex / time-varying boundary conditions.

[0005] The present application provides a thermal image sequence down-sampling reconstruction method based on tensor space constraints, which includes:

[0006] The core tensor of the infrared image sequence is obtained through Tucker decomposition, and the core tensor is updated until a convergence condition is met, and the infrared image sequence is reconstructed through the updated core tensor;

[0007] The core tensor is updated, including:

[0008] The core tensor of the infrared image sequence is time-mode unfolded, and the core tensor slice under each time mode after unfolding is used to obtain a spatial reconstruction field under each time mode;

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

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

[0011] In one possible design, the core tensor of the infrared image sequence is obtained through Tucker decomposition, including:

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

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

[0014] The centralized tensor is decomposed into a core tensor and the product of three groups of factor matrices through Tucker decomposition, and the core tensor is obtained.

[0015] In one possible design, the spatial reconstruction field under each time mode is obtained using the core tensor slice under each time mode after unfolding, including:

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

[0017] ,

[0018] Wherein, is the spatial reconstruction field under the i th time mode, is the core tensor slice under the i th time mode, and 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, thereby obtaining 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] Construct the initial state distribution function 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 modality to 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] wherein, is a loss function, the expression is , is the core tensor slice in the th time modality, represents the position index of the core tensor , and are factor matrices, is the difference between the physical evolution field and the corresponding spatial reconstruction field in the th time modality, and represent the pixel positions in the row and column directions of the infrared image sequence respectively, , .

[0035] In one possible design, the updating of the core tensor slice by the Adam optimization, and then updating the core tensor, includes:

[0036] The projection result is written in matrix form, and the first moment accumulation and the second moment accumulation are obtained by gradient accumulation;

[0037] The first moment accumulation and the second moment accumulation are bias corrected, and the corrected result is used to update the core tensor slice.

[0038] In one possible design, the first moment accumulation and the second moment accumulation are obtained by gradient accumulation, including:

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

[0040] ,

[0041] ,

[0042] wherein, is the gradient of the core tensor slice in the th time modality, and are the first moment accumulation and the second moment accumulation respectively, and are the first moment decay factor and the second moment decay factor respectively;

[0043] The first moment accumulation and the second moment accumulation are bias corrected according to the following formula:

[0044] ,

[0045] ,

[0046] wherein, and are the first and second moment accumulations after bias correction, respectively;

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

[0048] ,

[0049] where, is the learning rate, is a constant to prevent division by zero, and are the core tensor slices in the first and second time modalities, respectively. In one possible design, the convergence condition comprises:

[0050] ,

[0051] where, is an iteration threshold,

[0052] denotes the norm, and are the core tensor slices in the first and second time modalities, respectively. The beneficial effects of the present application are:

[0053]

[0054] ​​​​The application discloses a heat map sequence downsampling reconstruction method based on core tensor space physical constraints. The application discloses a heat map sequence downsampling reconstruction method based on core tensor space physical constraints, which realizes the closed-loop coupling of "reconstruction-physical evolution-residual reverse projection" in the core tensor space by embedding the differentiable multi-relaxation time lattice Boltzmann heat diffusion projection into Tucker decomposition optimization, can restore high-fidelity space-time temperature field under only partial time sequence frame observation, and simultaneously maintains the dual consistency of observation data and heat diffusion dynamics; gradually adopting adaptive update of the core tensor gradient and repeated projection of the physical constraint, effectively inhibiting non-physical oscillation and edge oversmoothing, reducing amplitude-phase deviation, enabling high peak signal-to-noise ratio / structural similarity and stable defect signal-to-noise ratio to be obtained under extremely low sampling rate (such as 5%-10%), and maintaining the natural compatibility to the phase-locked, fractional Fourier and other downstream feature extraction algorithms, thereby significantly reducing the acquisition bandwidth and storage pressure and improving the online detection real-time performance. These advantages enable the heat map sequence downsampling reconstruction method based on core tensor space physical constraints to exhibit strong adaptability and precision in the face of complex environments, non-uniform excitation (sine / chirp, etc.), various boundary conditions and various materials, overcome the limitations of traditional methods in cross-sampling rate generalization and boundary sensitivity, and can realize the active infrared thermal imaging rapid and high-precision detection of composite material delamination / peeling, coating defects, electronic device thermal anomalies and aerospace components.

