Correction method of aerodynamic thermal radiation effect based on multi-scale Chebyshev polynomial fitting
The method addresses aerodynamic thermal radiation interference in high-speed aircraft by using multi-scale Chebyshev polynomial fitting and iterative optimization for accurate image reconstruction, improving detection and navigation.
Patent Information
- Application Number
- CN202111656339.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-12-31
- Publication Date
- 2024-12-24
- Estimated Expiration
- 2041-12-31
AI Technical Summary
Existing aerodynamic thermal radiation effects interfere with infrared imaging and navigation positioning in high-speed aircraft, causing signal degradation and detector saturation, which current correction algorithms fail to adequately address.
A method combining multi-scale Chebyshev polynomial fitting with gradient domain surface fitting regularization and iterative optimization to correct aerodynamic thermal radiation effects, using Chebyshev orthogonal polynomials for image reconstruction and alternating iterative methods to minimize residuals.
Provides highly accurate and residue-free correction of aerodynamic thermal radiation effects, enhancing imaging detection and navigation positioning with reduced iterative optimization times and improved robustness.
Smart Images
Figure CN114359093B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the field of aerodynamic thermal radiation effect correction, and in particular relates to a method for correcting aerodynamic thermal radiation effect based on multi-scale Chebyshev polynomial fitting. Background Art
[0002] In recent years, infrared imaging detection and navigation positioning technology has been increasingly used in various advanced high-speed aircraft. When a high-speed aircraft flies at high speed in the atmosphere, due to strong aerodynamic heating, a high-temperature shock wave layer exists around its optical hood. The shock wave radiation spectrum covers from ultraviolet to long-wave infrared. The gas density, temperature, and composition in the high-temperature shock wave are highly uneven, and strong infrared radiation is generated, which produces thermal radiation noise interference on the detector imaging, causing serious degradation of the target image, which is called the aerodynamic thermal radiation effect.
[0003] The aerodynamic thermal radiation effect will interfere with the target's infrared signal, reduce the seeker's detection signal-to-noise ratio of the target, and even cause the infrared detector to be saturated and unable to accurately distinguish the signal from the target, causing the infrared guidance system to weaken its ability to detect, track and identify the target.
[0004] At present, corresponding multi-scale aerodynamic thermal radiation effect correction algorithms and binary polynomial surface fitting correction algorithms are already available, but there is no correction algorithm that combines the gradient domain surface fitting regularization term with the advantages of multi-scale iterative optimization estimation. Summary of the invention
[0005] The purpose of the present invention is to provide a method for correcting aerodynamic thermal radiation effects based on multi-scale Chebyshev polynomial fitting, combining the gradient domain surface fitting regularization term with the advantages of multi-scale iterative optimization estimation to correct aerodynamic thermal radiation effects.
[0006] To achieve the above object, the present invention provides a method for correcting aerodynamic thermal radiation effect based on multi-scale Chebyshev polynomial fitting, comprising the following steps:
[0007] S2, taking the center of the degraded image as the coordinate origin, and determining a symmetrical coordinate system with the coordinate origin;
[0008] S3, using downsampling method to build a multi-scale image pyramid of degraded images;
[0009] S4, selecting Chebyshev orthogonal polynomials as a basis to obtain an orthogonal polynomial system;
[0010] S5, using Chebyshev orthogonal polynomial surface fitting to construct regularized constraints and perform modeling;
[0011] S6, updating and estimating the corresponding coefficients in the Chebyshev orthogonal polynomial function, the thermal radiation effect map b, and the potential clear image s by an alternating iterative method;
[0012] S7, upsampling the obtained thermal radiation effect map b and the potential clear image s to the upper scale and iterating again, and finally obtaining the thermal radiation effect map and the potential clear image with the same resolution as the input.
[0013] Furthermore, the method further comprises:
[0014] S1. Perform filtering preprocessing on the degraded image. Specifically, perform filtering preprocessing on the degraded image twice by using non-local mean filtering.
[0015] Furthermore, a bilinear interpolation downsampling method is adopted.
