An adaptive reconstruction method for laser absorption spectroscopy tomography

Abstract

This invention proposes an adaptive reconstruction method for laser absorption spectral tomography images. The absorptivity distribution is represented as a linear combination of B-spline basis functions in polar coordinates. A piecewise density function is constructed based on the radial gradient of the absorptivity, determining the number of nodes to be assigned radially, with the nodes uniformly distributed circumferentially. The basis function coefficients are solved to obtain the initial absorptivity distribution. Based on the uniformly distributed test points in the imaging region, the absorptivity gradient and curvature at each test point are calculated, and a weighted summation index is constructed. If the value of this index near any node exceeds a threshold, a new node is inserted radially and circumferentially at that node, and the basis function coefficients are recalculated to update the absorptivity distribution. This process is repeated until the maximum number of control points is reached or the reconstruction error is less than a set value, at which point the imaging result is output. This invention, through dynamic optimization of node configuration, can significantly improve the imaging accuracy and resolution of flame temperature, and has important application value in the field of combustion diagnostics.

Description

Technical Field

[0001] This invention belongs to the field of laser absorption spectral tomography imaging technology, specifically relating to an adaptive reconstruction method for laser absorption spectral tomography images. It is particularly suitable for the inversion of flame field parameters with radial gradient characteristics, and can significantly improve the imaging accuracy and resolution of component concentration in flame temperature, which has important application value in the field of combustion diagnosis. Background Technology

[0002] Combustion diagnostic technology aims to monitor and analyze key parameters during the combustion process, enabling real-time optimization and adjustment. The combustion process affects major parameters such as the temperature of the air surrounding the flame and the concentration of gas components. Therefore, measuring the temperature of the gas around the flame and the concentration of major components is an important means of monitoring the combustion process. In recent years, with the emergence and continuous development of tunable diode laser absorption spectroscopy (TDLAS), its wide measurement range, high sensitivity, and non-invasive nature have demonstrated its applicability in combustion measurement. By measuring the absorption attenuation of the laser after passing through the test field, the absorptivity can be inferred, and then key parameters such as temperature and component concentration can be calculated. When combined with multi-angle projection measurements, tunable diode laser absorption tomography (TDLAT) technology can reconstruct two-dimensional / three-dimensional field distributions, providing a visual reference for the analysis and diagnosis of the combustion process.

[0003] Image reconstruction methods in laser absorption spectroscopy tomography can be mainly divided into two categories: analytical reconstruction methods and iterative reconstruction methods. Analytical reconstruction methods utilize absorption spectral data with complete projection angles to achieve high-precision image reconstruction. Typical algorithms include inverse Abel transform and filtered back projection (FBP). For axisymmetric flames, Villarreal et al., in their paper "Frequency-Resolved Absorption Tomography with Tunable Diode Lasers" published in *Applied Optics*, Vol. 44, No. 31, pp. 6786-6795, used inverse Abel transform to reconstruct the temperature distribution and carbon dioxide mole fraction distribution of a flat-flame combustion furnace, achieving a spatial resolution of 1.56 mm × 1.56 mm. To obtain complete projection data, they used a movable platform to translate the flat-flame combustion furnace, allowing the laser to pass through different positions of the flame, thus resulting in a lower temporal resolution. For non-axisymmetric flames, Busa et al., in their paper "Demonstration of Capability of Water Flux Measurement in a Scramjet Combustor using Tunable Diode Laser Absorption Tomography and Stereoscopic PIV" published at the 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, collected projection data of 1800 laser paths at 72 projection angles over nearly one hour using a rotating fan-shaped laser beam. They then used the FBP algorithm to invert the two-dimensional distribution of temperature and water vapor concentration at the exit of the supersonic combustion tunnel. However, this measurement scheme was too time-consuming and unsuitable for dynamic monitoring of the combustion field. Furthermore, in harsh physical environments such as combustion diagnostics, the optical access window is severely limited, resulting in sparse and finite-angle projection data. This leads to severe fringe artifacts and distortion in the reconstruction results of analytical reconstruction methods under sparse projection.