[0055] In summary, the application is suitable for the fields of composite structure health monitoring, coating evaluation, electronic packaging thermal analysis and aerospace component nondestructive testing, and is particularly suitable for online NDT scenes with synchronous needs of high space-time resolution and low data amount transmission. BRIEF DESCRIPTION OF DRAWINGS

[0056] Figure 1 A schematic diagram of simulating heat diffusion for a D2Q9 model of the lattice Boltzmann method;

[0057] Figure 2 A flowchart of the heat map sequence downsampling reconstruction method based on core tensor space physical constraints described in the embodiment;

[0058] Figure 3 A schematic diagram of reconstruction comparison results of infrared image sequences of a glass fiber plate under sinusoidal excitation at different sampling rates;

[0059] Figure 4 A schematic diagram of reconstruction comparison results of infrared image sequences of a glass fiber plate under chirp excitation at different sampling rates;

[0060] Figure 5 A schematic diagram of infrared feature map comparison results of a glass fiber plate at different sampling rates;

[0061] Figure 6A flowchart of the tensor space constraint based thermal image sequence down-sampling reconstruction method. DETAILED DESCRIPTION

[0062] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the scope of protection of the present application. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0063] At present, in order to reconstruct thermal image sequences under under-sampling conditions to improve defect detection effect and facilitate system integration, researchers have proposed a variety of numerical and signal processing schemes; there are also several practical skills under specific excitation protocols (such as synchronous under-sampling phase-locked thickness measurement, linear frequency modulation excitation combined with frequency domain cross-correlation, hierarchical edge detection after logarithmic domain polynomial fitting), but these methods are difficult to form a general reconstruction mechanism that can cross sampling rate, material and boundary conditions. Overall, the common means in the industry mainly include: compressed sensing, which can achieve high data efficiency and interpretability with the help of sparse prior and matching pursuit / Bayesian framework, but the performance is highly sensitive to sparse basis and regularization weight, and is prone to smoothing and ringing artifacts under high modulation depth or complex / time-varying boundary, especially at low sampling rate; low-rank matrix / tensor completion, which relies on global low-rank prior to compactly describe the dominant thermal mode and is suitable for simple boundary smoothing scenarios, but the intrinsic rank rises under non-uniform excitation such as sine / chirp, and a single global low-rank will weaken data consistency, leading to structured noise and amplitude-phase deviation near the defect boundary, especially at very low sampling rate; deep learning, which has flexibility and fast reasoning after training, but often requires large-scale multi-material, multi-excitation data to ensure generalization, and physical constraint neural networks introduce partial differential residuals and boundary / initial conditions in the form of soft penalty, and the performance is sensitive to boundary parameter calibration.

[0064] In summary, the existing methods generally face problems such as oversmoothing, artifacts, structured noise, and sensitivity to prior / data size / weight tuning under low sampling rate, strong modulation, and complex boundary conditions, and there is an urgent need to deeply couple explicit physical models and efficient differentiable optimization strategies in the reconstruction process to ensure consistency with observed data and thermal diffusion dynamics, and maintain compatibility with downstream defect feature extraction.

[0065] In existing research, the invention patent with publication number CN111052173A discloses a method for reconstructing a dense super-resolution image from a low-information-content image. This method uses sparse positioning images and / or low-resolution wide-field images as input, directly outputs dense SR results through a trained artificial neural network, and realizes undersampling reconstruction from few-frame data to high-resolution images based on pair / triplet training data and L2 or cGAN objective functions. However, this method does not show the modeling of physical priori and boundary conditions, and its performance depends on the distribution of training data and loss design, and there are limitations in cross-scene generalization. The invention patent with publication number CN112884644A discloses multi-scale coded aperture spectral time compressed sensing imaging, which uses DMD two-way complementary coding to realize inversion reconstruction of time compression (single frame→multi-frame sequence) and spectral aliasing (single frame→multi-spectral sequence), and realizes time-spectral joint compression and super-resolution based on time-space registration and maximum posteriori (MAP) optimization. However, this method has high requirements for system calibration and registration, there is information trade-off between dimensions, and the system complexity is large, and the robustness to non-ideal hardware and noise conditions is limited. The invention patent with publication number CN108010064A discloses motion cell sequence reconstruction and tracking based on active contour and Kalman filtering, which uses Kalman preprocessing and SVD feature vector reconstruction of adjacent N+1 frames to obtain a "feature image sequence", and then uses active contour segmentation combined with inter-frame / intra-frame position correction to realize stable positioning. However, this method is designed for target tracking scenes, and does not aim at physical field undersampling sequence reconstruction and cross-sampling rate generalization, and is sensitive to initial boundaries and noise in complex backgrounds.