[0016] Further, step S4 is specifically as follows:
[0017] Assume the image size of the degraded image is M×N, (r,c) is the coordinate of the point in the coordinate system;
[0018] Choose Chebyshev orthogonal polynomial as basis function, let P z (r) is the z-th order polynomial, according to the coordinates in the r direction The point set {r1,r2,…,r M}Construct the corresponding orthogonal polynomial system {P0(r),P1(r),…,P n (r)}; is the floor function;
[0019] According to the three-term recursive relation of the polynomial, the orthogonal polynomial {P k (r)}(k=0,1,...,n) has the following recursive relationship:
[0020]
[0021] Where P k (r) is a k-order polynomial with the highest term coefficient being 1, and {P k (r)} Orthogonality shows that:
[0022]
[0023]
[0024] From formulas (1), (2), and (3), we can obtain the orthogonal polynomial system {P0(r),…,P n (r)} is:
[0025] {1,r-α,…,(r-αk ) k-1 (r)-β k-1 P k-2 (r)}k=2,3,…,n⑷
[0026] Since the image is symmetrical, we can obtain the orthogonal polynomial system {Q0(c),…,Q n (c)} is:
[0027] {1,c-α,…,(c-α k' )Q k'-1 (c)-β k'-1 Q k'-2 (c)}k'=2,3,…,n ⑸
[0028] Therefore, from formulas (4) and (5), we can obtain the Chebyshev orthogonal polynomial system {P0(r)Q0(c),P0(r)Q1(c)…,P n (r)Q n (c)}:
[0029] {1,r-α,c-α,…,((r-α k ) k-1 (r)-β k-1 P k-2 (r))((c-α k' )Q k'-1 (c)-β k'-1 Q k'-2 (c))}⑹
[0030] Thus, the row vector W of Chebyshev orthogonal polynomials is established.
[0031] Further, step S5 is specifically as follows:
[0032] The degradation model of the degraded image is expressed as:
[0033] g=s+b+n⑺
[0034] Among them, g represents the degraded image, s represents the potential clear image, b represents the aerodynamic thermal radiation effect map, and n represents the noise;
[0035] In the data item Add the constraints of its gradient domain based on And add the L0 norm constraint of the potential clear image s in the gradient domain; use the product Wa of the row vector W containing all Chebyshev orthogonal polynomials and the column vector a composed of all its corresponding coefficients to approximate the aerodynamic thermal radiation effect diagram b, so add the L2 norm constraint of the gradient domain The following energy function is constructed:
[0036]
[0037] Among them, α, β, γ are weights, ||·||0 represents the L0 norm, which indicates the number of non-zero elements, and ||·||2 represents the L2 norm. Represents the gradient operator.
[0038] Further, step S6 is specifically as follows:
[0039] The thermal radiation effect diagram is estimated by alternately solving the following equations: and potential clear images
[0040]
[0041]
[0042] For solving the b subproblem, given an s, formula (10) can be rewritten as the following least squares problem:
[0043]
[0044] in Represent the gradients in the horizontal and vertical directions respectively;
[0045] a is iteratively updated by:
[0046] a=(W T W) -1 W T b ⒀
[0047] Formula (12) is solved to obtain formula (14), and b is iteratively updated using formula (14):
[0048]
[0049] Where F(·) represents Fourier transform, F -1 (·) represents the inverse Fourier transform, D1 and D2 represent the derivative operation matrices in the horizontal and vertical directions, respectively;
[0050] For solving the s subproblem, given a b, formula (11) can be rewritten as follows:
[0051]
[0052] Using the alternating iterative solution method, introduce the variable u r 、u c To make a constraint, formula (15) is rewritten as:
[0053]
[0054] By using Split Bregman iteration to enforce the constraints, equation (16) can be rewritten as:
[0055]
[0056] where t r ,t c is the Bregman variable;
[0057] An iterative update is performed using the following formula:
[0058]
[0059]
[0060]
[0061]
[0062]
[0063] in represents the conjugate operation, Represents component-wise multiplication or division.