[0004] In contrast, iterative reconstruction methods transform the image reconstruction process of laser absorption spectroscopy tomography into an iterative solution of a system of equations. This allows them to handle underdetermined equations and, even when the number of beams is far less than the number of reconstruction grids, they can still obtain physically reasonable approximate solutions. Depending on the solution strategy, iterative methods can be divided into nonlinear and linear methods. Nonlinear methods are directly based on the radiative transfer physical model of TDLAS (such as the temperature-concentration coupling relationship of Beer-Lambert's law), directly reconstructing the temperature and concentration fields through optimization algorithms. Theoretically, these methods have the highest accuracy, but they are computationally complex, have difficulty guaranteeing convergence, and are sensitive to initial conditions. Linear methods, on the other hand, first locally linearize the physical model, discretize the region to be reconstructed into a grid, and express the absorption coefficient as a linear combination of grid values, thus transforming the problem into solving a system of linear equations. Then, an iterative algorithm is used to solve the problem. This type of method is computationally efficient and relatively simple to implement. Typical linear iterative reconstruction algorithms include the Tikhonov regularization method, the Landweber algorithm, the Algebraic Reconstruction Technique (ART), and the Simultaneous Algebraic Reconstruction Technique (SART). In their paper "Tomographic Imaging of Carbon Dioxide in the Exhaust Plume of Large Commercial Aero-Engines," published in *Applied Optics*, Volume 61, Issue 28, pp. 8540-8552, Upadhyay et al. employed a fixed laser absorption spectral tomography sensor with 126 laser paths arranged at 6 projection angles. They reconstructed the carbon dioxide distribution of the aero-engine exhaust plume using the Tikhonov regularization method and the Landweber algorithm, achieving an imaging frame rate of 1.25 fps and a spatial resolution of approximately 60 mm × 60 mm. In their paper "Simultaneous Measurement of 2-Dimensional H2O Concentration and Temperature Distribution in Premixed Methane / Air Flame using TDLAS-Based Tomography Technology" published in Optics Communications, Volume 346, pp. 53-63, Wang et al. designed a fixed laser absorption spectral tomography sensor with 24 laser paths across 4 projection angles. They used the ART algorithm to reconstruct the 2D distribution of flame temperature and water molecule concentration, achieving a temporal resolution of 1 ms, but a spatial resolution of only 4 pixels × 4 pixels.In their paper "A WMS-Based TDLAS Tomographic System for Distribution Retrievals of Both Gas Concentration and Temperature in Dynamic Flames," published in IEEE Sensors Journal, Volume 20, Issue 8, pp. 4179-4188, Zhao et al. used a fixed five-angle fan-beam laser absorption tomography sensor and the SART algorithm to reconstruct the two-dimensional distributions of temperature and water molecule concentration at the outlet of a flat-flame combustion furnace and a wind tunnel. The sensor employs a time-division multiplexing laser control strategy to measure 120 projections, achieving an imaging frame rate of up to 500 fps and a spatial resolution of 30 pixels × 30 pixels. This demonstrates that iterative reconstruction methods are suitable for image reconstruction using fixed laser absorption tomography sensors with a limited number of projections, facilitating higher temporal resolution and meeting the dynamic monitoring needs of complex combustion fields. However, due to the limited number of available projections, the equations to be solved in iterative reconstruction methods are often ill-conditioned and underdetermined. Because measurement information is insufficient to uniquely determine all grid values, the solution space contains infinitely many sets of equations satisfying the distribution of the measurement data. Furthermore, minute measurement noise can be drastically amplified, leading to distorted reconstruction results. To address the ill-conditioned nature of linear iterative reconstruction, researchers primarily employ two approaches: incorporating prior information constraints and reducing the number of unknowns.

[0005] The core idea of ​​incorporating prior information constraints is to introduce additional physical or statistical constraints during the iterative solution process, and to limit the solution space to a subset that conforms to prior knowledge through regularization strategies. Si et al., in their paper "Two-Step TDLAS Tomographic Reconstruction for Temperature Imaging" published at the 2022 IEEE International Instrumentation and Measurement Technology Conference, proposed a two-step TDLAS tomographic reconstruction method. The first step, based on the prior information that the flow field parameter distribution has smoothness, uses Tikhonov regularization to achieve smoothness constraints. The second step uses the absorbance distribution reconstructed in the first step to reproject, calculates the residual between it and the original measurement data, and thus recovers details. This method can solve the problem of image detail loss and obvious artifacts caused by global smoothness constraints in traditional single-step iterative algorithms under sparse projection. However, the trade-off between smoothness and detail depends on empirical parameters and lacks adaptability to the multi-scale characteristics of complex flow fields. In their paper "Acoustic Tomography of Two Dimensional Velocity Field by Using Meshless Radial Basis Function and Modified Tikhonov Regularization Method," published in *Measurement*, Volume 175, pages 109-107, Zhang et al. designed a new regularization matrix by utilizing prior information about the local continuity of the flow field in physical space. Each row of this matrix corresponds to an unknown parameter (such as a velocity component coefficient), and its construction rule forces the minimization of the difference between the value at a given point and the weighted average of its neighboring values. This is equivalent to adding a constraint term to the objective function that "the difference between adjacent points should be small." While this method is intuitive and physically grounded, for cases where the distribution is discontinuous, forcibly smoothing sharp features may lead to blurred reconstructions.