[0066] Therefore, in order to solve the problems of sequence reconstruction difficulty, noise and over-smoothing of active infrared thermal wave imaging detection under low sampling rate, limited bandwidth and storage, non-uniform excitation, and complex / time-varying boundary conditions as much as possible, the present 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 continuous and high-precision space-time temperature fields from a small amount of low-dimensional observations, and is compatible with subsequent defect feature extraction and automatic identification. Thus, the data acquisition and transmission pressure is effectively reduced, and the online detection real-time performance and robustness are improved. The present embodiment will be described in detail below with reference to the accompanying drawings. Figures 1 to 6 The scheme of the present embodiment will be described in detail.

[0067] Through the D2Q9 discrete velocity model, the collision and migration (moving the distribution function along the velocity direction) of the multi-relaxation-time lattice Boltzmann method is used to numerically solve the two-dimensional heat diffusion equation. In the two-dimensional case, the steady-state or transient heat diffusion / heat conduction equation can be written as:

[0068] ,

[0069] wherein T is the temperature field, x is the position, t is the time, D is the thermal diffusivity, denotes the Laplacian operator.

[0070] Conventional finite difference, finite element or finite volume methods discretize this partial differential equation directly. The multirelaxation time lattice Boltzmann method, on the other hand, solves the problem by constructing a discrete velocity Boltzmann equation equivalent to the original one, using the idea of "collision + migration". To simulate heat diffusion, only the distribution function of the "scalar field", i.e. the temperature field, is needed. Therefore, as shown in FIG. 1, the D2Q9 model of the lattice Boltzmann method can be used to discretize the velocity space: Figure 1

[0071] The D2Q9 model discretizes the distribution function on a planar grid into 9 velocity directions wherein , , , , , , , , , The direction of rest, and the remaining 8 directions cover the 8 neighboring grid points around. The distribution function in the velocity direction is denoted as , which represents the temperature quantity carried on the discrete velocity, and the macroscopic temperature field of the D2Q9 model can be obtained by the following formula:

[0072] .

[0073] When calculating the equilibrium distribution, there is a weight coefficient corresponding to each velocity direction . In the D2Q9 model , , Through the above triple discretization of velocity direction + grid + time step, the lattice Boltzmann method can only store a limited number of distribution functions at each grid point for updating, without having to integrate on the continuous velocity space. The multirelaxation time lattice Boltzmann method assigns different relaxation rates to different modes in the "moment / modal space", thereby improving numerical stability and physical accuracy.

[0074] First, the velocity space distribution vector is projected to the modal space by a linear transformation matrix to obtain the modal space distribution vector , wherein the transformation matrix​ is denoted as:

[0075] .

[0076] Then, the diagonal relaxation matrix is relaxed for each mode separately.

[0077] where the diagonal relaxation matrix is denoted as: .

[0078] The core process of solving heat diffusion by LBM includes collision and streaming. The collision process is denoted as:

[0079] ,

[0080] where, The post-collision modal space distribution vector, equilibrium modal is determined by D2Q9 weight coefficients and the temperature field, i.e. the distribution of each discrete direction is proportional to the macroscopic temperature of the point is allocated to different directions by weight coefficients .

[0081] Finally, the post-collision distribution is transformed back to the velocity space and streaming is completed through the post-streaming velocity space distribution vector .

[0082] ,

[0083] where, is the time interval.

[0084] The thermal diffusion coefficient under non-dimensionalization or specific lattice scale generally exists an approximate relationship:

[0085] ,

[0086] where, is the sound speed of the lattice model, which is mostly taken as = 1 / 3 (dimensionless). When the relaxation rate related to thermal diffusion satisfies the relationship in the formula, the obtained macroscopic temperature evolution equation is exactly the heat diffusion equation.

[0087] The new distribution function after streaming is obtained for the next collision.

[0088] In summary, the LBM method is used, i.e. through collision and streaming, iteration is continuously carried out, and the temperature field is simulated from the initial time to a specified time evolution process. In order to make the numerical simulation consistent with the actual physical background, appropriate boundary conditions need to be set. In this embodiment, only the hotspot heat map is intercepted for calculation for the convenience of calculation and observation, so periodic boundary is used for processing.