[0064] Further, step S7 is specifically as follows:
[0065] After the degraded image of the minimum scale is processed by steps S4-S6, a potential clear image and a thermal radiation effect map are obtained, which are then upsampled to obtain an initial estimate of the upper scale. Steps S4-S6 are repeated to iteratively update the potential clear image and the thermal radiation effect map of the scale, and finally a clear image and a thermal radiation effect map consistent with the original resolution are obtained.
[0066] Compared with the prior art, the present invention has the following advantages and beneficial effects:
[0067] The aerodynamic thermal radiation effect correction method based on multi-scale Chebyshev polynomial fitting of the present invention can provide a thermal radiation effect correction method for infrared images that produce thermal radiation effects, can obtain a highly accurate and residue-free aerodynamic thermal radiation effect correction image with a relatively small number of iterative optimization times, can meet the needs of high-quality imaging detection and navigation positioning, and has the advantages of a small number of iterative optimization times, high robustness, high accuracy, and no residue in the aerodynamic thermal radiation effect correction image. BRIEF DESCRIPTION OF THE DRAWINGS
[0068] Figure 1 Correction flow chart for aerodynamic heat radiation effect;
[0069] Figure 2 It is a schematic diagram of multi-scale iteration;
[0070] Figure 3 is the original degraded image;
[0071] Figure 4 Estimation of thermal radiation effect diagram;
[0072] Figure 5 It is the correction diagram for thermal radiation effect;
[0073] Figure 6 (a) is the minimum scale thermal radiation effect map estimation b4; Figure 6 (b) is the thermal radiation effect diagram to estimate b3; Figure 6 (c) estimate b2 for the thermal radiation effect diagram; Figure 6 (d) is the thermal radiation effect diagram to estimate b1; Figure 6 (e) Estimation of b0 for the thermal radiation effect map consistent with the original resolution;
[0074] Figure 7 (a) is the minimum scale potential clear image s4; Figure 7 (b) is the potential clear image s3; Figure 7 (c) is the potential clear image s2; Figure 7 (d) is the potential clear image s1; Figure 7 (e) is the potential clear image s0 that is consistent with the original resolution. DETAILED DESCRIPTION
[0075] In order to make the purpose, technical scheme and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.
[0076] The present invention discloses a method for correcting aerodynamic thermal radiation effects based on multi-scale Chebyshev polynomial fitting, which can correct aerodynamic thermal radiation effects by multi-scale Chebyshev orthogonal polynomial fitting. Specifically, the initial thermal radiation effect low-frequency image is obtained by filtering, and Chebyshev orthogonal polynomial surface fitting is performed. The fitted image is used as the initial value of multi-scale iterative optimization to reduce the number of iterative optimizations. The present invention uses Chebyshev orthogonal polynomial fitting surfaces, and its orthogonality can effectively avoid the problem of ill-conditioned coefficient matrices of binary polynomials due to the increase in the order of the polynomials, so that the algorithm in the present invention has robustness. In addition, the present invention unifies multi-scale optimization iteration and Chebyshev orthogonal polynomial surface fitting into the correction model for the first time, so as to improve the accuracy and obtain a residual-free aerodynamic thermal radiation effect correction map.
[0077] The aerodynamic thermal radiation effect correction method based on multi-scale Chebyshev polynomial fitting in the embodiment of the present invention is as follows: Figure 1 As shown, the specific steps include:
[0078] S1. In order to reduce the adverse effects of noise and high-frequency information on the results, the degraded image is preprocessed twice using non-local mean filtering (NLM) to obtain a low-frequency smoothed degradation image after preprocessing.
[0079] S2. Use the center point of the degradation graph as the origin to determine a symmetrical coordinate system. Let (i, j) be the coordinates of any point in the original coordinate system, (r, c) be the coordinates of the corresponding point in the new coordinate system, and the image size of the degradation graph be M×N. Then the relationship between the point with coordinates (r, c) in the new coordinate system and the point with coordinates (i, j) in the original coordinate system is: in is the floor function.
[0080] S3. Use bilinear interpolation downsampling method to build a multi-scale image pyramid.