[0006] One method to reduce the number of unknowns is to represent the two-dimensional distribution to be reconstructed as a linear combination of several basis functions. This transforms the high-dimensional problem of "one unknown per discrete grid" into a low-dimensional problem of "solving a small number of basis function coefficients," thereby fundamentally alleviating the underdeterminacy of the equation system. In their paper "Sparse Zernike Fitting for Dynamic LAS Tomographic Images of Temperature and Water Vapor Concentration," published in IEEE Transactions on Instrumentation and Measurement, Volume 71, page 5009314, Gao et al. used a finite number of Zernike orthogonal polynomials to fit a continuous absorbance distribution, converting the unknowns into coefficients of the Zernike polynomials, effectively reducing the number of unknowns to be solved. At a spatial resolution of 30 × 30, the image reconstruction error of the Zernike fitting method is comparable to that of the SART and Landweber algorithms. However, when the spatial resolution is increased to 70 × 70, the error of the Zernike fitting method is only one-sixth that of the two classic iterative reconstruction algorithms, achieving high spatial resolution and high accuracy image reconstruction. However, the Zernike polynomial has a relatively large fitting error for continuous asymmetric distributions. To improve the fitting accuracy of basis functions for local details of asymmetric distributions, Gao et al. published a paper titled "Radial Basis Function Coupled SART Method for Dynamic LAS Tomography" in IEEE Transactions on Instrumentation and Measurement, Volume 72, page 4500-110. This paper uses a compactly supported radial basis function to fit the absorbance distribution, converting the solution into fitting coefficients of the compactly supported radial basis function, and then uses the SART algorithm to iteratively solve for the fitting coefficient vector. Compared with the results of directly reconstructing the absorptivity distribution using the SART algorithm, this method has smaller image reconstruction errors, and the reconstruction errors do not increase with the increase of spatial resolution, effectively improving the accuracy and spatial resolution of image reconstruction.In their paper "Two-Dimensional Temperature Field Distribution Reconstruction Based on LeastSquare Method and Radial Basis Function Approximation," published in Mathematical Problems in Engineering, Volume 2017, page 1213605, Jia et al. used the least squares method to calculate the center temperature values ​​of each grid block from the time-of-flight data of acoustic waves as known points. They then used radial basis functions to fit and solve for the weight coefficients of the global distribution, ultimately reconstructing the entire two-dimensional temperature field. Compared to using least squares and radial basis functions alone, this method provides a more complete display of isotherm contour maps. In their paper "Robust Temperature and Gas Concentration Imaging by LAS Tomography with Adaptive Basis Function Fitting and Artifact Removal," published in IEEE Transactions on Instrumentation and Measurement, Volume 73, page 4505811, Zhang et al. introduced a modified Mexican hat function as the basis function. They then used a two-step adaptive optimization of the basis function parameters and utilized temperature-concentration distribution similarity to locate and remove artifacts. This demonstrates the crucial importance of constructing a basis function model that can dynamically and adaptively adjust its parameterized resolution and expressive power based on the characteristics of the flow field to be reconstructed. This allows for the simultaneous high-precision reconstruction of the global profile and local details of complex multi-scale flow fields without significantly increasing the number of unknowns.

[0007] Based on the above background, this invention proposes an adaptive reconstruction method for laser absorption spectral tomography images. The method uses B-spline basis functions to fit the absorbance distribution, sets initial non-uniform nodes based on prior information about flame distribution characteristics, and employs a least-squares asymptotic iterative approximation algorithm to solve for the control coefficients, obtaining the current reconstructed distribution. The gradient and curvature of the reconstructed distribution are normalized and then weighted and summed to construct a comprehensive index. If the maximum value of the comprehensive index exceeds a threshold within a parameter interval, a new node is inserted in that interval, achieving adaptive node refinement. Summary of the Invention

[0008] (a) Technical problems to be solved

[0009] The purpose of this invention is to provide an adaptive reconstruction method for laser absorption spectral tomography images, which addresses the problem that the limited number of laser beams that can be arranged in actual combustion equipment results in projection data that is much smaller than the number of grids to be reconstructed, leading to a highly ill-posed reconstruction problem.