[0089] Pure data-driven can efficiently extract the main modal of thermal field from a small amount of sampling data, but it ignores the physical evolution rule of heat diffusion. Pure physical driving can ensure physical consistency, but it is computationally intensive and insufficient in representing the details of the whole frame. The idea of this embodiment is: first, reduce the three-dimensional thermal field to low rank by Tucker decomposition, and then optimize the low-dimensional core tensor, saving a lot of calculation. Then, through the multi-relaxation time lattice Boltzmann operator, the heat diffusion physical constraint is imposed on each time modal, and the reconstruction result not only conforms to the sampling data, but also follows the heat diffusion dynamics. Finally, using the Adam optimizer, the core tensor gradually approaches the solution that satisfies the physical law under controllable iteration times and convergence criteria. The flow chart of the algorithm is shown in Figure 2 .

[0090] According to Figure 2 the thermal image sequence downsampling reconstruction method based on core tensor space physical constraint, the original infrared image sequence is obtained by detecting the glass fiber plate preform defect by active infrared thermal imaging method, and then the original infrared image sequence under different sampling rates is reconstructed by using the method described in this embodiment. The reconstructed image sequence is processed by phase locking and fractional Fourier to obtain an infrared feature map.

[0091] Step one: before the method starts, parameters including material thermal diffusion coefficient , lattice Boltzmann method heat diffusion evolution step, TV regularization coefficient , the number of iterations of overall optimization, initial learning rate, learning rate decay coefficient, etc. need to be set.

[0092] In this embodiment, the material thermal diffusion coefficient of the glass fiber plate is set to 1.15×10-7m2 / s, the LBM heat diffusion evolution step is set to 10, the TV regularization coefficient is set to 1×10-4, the number of iterations of overall optimization is set to 200 times, the initial learning rate is 0.5, and the learning rate decay coefficient is 0.98.

[0093] Step two: the original infrared image sequence contains all the spatiotemporal temperature data, so the original infrared image sequence can be represented as a third-order tensor , and the mean field is calculated.

[0094] Set For the sampling frame index set, there are:

[0095] ,

[0096] ,

[0097] where, , represents the image pixel point position, is the image frame number, , the position of the pixel point in the tensor, the first frame corresponding time, and respectively represent the rows and columns of the original infrared image sequence, represent the time dimension of the original infrared image sequence.

[0098] Step three: standardize each pixel to zero mean and unit scale, unify the dynamic dimension of different pixels, and avoid the dominance of some high-energy pixels in decomposition. Center the infrared image sequence data and generate a centralized tensor :

[0099] ,

[0100] where, the intermediate variable , represents the standard deviation.

[0101] Step four: Tucker decomposition can express as the modular product of the core tensor and three sets of factor matrices:

[0102] ,

[0103] where, is the core tensor, , , respectively represent the row direction, column direction, and frame sequence direction of the core tensor. The factor matrix , , is the orthogonal basis corresponding to the row, column, and time sequence direction, and respectively represent the pixel position in the row and column direction of the infrared image sequence, represent the frame number of the infrared image sequence.

[0104] Step five: in order to realize the multi-relaxation time lattice Boltzmann constraint, the The model is decomposed into several "time mode + spatial shape" interpretable blocks, which facilitates the application of physical constraints and gradient return per mode. The core tensor is unfolded in time mode, and given the core tensor slice of the th time mode , the corresponding spatial reconstruction field can be expressed as:

[0105] .

[0106] Step six: normalize the above as the initial temperature field to match the LBM numerical stability domain; change the spatial slice of the tensor reconstruction into an LBM initial state distribution function that can be evolved by diffusion :

[0107] ,

[0108] wherein is the D2Q9 model weight.

[0109] Step seven: use the lattice Boltzmann method to make the above collision and migration to obtain the final state distribution function , and the physical evolution field is expressed as:

[0110] .

[0111] Step eight: calculate the difference between the spatial reconstruction field and the physical evolution field, i.e., the residual of the violation of the heat diffusion equation ,

[0112] .

[0113] If the reconstruction field completely conforms to the diffusion physics, then . Therefore, can be used as a measure of hard physical constraints to punish components that do not conform to the heat diffusion law (e.g., over-smoothing or non-physical oscillation).

[0114] Step nine: to realize the optimization of the core tensor gradient, project the residual to the position of the core tensor , and the loss function is defined as:

[0115] ,

[0116] , wherein represents the position index of the core tensor , ​​, core tensor slice The gradient of the core tensor is expressed as:

[0117] ,

[0118] The above formula is written in matrix form as:

[0119] ,

[0120] wherein, is the gradient of the core tensor .