[0081] Assume that g is a degraded image with a size of M×N, such as Figure 2 As shown, an image pyramid [g0, g1, g2, g3, g4] of the degradation graph g is established, where g0 is the original resolution [M, N], g1-g4 are the results of downsampling g using bilinear interpolation, and the image resolutions are [0.8×M, 0.8×N], [0.6×M, 0.6×N], [0.4×M, 0.4×N], and [0.2×N, 0.2×N], respectively.
[0082] S4. Select Chebyshev orthogonal polynomials as a basis to obtain an orthogonal polynomial system.
[0083] Choose Chebyshev orthogonal polynomial as basis function, let P z (r) is the z-th order polynomial, according to the coordinates in the r direction The point set {r1,r2,…,r M}Construct the corresponding orthogonal polynomial system {P0(r),P1(r),…,P n (r)}. According to the three-term recursive relation of the polynomial, the orthogonal polynomial {P k (r)}(k=0,1,...,n) has the following recursive relationship:
[0084]
[0085] Where P k (r) is a k-order polynomial with the highest term coefficient being 1, and {P k (r)} Orthogonality shows that:
[0086]
[0087]
[0088] From formulas (1), (2), and (3), we can obtain the orthogonal polynomial system {P0(r),…,P n (r)}:
[0089] {1,r-α,…,(r-α k ) k-1 (r)-β k-1 P k-2 (r)}k=2,3,…,n⑷
[0090] Since the image is symmetrical, we can obtain the orthogonal polynomial system {Q0(c),…,Q n (c)}:
[0091] {1,c-α,…,(c-α k' )Q k'-1 (c)-β k'-1 Q k'-2 (c)}k'=2,3,…,n ⑸
[0092] Therefore, from formulas (4) and (5), we can obtain the Chebyshev orthogonal polynomial system {P0(r)Q0(c),P0(r)Q1(c)…,P n (r)Q n (c)}:
[0093] {1,r-α,c-α,…,((r-α k ) k-1(r)-β k-1 P k-2 (r))((c-α k' )Q k'-1 (c)-β k'-1 Q k'-2 (c))}⑹
[0094] S5. Use Chebyshev orthogonal polynomial surface fitting to construct regularized constraints and perform modeling.
[0095] The degradation model of the degraded image can be expressed as:
[0096] g=s+b+n⑺
[0097] Where g represents the degraded image, Figure 3 is the original degraded image; s represents the potential clear image, Figure 5 a is the thermal radiation effect correction diagram; b is the aerodynamic thermal radiation effect diagram, Figure 4 is the thermal radiation effect map estimation; n represents the noise.
[0098] In the data item Add the constraints of its gradient domain based on And the L0 norm constraint of the potential clear image s in the gradient domain is added. It is hoped that the product Wa of the row vector W containing all Chebyshev orthogonal polynomials and the column vector a composed of all its corresponding coefficients can be used to approximate the aerodynamic thermal radiation effect diagram b, so the L2 norm constraint of the gradient domain is added The following energy function is constructed:
[0099]
[0100] Among them, α, β, γ are weights, ||·||0 represents the L0 norm, which indicates the number of non-zero elements, and ||·||2 represents the L2 norm. Represents the gradient operator.
[0101] Taking the Chebyshev orthogonal polynomial with the highest order of 4 as an example, W can be obtained by formula (6):
[0102] W={P0(r)Q0(c),P0(r)Q1(c),…,P4(r)Q4(c)} ⑼
[0103] S6. Update and estimate the corresponding coefficients in the Chebyshev orthogonal polynomial function, the thermal radiation effect map b, and the potential clear image s through an alternating iterative method.
[0104] Due to the existence of L0 norm in formula (8), it is very difficult to minimize the solution. Therefore, the thermal radiation effect diagram estimation is obtained by alternately solving the following formulas: and potential clear images
[0105]
[0106]
[0107] For solving the b subproblem, given an s, formula (10) can be written as the following least squares problem:
[0108]
[0109] in Represent the gradients in the horizontal and vertical directions respectively.
[0110] a is iteratively updated by:
[0111] a=(W T W) -1 W T b ⒀
[0112] Solving formula (12) yields formula (14), and using formula (14) to iteratively update b:
[0113]
[0114] Where F(·) represents Fourier transform, F -1 (·) represents the inverse Fourier transform, and D1 and D2 represent the derivative operation matrices in the horizontal and vertical directions, respectively.