[0010] (II) Technical Solution

[0011] This invention, namely an adaptive reconstruction method for laser absorption spectral tomography images, mainly includes the following steps:

[0012] Step 1: Basic Parameter Settings. Generate uniformly distributed test points in the parameter domain, calculate the sensitivity matrix, obtain the projected data vector, set the B-spline order, and set the initial control points.

[0013] In this invention, nodes refer to the boundary points that divide the parameter domain into intervals, used to construct B-spline basis functions; control points are the coefficients of the B-spline basis functions, representing unknowns to be solved; test points are discrete points regularly sampled in the parameter domain, used to discretize the continuous absorbance distribution to establish an imaging model. The relationship among the three is as follows: the absorbance values ​​at all test points are obtained by interpolating the control points using the B-spline basis functions.

[0014] Test points are evenly distributed across the parameter domain according to a rectangular grid, with radial step sizes between adjacent test points. Circumferential step length , and The numbers of test points are in the radial and circumferential directions, respectively. Therefore, the parameter coordinates of each test point are... For a discrete location in the corresponding imaging region, the first Radial parameters at each test point and circumferential parameters exist The values ​​are uniformly selected within the test point, and the physical coordinates of the test point are... Determined by polar coordinate transformation:

[0015]

[0016]

[0017] in, Normalized radial parameters and circumferential parameters for:

[0018]

[0019] in, is the radius of the circular region of interest, and all test points are within the circular region.

[0020] From the sensitivity matrix and the projected data vector, the absorptivity distribution can be obtained. The model for laser absorption spectral tomography is as follows:

[0021]

[0022] in, yes The sensitivity matrix is ​​calculated based on the optical path layout of the laser absorption spectroscopy tomography sensor and the physical region division corresponding to the test points in the reconstructed image. elements in Indicates the first The projected light rays are at the first Each test point corresponds to a length within the physical region. Indicates the total number of projected rays. This represents the total number of test points in the reconstructed image, satisfying... , yes The 3D projection data vector is obtained by measuring a laser absorption spectroscopy tomography sensor. yes The absorption rate distribution of the dimension.

[0023] Step 2: Generate the initial absorptivity distribution. In the radial parameter direction, construct a piecewise constant density function based on the radial gradient distribution characteristics of the region to be measured. This results in dense nodes in the central region and sparse nodes in the peripheral region; the radial parameter range is... The area is divided into a central area, a transition area, and an outer area, with the boundaries of each area defined as follows: and ,satisfy Density function for:

[0024]

[0025] Wherein, the density function values ​​satisfy The higher the density value, the denser the nodes in the region. The density value can be customized based on the distribution characteristics. In this invention, a node refers to a location point in the parameter domain, used to divide the parameter interval. The node vector determines the support range of the basis function. Based on the density function, the number of internal nodes to be arranged in each region is determined, and the total number of radial internal nodes is:

[0026]

[0027] in, Number of radial control points Given the B-spline order, the number of nodes in each region is distributed proportionally as follows:

[0028]

[0029] in, , , These represent the number of nodes allocated to the central area, transition area, and outer area, respectively, and satisfy the following conditions: The nodes are evenly distributed in the central area, transition area, and outer area, and their locations are as follows: , and :

[0030]

[0031]

[0032]

[0033] All internal nodes are arranged in ascending order to form a radial internal node vector. To satisfy the endpoint requirements of the B-spline basis function, the radial node vector is repeated at both ends. It is formed by concatenating the secondary boundary value and the internal node:

[0034]

[0035] Circumferential parameters The direction uses a uniform node vector, and the number of circumferential control points is [number missing]. Then the uniform node vector is:

[0036]

[0037] Based on the generated node vectors and the set B-spline order Construct the basis function matrix For the first There are test points, and their parameter coordinates are: Its corresponding basis function value is:

[0038]

[0039] Here, the control points are the coefficients corresponding to the B-spline basis functions, and their number is equal to the number of basis functions. , B-spline basis functions Defined by the Cox-de Boor recurrence relation:

[0040] when hour:

[0041]

[0042] when hour:

[0043]

[0044] in, For the first node in the node vector For nodes, at the boundary, when At that time, only the first basis function Other basis functions , …, All are 0; when At that time, there is only the last basis function. Other basis functions , .