[0121] Step ten: optimize the core tensor using Adam, gradually approaching the solution that meets the physical law, and obtain by gradient accumulation:

[0122] ,

[0123] ,

[0124] wherein, is the first moment accumulation, is the second moment accumulation, =0.9 is the first moment decay factor, =0.999 is the second moment decay factor.

[0125] Bias correction can be obtained:

[0126] ,

[0127] ,

[0128] wherein, is the first moment after bias correction, is the second moment after bias correction.

[0129] The tensor is updated to obtain:

[0130] ,

[0131] wherein, is the learning rate, is a constant to prevent division by zero, which is taken as 10-8 in the embodiment.

[0132] Step eleven: repeat the above steps seven to ten until the following convergence condition is met:

[0133] ,

[0134] wherein, is the iteration threshold, represents the norm.

[0135] If the maximum number of iterations has been reached or the convergence criterion is met, the algorithm iteration ends.

[0136] Step twelve: visualize and output the reconstruction result The final reconstructed thermal image sequence is saved and fed into downstream feature extraction algorithms to show the defect region feature map. Compared with the original image sequence, the effect of down-sampling reconstruction is evaluated, and the accuracy of defect detection and positioning is confirmed.

[0137] Figure 3 and Figure 4 are respectively the comparison results of different sampling rates of the reconstructed glass fiber plate preform defect infrared image sequence under sinusoidal excitation and chirp excitation. Figure 5 is the comparison result of different sampling rates of the glass fiber plate preform defect infrared feature map.

[0138] The reconstruction strategy of this embodiment introduces an explicit thermal diffusion physical constraint in the core tensor space, which can recover a continuous and high-precision spatiotemporal temperature field from a small amount 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 thermal image sequence down-sampling reconstruction method based on the core tensor space physical constraint in the present application realizes the closed-loop coupling of “reconstruction-physical evolution-residual back projection” in the core tensor space by embedding the differentiable multi-relaxation time lattice Boltzmann thermal diffusion projection into the Tucker decomposition optimization, which can recover a high-fidelity spatiotemporal temperature field under only partial time sequence frame observation, and at the same time maintain the consistency of the observation data and thermal diffusion dynamics; gradually using adaptive update of the core tensor gradient and repeated projection of the physical constraint, effectively suppressing non-physical oscillation and edge oversmoothing, reducing the amplitude-phase deviation, so that a high peak signal-to-noise ratio / structural similarity and stable defect signal-to-noise ratio can still be obtained under very low sampling rate (such as 5%-10%), and the natural compatibility with downstream feature extraction algorithms such as phase locking and fractional Fourier is maintained, thereby significantly reducing the acquisition bandwidth and storage pressure, and improving the real-time performance of online detection. These advantages make the thermal image sequence down-sampling reconstruction method based on the core tensor space physical constraint exhibit strong adaptability and accuracy in the face of complex environments, non-uniform excitation (sinusoidal / chirp, etc.), various boundary conditions and various materials, overcoming the limitations of traditional methods in cross-sampling rate generalization and boundary sensitivity, and enabling rapid and high-precision detection of active infrared thermography for composite material delamination / debonding, coating defects, electronic device thermal anomalies and aerospace components. The present application is suitable for precise non-destructive testing and condition evaluation of defects / damages in the fields of aerospace composites and microelectronic devices.

[0140] While the application has been described with reference to particular embodiments thereof, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present application. It will thus be appreciated that numerous modifications can be made to the illustrative embodiments and that other arrangements can be devised without departing from the spirit and scope of the present application as defined by the appended claims. It is intended that the scope of the present application extends to all such modifications and arrangements. It is to be understood that the use of the conjunctive "and" and the conjunctive "or" are both inclusive and not exclusive.

Claims

1. A method for heat map sequence down-sampling reconstruction based on tensor space constraints, characterized in that, The application relates to a method for reconstructing an infrared image sequence, and belongs to the technical field of infrared image reconstruction. The method comprises the following steps: obtaining a core tensor of the infrared image sequence through Tucker decomposition, and updating the core tensor until a convergence condition is met, so that the infrared image sequence is reconstructed through the updated core tensor; the step of updating the core tensor comprises: performing time mode expansion on the core tensor of the infrared image sequence, and obtaining a spatial reconstruction field in each time mode by using core tensor slices in each time mode after expansion; applying a heat diffusion physical constraint on the spatial reconstruction field in each time mode by using a lattice Boltzmann method to obtain a physical evolution field in each time mode; 2. The tensor space constraint based heat map sequence down-sampling reconstruction method of claim 1, wherein, projecting a difference between the physical evolution field in each time mode and a corresponding spatial reconstruction field to a corresponding position of the core tensor, and updating the core tensor slices through Adam optimization, and then updating the core tensor. the step of obtaining the core tensor of the infrared image sequence through Tucker decomposition comprises: representing the infrared image sequence as a three-order tensor, and calculating a mean field by using the three-order tensor; decomposing the centered tensor into a core tensor and three sets of factor matrices by Tucker decomposition a Hadamard product, and thereby obtaining the core tensor.