[0115] For solving the s subproblem, given a b, formula (11) can be rewritten as follows:
[0116]
[0117] Because formula (15) has the L0 norm, it is very difficult to solve. Therefore, the alternating iterative solution method is used to introduce the variable u r 、u c To make a constraint, formula (15) can be rewritten as:
[0118]
[0119] By using Split Bregman iteration to enforce the constraints, equation (16) can be rewritten as:
[0120]
[0121] where t r ,t c is the Bregman variable.
[0122] An iterative update is performed using the following formula:
[0123]
[0124]
[0125]
[0126]
[0127]
[0128] in represents the conjugate operation, Represents component-wise multiplication or division.
[0129] S7, upsampling the obtained thermal radiation effect map b and the potential clear image s to the upper scale and iterating again, and finally obtaining the thermal radiation effect map and the potential clear image with the same resolution as the input.
[0130] like Figure 2 , Figure 6 and Figure 7 As shown, after the minimum scale degraded image g4 is processed by steps S4-S6, the potential clear image s4 and the thermal radiation effect map b4 are obtained, which are then upsampled to obtain the initial estimate of the upper scale, and steps S4-S6 are repeated to iteratively update the potential clear image s3 and the thermal radiation effect map b3 of this scale; similarly, s2, b2, s1, b1 can be obtained, and finally s0, b0 consistent with the original resolution are obtained.
[0131] In summary, the present invention discloses a method for correcting aerodynamic thermal radiation effects based on multi-scale Chebyshev polynomial fitting, comprising the following steps: using non-local mean filtering (NLM) to perform two filtering processes on the degraded image to obtain a low-frequency smoothed degradation image after preprocessing; using the image center as the coordinate origin, and determining a symmetrical coordinate system with the coordinate origin; using a bilinear interpolation downsampling method to establish a multi-scale image pyramid; selecting Chebyshev orthogonal polynomials as a basis to obtain an orthogonal polynomial system; using Chebyshev orthogonal polynomial surface fitting to construct regularized constraints and perform modeling; updating and estimating each coefficient, thermal radiation effect map and potential clear image in the Chebyshev orthogonal polynomial function by an alternating iterative method; upsampling the obtained thermal radiation effect map and potential clear image to an upper scale and iterating again, and finally obtaining a thermal radiation effect map and potential clear image with the same resolution as the input. The present invention can correct aerodynamic thermal radiation effects by multi-scale Chebyshev orthogonal polynomial fitting.
[0132] It should be pointed out that, according to the needs of implementation, the various steps / components described in this application can be split into more steps / components, and two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention.
[0133] It will be easily understood by those skilled in the art that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.
Claims
1. A method for correcting aerodynamic thermal radiation effects based on multi-scale Chebyshev polynomial fitting, characterized in that: The following steps are involved: S2, taking the center of the degraded image as the coordinate origin, and determining a symmetrical coordinate system with the coordinate origin; S3, using downsampling method to build a multi-scale image pyramid of degraded images; S4, selecting Chebyshev orthogonal polynomials as a basis to obtain an orthogonal polynomial system; S5, using Chebyshev orthogonal polynomial surface fitting to construct regularized constraints and perform modeling; S6, updating and estimating the corresponding coefficients in the Chebyshev orthogonal polynomial function, the thermal radiation effect map b, and the potential clear image s by an alternating iterative method; S7, upsampling the obtained thermal radiation effect map b and the potential clear image s to the upper scale and iterating again, and finally obtaining the thermal radiation effect map and the potential clear image with the same resolution as the input; Wherein, step S5 is specifically as follows: The degradation model of the degraded image is expressed as: g=s+b+n⑺where g represents the degraded image, s represents the potential clear image, b represents the aerodynamic thermal radiation effect map, and n represents the noise; In the data item Add the constraints of its gradient