[0045] Based on the continuous nature of the absorptivity distribution, the absorptivity distribution... It can be represented by a linear combination of B-spline basis functions:

[0046]

[0047] in, For the basis function matrix, Let be the control point to be solved, and let and will Substitute into the formula The imaging model is transformed into:

[0048]

[0049] Solving for the absorptivity distribution in dimensionality is transformed into finding control points. The solution is obtained using a least-squares asymptotic iterative approximation algorithm with non-negativity constraints:

[0050]

[0051] Where λk is the step size.

[0052] Step 3: Implement adaptive node refinement, calculate the weighted sum of gradient magnitude and curvature of the current reconstructed projection, and construct a comprehensive index.

[0053] The Sobel operator is used to compute discrete gradients, and its convolution kernel is defined as follows:

[0054]

[0055] Preliminary reconstruction results can be obtained from the initial nodes. The current reconstruction absorption rate distribution is as follows: , No. Center coordinates of each test point The test points are arranged in a regular rectangle in the physical domain, with a number of rows. , number of columns The spacing between adjacent test points is constant. The Sobel operator is used to calculate the gradient magnitude at each test point. Gradient components are calculated via convolution:

[0056]

[0057]

[0058] The gradient magnitude for each test is then:

[0059]

[0060] A larger gradient magnitude indicates a more drastic change in the region. Curvature is also added as a supplementary indicator, approximating curvature using the Laplacian operator, which measures the degree of local bending through the sum of second-order differences.

[0061]

[0062] The gradient magnitude and curvature are integrated into a unified and refined evaluation metric, using weighted coefficients. To balance the contributions of both, the gradient magnitude and curvature are normalized, and then a weighted sum is performed:

[0063]

[0064] in, This is the curvature weighting coefficient, with a value range of... This is used to balance the contributions of gradient and curvature to refinement.

[0065] Radial node vector Repeated from both ends The secondary boundary value is concatenated with the internal node, and extracted. All distinct node values ​​in the array, sorted in ascending order. Then the radial parameter interval formed by the two nodes is Similarly, extract the circumferential node vector. All distinct node values ​​in the array, sorted in ascending order. Then the radial parameter interval formed by the two nodes is For each test point Its parameter coordinates are The comprehensive index is ,according to The test points are grouped according to the interval, the first... All test points in the radial interval The maximum value is If there are no test points within the interval, then Similarly, according to The test points are grouped according to the interval, the first... All test points in the circumferential interval The maximum value is Set the threshold coefficient as , Then the thresholds for the radial and circumferential directions are respectively:

[0066]

[0067]

[0068] For each radial interval ,like Then the midpoint of that interval Insert a new radial node at the specified location; for each circumferential interval ,like Then the midpoint of that interval Insert a new circumferential node at the specified location.

[0069] Merge the newly retained nodes after filtering into the current radial node vector. and circumferential node vector And keep the nodes repeating at both ends. The secondary boundary value is used to reconstruct the B-spline basis function matrix using the updated node vectors. Update system matrix Resolve for control points A new absorption rate distribution was obtained. Repeat the above process of adaptive encryption of nodes and generation of new absorption rate distribution until the total number of control points reaches the preset upper limit or the projection residual is less than the set minimum value, then stop the iteration and output the absorption rate distribution result.

[0070] Beneficial effects

[0071] The beneficial effects of this invention lie in proposing an adaptive reconstruction method for laser absorption spectral tomography images. The absorption rate representation is transformed from pixel-by-pixel discretization to B-spline coefficient solving, significantly reducing the dimensionality of unknowns and improving the ill-conditioned nature of the problem. After setting non-uniform initial nodes using prior knowledge, gradient refinement is employed to achieve further adaptive node arrangement, making the node distribution more consistent with the reconstruction distribution and further improving reconstruction accuracy. Attached Figure Description

[0072] Appendix Figure 1 Flowchart of an adaptive reconstruction method for laser absorption spectral tomography images

[0073] Appendix Figure 2 Schematic diagram of the beam layout of a laser absorption spectroscopy tomography sensor.