3. The tensor space constraint based heat map sequence down-sampling reconstruction method of claim 1, wherein, centralizing and normalizing the infrared image sequence by using the three-order tensor and the mean field to obtain a centralization tensor; the step of obtaining the spatial reconstruction field in each time mode by using the core tensor slices in each time mode after expansion comprises: ， wherein, is the spatially reconstructed field for the th time instance, is the core tensor slice for the th time instance, and are factor matrices.

4. The tensor space constraint based heat map sequence down-sampling reconstruction method of claim 1, wherein, the spatial reconstruction field in each time mode is obtained through the following formula: the step of applying the heat diffusion physical constraint on the spatial reconstruction field in each time mode by using the lattice Boltzmann method to obtain the physical evolution field in each time mode comprises: constructing an initial state distribution function by using the spatial reconstruction field in each time mode; obtaining a final state distribution function by using the lattice Boltzmann method to perform collision and migration on the initial state distribution function; 5. The tensor space constraint based heat map sequence down-sampling reconstruction method according to claim 4, wherein, obtaining the physical evolution field based on the final state distribution function. the step of constructing the initial state distribution function by using the spatial reconstruction field in each time mode comprises: ， wherein is the initial distribution function for the discrete direction in the lattice Boltzmann method, is the spatial reconstruction field under the time mode, is the weight for the discrete direction.

6. The tensor space constraint based heat map sequence down-sampling reconstruction method according to claim 5, wherein, constructing the initial state distribution function according to the following formula: the step of obtaining the physical evolution field based on the final state distribution function comprises: ， wherein, is a physical evolution field, is a terminal distribution function in the discrete direction of the lattice Boltzmann method, is a number of collision and migration steps in the lattice Boltzmann method.

7. The tensor space constraint based heat map sequence down-sampling reconstruction method of claim 1, wherein, obtaining the physical evolution field according to the following formula: the step of projecting the difference between the physical evolution field in each time mode and the corresponding spatial reconstruction field to the corresponding position of the core tensor comprises: ， wherein, is a loss function, the expression is , is the core tensor slice in the th temporal modality, denotes the position index of the core tensor , and are factor matrices, is the difference between the physical evolution field and the corresponding spatial reconstruction field in the th temporal modality, and denote the pixel positions in the row and column directions of the infrared image sequence, respectively, , .

8. The tensor space constraint based heat map sequence down-sampling reconstruction method of claim 7, wherein, projecting the difference between the physical evolution field in each time mode and the corresponding spatial reconstruction field to the corresponding position of the core tensor through the following formula: the step of updating the core tensor slices through Adam optimization, and then updating the core tensor comprises: writing the projection result in a matrix form, and obtaining a first moment accumulation and a second moment accumulation through gradient accumulation; 9. The tensor space constraint based heat map sequence down-sampling reconstruction method of claim 8, wherein, performing bias correction on the first moment accumulation and the second moment accumulation, and updating the core tensor slices by using the correction result. the step of obtaining the first moment accumulation and the second moment accumulation through gradient accumulation comprises: ， ， wherein, is the gradient of the core tensor slice at the th time modality, and are the first and second order moment accumulations, respectively, and are the first and second order moment decay factors, respectively. obtaining the first moment accumulation and the second moment accumulation according to the following formula: ， ， wherein, and are the first and second order cumulants after bias correction, respectively. performing bias correction on the first moment accumulation and the second moment accumulation according to the following formula: ， where, is the learning rate, is a constant to prevent division by zero, and are the core tensor slices in the and time modalities, respectively.

10. The tensor space constraint based heat map sequence down-sampling reconstruction method of claim 1, wherein, updating the core tensor slices according to the following formula: the convergence condition comprises: ， wherein, is an iteration threshold, denotes a norm, and are core tensor slices in the first and time modalities, respectively.

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