domain based on And add the L0 norm constraint of the potential clear image s in the gradient domain; use the product Wa of the row vector W containing all Chebyshev orthogonal polynomials and the column vector a composed of all its corresponding coefficients to approximate the aerodynamic thermal radiation effect diagram b, so add the L2 norm constraint of the gradient domain The following energy function is constructed: Among them, α, β, γ are weights, ||·||0 represents the L0 norm, which indicates the number of non-zero elements, and ||·||2 represents the L2 norm. represents the gradient operator; Step S6 is specifically as follows: The thermal radiation effect diagram is estimated by alternately solving the following equations: and potential clear images For solving the b subproblem, given an s, formula (10) can be rewritten as the following least squares problem: in Represent the gradients in the horizontal and vertical directions respectively; a is iteratively updated by: a=(W T w) -1 W T b⒀ Formula (12) is solved to obtain formula (14), and b is iteratively updated using formula (14): Where F(·) represents Fourier transform, F -1 (·) represents the inverse Fourier transform, D1 and D2 represent the derivative operation matrices in the horizontal and vertical directions, respectively; For solving the s subproblem, given a b, formula (11) can be rewritten as follows: Using the alternating iterative solution method, introduce the variable u r 、u c To make a constraint, formula (15) is rewritten as: By using Split Bregman iteration to enforce the constraints, equation (16) can be rewritten as: where t r ,t c is the Bregman variable; An iterative update is performed using the following formula: in represents the conjugate operation, Represents component-wise multiplication or division.
2. The aerodynamic thermal radiation effect correction method based on multi-scale Chebyshev polynomial fitting according to claim 1 is characterized in that: The method further includes: S1. Perform filtering preprocessing on the degraded image.
3. The aerodynamic thermal radiation effect correction method based on multi-scale Chebyshev polynomial fitting according to claim 2 is characterized in that: The degraded image is preprocessed twice using non-local means filtering.
4. The aerodynamic thermal radiation effect correction method based on multi-scale Chebyshev polynomial fitting according to claim 1 is characterized in that: A bilinear interpolation downsampling method is used.
5. The aerodynamic thermal radiation effect correction method based on multi-scale Chebyshev polynomial fitting according to claim 1 is characterized in that: Step S4 is specifically as follows: Assume the image size of the degraded image is M×N, (r,c) is the coordinate of the point in the coordinate system; Choose Chebyshev orthogonal polynomial as basis function, let P z (r) is the z-th order polynomial, according to the coordinates in the r direction The point set {r1,r2,…,r M }Construct the corresponding orthogonal polynomial system {P0(r),P1(r),…,P n (r)}; is the floor function; According to the three-term recursive relation of the polynomial, the orthogonal polynomial {P k (r)}(k=0,1,…,n) has the following recursive relationship: Where P k (r) is a k-order polynomial with the highest term coefficient being 1, and {P k (r)} Orthogonality shows that: From formulas (1), (2), and (3), we can obtain the orthogonal polynomial system {P0(r),…,P n (r)} is: {1,r-α,…,(r-α k ) k-1 (r)-β k-1 P k-2 (r)}k=2,3,…,n⑷Since the image is symmetrical, the orthogonal polynomial system {Q0(c),…,Q n (c)} is: {1,c-α,…,(c-α k' )Q k'-1 (c)-β k'-1 Q k'-2 (c)}k'=2,3,…,n⑸Therefore, from formulas (4) and (5), we can obtain the Chebyshev orthogonal polynomial system {P0(r)Q0(c),P0(r)Q1(c)…,P n (r)Q n (c)}: {1,r-α,c-α,…,((r-α k ) k-1 (r)-β k-1 P k-2 (r))((c-α k' )Q k'-1 (c)-β k'-1 Q k'-2 (c))}⑹Thus establish the row vector W of the Chebyshev orthogonal polynomial.
6. The aerodynamic thermal radiation effect correction method based on multi-scale Chebyshev polynomial fitting according to claim 1 is characterized in that: Step S7 is specifically as follows: After the degraded image of the minimum scale is processed by steps S4-S6, a potential clear image and a thermal radiation effect map are obtained, which are then upsampled to obtain an initial estimate of the upper scale. Steps S4-S6 are repeated to iteratively update the potential clear image and the thermal radiation effect map of the scale, and finally a clear image and a thermal radiation effect map consistent with the original resolution are obtained.