[0074] Appendix Figure 3 The original distribution of temperature

[0075] Appendix Figure 4 The original distribution of water molecule mole fraction

[0076] Appendix Figure 5 Temperature reconstruction image

[0077] Appendix Figure 6 Reconstructed image of water molecule mole fraction

[0078] Detailed Implementation

[0079] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described below in conjunction with specific embodiments and with reference to the accompanying drawings.

[0080] This example demonstrates image reconstruction based on the principle of laser absorption spectroscopy tomography, employing an adaptive B-spline-based laser absorption spectroscopy tomography image reconstruction method. A schematic diagram of the beam layout of the laser absorption spectroscopy tomography sensor used in this example is attached. Figure 2 As shown in the diagram. The sensor uses a regular pentagonal frame, with five sector-shaped laser sources arranged at the vertices of the pentagon. Twelve detectors are evenly spaced between each pair of adjacent laser sources. The laser emitted from each sector-shaped laser source can be received by 24 detectors on the opposite side, generating a total of 120 projection fibers, i.e., M=120. The number of test points is set to 2500, i.e., N=2500. The setup is shown in the attached diagram. Figure 3 and attached Figure 4 The original distribution of temperature and water molecule mole fraction is shown in a set of circles.

[0081] This example uses a center wavenumber of 7185.6 cm⁻¹. -1 and 7444.4cm -1 Two water molecule absorption lines were observed, and the temperature and water molecule mole fraction were reconstructed using the colorimetric principle.

[0082] The specific implementation steps of the image reconstruction process are as follows:

[0083] Step 1: Basic parameter settings.

[0084] This includes calculating the sensitivity matrix, obtaining the projected data vector, setting the B-spline order, and setting the initial control points;

[0085] Based on the optical path layout of the laser absorption spectroscopy tomography sensor and the mesh division of the reconstructed image, calculate dimensional sensitivity matrix Based on the principle of laser absorption spectroscopy, using the wavelength modulation method, the projected values ​​of the normalized second harmonic peaks of the two spectral lines along each laser path are calculated from the original distributions of temperature and water molecule concentration. dimensional projected data vector Set the order of the B-spline. ,set up Initial number of control points for direction , Initial number of control points for direction .

[0086] Step 2: Generate non-uniform initial nodes to initially reconstruct the absorption rate distribution.

[0087] A non-uniform node distribution is adopted in the radial direction to achieve a priori adaptive distribution of "dense at the center and sparse at the edges". Based on the characteristics of the flame radial gradient distribution, the radial parameter range is defined. The area is divided into a central area, a transition area, and an outer area, with the boundaries of each area defined as follows: and ,satisfy Density function for:

[0088]

[0089] The total number of radial internal nodes is calculated to be 8. The number of internal nodes in each region is allocated according to the density ratio: 1 node in the central region, 5 nodes in the transition region, and 2 nodes in the outer region.

[0090] Based on the node vectors generated by the above settings and the set B-spline order... Construct the basis function matrix After multiplying it by the sensitivity matrix A, we obtain matrix H. Then, we use a least-squares asymptotic iterative approximation algorithm with non-negativity constraints to iteratively solve for the control coefficient vector. When the projection residual is less than 10 -8 If the number of control points exceeds 500, the iteration will terminate.

[0091] Step 3: Adaptively add nodes.

[0092] The Sobel operator is used to calculate the discrete gradient and curvature of the absorbance at each test point, and a comprehensive index is constructed. In this example, the curvature weighting coefficient is used. The maximum value of the comprehensive index within each parameter interval is calculated in both the radial and circumferential directions. If the value exceeds the threshold, a new node is inserted at the midpoint of that interval, the node vector is updated, and the above steps are repeated until the convergence condition is met, outputting the final control coefficient vector. The obtained control coefficient vector is then substituted into the imaging model to obtain the final absorbance distribution, and the temperature concentration distribution is calculated using the dual-wavelength reconstruction results. The calculated temperature distribution is shown in the attached figure. Figure 5 As shown in the attached image, the reconstructed image of the mole fraction of water molecules is... Figure 6 As shown. (Using...) The original distribution of temperature or mole fraction of water molecules is represented by... The image reconstruction error is defined as follows: (This refers to an image reconstructed from temperature or the mole fraction of water molecules.) The original distribution is discretized into a 50×50 grid. The absorbance at 50×50 test points in the reconstructed absorbance distribution in this example is compared with the absorbance of the original 50×50 grid for error calculation. The calculated results are attached... Figure 5 The image reconstruction error of the corresponding temperature-reconstructed image is 0.0524. Figure 6 The image reconstruction error for the corresponding water molecule mole fraction reconstruction image is 0.0764. Under the same conditions, using the joint algebraic reconstruction algorithm, the image reconstruction error for temperature is 0.2505, and the image reconstruction error for water molecule mole fraction is 0.2311. It is evident that, compared to the classic joint algebraic reconstruction algorithm, the image reconstruction method proposed in this invention effectively reduces the image reconstruction error.

[0093] The above description of the present invention and its embodiments is not limited thereto, and the accompanying drawings are only one embodiment of the present invention. Any structure or embodiment similar to this technical solution designed without departing from the spirit of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method of adaptive reconstruction of laser absorption spectroscopy tomograms, characterized in that, The absorptivity distribution of the region under test is represented as a linear combination of B-spline basis functions in the polar coordinate parameter domain. Control points are used as unknowns to replace the traditional grid-by-grid absorptivity solution, thus reducing the problem dimensionality. A piecewise density function is constructed radially based on flame gradient characteristics, and the number of radial nodes is allocated according to the density ratio. Circumferential nodes are uniformly distributed to obtain initial B-spline nodes. Then, a B-spline basis function matrix is ​​constructed based on the current nodes, and control points are solved using projection data to obtain the initial reconstructed distribution. Based on the uniformly distributed test points in the imaging region, the absorptivity gradient and curvature at each test point are calculated, and a weighted summation index is constructed. The node vector divides the radial and circumferential parameters into multiple intervals. The maximum value of the comprehensive index for all test points within each interval is taken. If this maximum value exceeds a set threshold, a new control point is inserted at the midpoint of that interval to achieve adaptive node densification. The node vector is updated, the threshold is increased, and the control points and absorptivity distribution are resolved. Finally, the above solution and densification steps are repeated until the maximum number of control points is reached or the projection residual is less than a set value. The reconstruction result at this point is output, yielding the final absorptivity distribution imaging result. The method is implemented according to the following steps: Step 1: Basic parameter settings; Generate uniformly distributed test points in the parameter domain, calculate the sensitivity matrix, obtain the projected data vector, set the B-spline order, and set the initial control points; Test points are evenly distributed across the parameter domain according to a rectangular grid, with radial step sizes between adjacent test points. Circumferential step length , and The numbers of test points are in the radial and circumferential directions, respectively. Therefore, the parameter coordinates of each test point are... For a discrete location in the corresponding imaging region, the first Radial parameters at each test point and circumferential parameters exist The values ​​are uniformly selected within the test point, and the physical coordinates of the test point are... Determined by polar coordinate transformation: wherein , a normalized radial parameter and a circumferential parameter are: wherein, R is the radius of the circular region of interest, all test points being within the circular region; From the sensitivity matrix and the projected data vector, the absorptivity distribution can be obtained. The model for laser absorption spectral tomography is as follows: in, yes The sensitivity matrix is ​​calculated based on the optical path layout of the laser absorption spectroscopy tomography sensor and the physical region division corresponding to the test points in the reconstructed image. elements in Indicates the first The projected light rays are at the first Each test point corresponds to the length of the physical region. Indicates the total number of projected rays. This represents the total number of test points in the reconstructed image, satisfying... , yes The 3D projection data vector is obtained by measuring a laser absorption spectroscopy tomography sensor. yes Absorption rate distribution in dimensionality; Step 2: Generate the initial absorptivity distribution; in the radial parameter direction, construct a piecewise constant density function based on the radial gradient distribution characteristics of the region to be measured. This results in dense nodes in the central region and sparse nodes in the peripheral region; uniformly distributed nodes are generated circumferentially, based on the generated nodes and the set B-spline order. Construct the basis function matrix For the first For each test point, the corresponding basis function value is: where, and are the number of radial and circumferential control points, respectively, , , B-spline basis functions defined by the Cox-de Boor recurrence formula. When time: When Time: in, For the first node in the node vector For nodes, at the boundary, when At that time, only the first basis function Other basis functions , …, All are 0; when At that time, there is only the last basis function. Other basis functions , ; According to the continuity of the absorption rate distribution, the absorption rate distribution may be represented by a linear combination of B-spline basis functions: wherein, is a basis function matrix, is a control point to be solved, let and substitute into the formula The imaging model is converted into: Solving for the absorptivity distribution in dimensionality is transformed into finding control points. The solution is obtained using a least-squares asymptotic iterative approximation algorithm with non-negativity constraints: wherein is a step size; Step 3: Implement adaptive node refinement; calculate the weighted sum of the gradient magnitude and curvature of the current reconstructed projection, and construct a comprehensive index: in, For gradient magnitude, For curvature, The curvature weight coefficient maps the comprehensive index to the parameter domain. The maximum value of the comprehensive index in each parameter interval is calculated in the radial and circumferential directions. If it exceeds the threshold, a new node is inserted at the midpoint of the interval, the node vector is updated, and the absorptivity distribution under the current node is recalculated until the number of control points is greater than the set maximum number of control points or the projection residual meets the requirements. The final absorptivity distribution is then output, and the temperature concentration distribution is calculated using the dual-wavelength reconstruction results.

2. The adaptive reconstruction method for laser absorption spectral tomography images according to claim 1, characterized in that, The method for generating the non-uniform initial node vector in claim 1 is as follows: Based on the radial gradient distribution characteristics of the region to be measured, the radial parameter interval is determined. The area is divided into a central area, a transition area, and an outer area, with the boundaries of each area defined as follows: and ,satisfy Define the density function: Wherein, the density function value satisfies The greater the density value is, the more nodes in the region are. According to the distribution characteristics, the density value can be customized. According to the density function, the number of internal nodes arranged in each region is determined, and the total number of radial internal nodes is: wherein, the number of control points in the radial direction, is the order of B-spline, and the number of nodes in each region is distributed in proportion to: in, , , These represent the number of nodes allocated to the central area, transition area, and outer area, respectively, and satisfy the following conditions: The nodes are evenly distributed in the central area, transition area, and outer area, and their locations are as follows: , and : All internal nodes are arranged in ascending order to form a radial internal node vector. To satisfy the endpoint requirements of the B-spline basis function, the radial node vector is repeated at both ends. It is formed by concatenating the secondary boundary value and the internal node: Circumferential parameters The direction uses a uniform node vector, and the number of circumferential control points is [number missing]. Then the uniform node vector is: 。 3. The method of claim 1, wherein, The specific process of adaptive node refinement in claim 1 is as follows: The Sobel operator is used to compute discrete gradients, and its convolution kernel is defined as follows: Preliminary reconstruction results can be obtained from the initial nodes. The current reconstruction absorption rate distribution is as follows: , No. Physical coordinates of each test point The Sobel operator is used to calculate the gradient magnitude at each test point. Gradient components are calculated via convolution: The gradient magnitude at each test point is: A larger gradient magnitude indicates a more drastic change in the region. Curvature is also added as a supplementary indicator, approximating curvature using the Laplacian operator, which measures the degree of local bending through the sum of second-order differences. The gradient magnitude and curvature are integrated into a unified and refined evaluation metric, using weighted coefficients. To balance the contributions of both, the gradient magnitude and curvature are normalized, and then a weighted sum is performed: wherein, is a curvature weight coefficient, taking a value range for balancing the contribution of gradient and curvature to thinning; Radial node vector Repeated from both ends The secondary boundary value is concatenated with the internal node, and extracted. All distinct node values ​​in the array, sorted in ascending order. Then the radial parameter interval formed by the two nodes is Similarly, extract the circumferential node vector. All distinct node values ​​in the array, sorted in ascending order. Then the radial parameter interval formed by the two nodes is For each test point Its parameter coordinates are The comprehensive index is ,according to The test points are grouped according to the interval, the first... All test points in the radial interval The maximum value is If there are no test points within the interval, then Similarly, according to The test points are grouped according to the interval, the first... All test points in the circumferential interval The maximum value is Set the threshold coefficient as , Then the thresholds for the radial and circumferential directions are respectively: For each radial interval ,like Then the midpoint of that interval Insert a new radial node at the specified location; for each circumferential interval ,like Then the midpoint of that interval Insert a new circumferential node at the specified location; Merge the newly retained nodes after filtering into the current radial node vector. and circumferential node vector And keep the nodes repeating at both ends. The secondary boundary value is used to reconstruct the B-spline basis function matrix using the updated node vectors. Update system matrix Resolve the control coefficient vector A new absorption rate distribution was obtained. Repeat the above process of adaptive encryption of nodes and generation of new absorption rate distribution until the total number of control points reaches the preset upper limit or the projection residual is less than the set minimum value, then stop the iteration and output the absorption rate distribution result.

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