CN114359093A - Pneumatic heat radiation effect correction method based on multi-scale chebyshev polynomial fitting - Google Patents

Pneumatic heat radiation effect correction method based on multi-scale chebyshev polynomial fitting Download PDF

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CN114359093A
CN114359093A CN202111656339.3A CN202111656339A CN114359093A CN 114359093 A CN114359093 A CN 114359093A CN 202111656339 A CN202111656339 A CN 202111656339A CN 114359093 A CN114359093 A CN 114359093A
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chebyshev
radiation effect
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时愈
陈际松
洪汉玉
张丽琴
杜敦伟
赵欣
张天序
桑农
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Wuhan Institute of Technology
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Abstract

The invention discloses a pneumatic heat radiation effect correction method based on multi-scale chebyshev polynomial fitting, which comprises the following steps: s2, taking the center of the degraded image as a coordinate origin, and determining a symmetrical coordinate system by using the coordinate origin; s3, establishing a multi-scale image pyramid of the degraded image by adopting a down-sampling method; s4, selecting a chebyshev orthogonal polynomial as a base to obtain an orthogonal polynomial system; s5, constructing a regularization constraint term by using chebyshev orthogonal polynomial surface fitting and modeling; s6, updating and estimating corresponding coefficients in the chebyshev orthogonal polynomial function, a heat radiation effect graph b and a potential clear image S by an alternate iteration method; and S7, upsampling b and S to an upper scale, and iterating again to finally obtain a thermal radiation effect graph and a potential clear image with the same resolution as the input. The method can correct the pneumatic thermal radiation effect through multi-scale chebyshev orthogonal polynomial fitting, and has the advantages of less iterative optimization times, high robustness, high precision and no residue in pneumatic thermal radiation effect correction images.

Description

Pneumatic heat radiation effect correction method based on multi-scale chebyshev polynomial fitting
Technical Field
The invention belongs to the field of pneumatic thermal radiation effect correction, and particularly relates to a pneumatic thermal radiation effect correction method based on multi-scale chebyshev polynomial fitting.
Background
In recent years, the infrared imaging detection and navigation positioning technology is applied to various advanced high-speed aircrafts more and more widely. When the high-speed aircraft flies in the atmosphere at a high speed, a high-temperature shock wave layer exists around the optical head cover of the high-speed aircraft due to strong pneumatic heating. The shock radiation spectrum covers from ultraviolet to long-wave infrared. The gas density, temperature and component height in the high-temperature shock wave are not uniform, strong infrared radiation is generated, thermal radiation noise interference is generated on the imaging of a detector, and the target image is seriously degraded, namely the aerodynamic thermal radiation effect.
The pneumatic thermal radiation effect can interfere the infrared signal of the target, the detection signal-to-noise ratio of the guide head to the target is reduced, even the infrared detector is saturated and cannot accurately distinguish the signal from the target, and the detection, tracking and identification capabilities of the infrared guide system to the target are weakened.
At present, a corresponding multi-scale aerodynamic thermal radiation effect correction algorithm and a binary polynomial surface fitting correction algorithm are provided, but a correction algorithm combining a gradient domain surface fitting regularization term and multi-scale iterative optimization estimation advantages is not provided.
Disclosure of Invention
The invention aims to provide a pneumatic thermal radiation effect correction method based on multi-scale chebyshev polynomial fitting, which combines a gradient domain surface fitting regularization term with multi-scale iterative optimization estimation advantages to correct the pneumatic thermal radiation effect.
In order to achieve the above object, the present invention provides a method for correcting an aerodynamic thermal radiation effect based on multi-scale chebyshev polynomial fitting, comprising the following steps:
s2, taking the center of the degraded image as a coordinate origin, and determining a symmetrical coordinate system by using the coordinate origin;
s3, establishing a multi-scale image pyramid of the degraded image by adopting a down-sampling method;
s4, selecting a chebyshev orthogonal polynomial as a base to obtain an orthogonal polynomial system;
s5, constructing a regularization constraint term by using chebyshev orthogonal polynomial surface fitting and modeling;
s6, updating and estimating corresponding coefficients in the chebyshev orthogonal polynomial function, a heat radiation effect graph b and a potential clear image S by an alternate iteration method;
and S7, upsampling the obtained thermal radiation effect graph b and the potential clear image S to an upper scale for iteration again, and finally obtaining the thermal radiation effect graph and the potential clear image with the same resolution as the input.
Further, the method also includes:
and S1, performing filtering preprocessing on the degraded image, specifically performing filtering preprocessing twice on the degraded image by using non-local mean filtering.
Furthermore, a bilinear interpolation downsampling method is adopted.
Further, step S4 specifically includes:
let the image size of the degraded image be M × N, (r, c) be the coordinates of the midpoint of the coordinate system;
selecting a chebyshev orthogonal polynomial as a basis function, and setting Pz(r) is a z-th order polynomial in terms of coordinates in the r direction of
Figure BDA0003448401500000021
Set of points of { r1,r2,…,rMConstructing a corresponding orthogonal polynomial system { P }0(r),P1(r),…,Pn(r) }; wherein
Figure BDA0003448401500000022
Is a lower integer function;
orthogonal polynomial { P) with coefficient of the highest order of 1 from polynomial trinomial recursion relationshipk(r) } (k ═ 0, 1.., n) has the following recurrence relation:
Figure BDA0003448401500000023
wherein P isk(r) is a polynomial of degree k with a coefficient of the highest term of 1, from { P }k(r) } orthogonality indicates:
Figure BDA0003448401500000024
Figure BDA0003448401500000025
from the equations (1), (2) and (3), an orthogonal polynomial system { P in the r direction can be obtained0(r),…,Pn(r) } is:
{1,r-α,…,(r-αk)Pk-1(r)-βk-1Pk-2(r)}k＝2,3,…,n ⑷
since the image is symmetrical, an orthogonal polynomial system { Q ] in the c-direction can be obtained in the same way0(c),…,Qn(c) The method is as follows:
{1,c-α,…,(c-αk')Qk'-1(c)-βk'-1Qk'-2(c)}k'＝2,3,…,n ⑸
thus, the chebyshev orthogonal polynomial system { P ] for fitting a curved surface on a two-dimensional plane is obtained from the equations (4), (5)0(r)Q0(c),P0(r)Q1(c)…,Pn(r)Qn(c)}：
{1,r-α,c-α,…,((r-αk)Pk-1(r)-βk-1Pk-2(r))((c-αk')Qk'-1(c)-βk'-1Qk'-2(c))} ⑹
Thereby establishing a row vector W of the chebyshev orthogonal polynomial.
Further, step S5 specifically includes:
the degradation model of the degraded image is represented as:
g＝s+b+n ⑺
wherein g represents a degraded image, s represents a potentially sharp image, b represents an aerodynamic thermoluminescence effect map, and n represents noise;
in data item
Figure BDA0003448401500000031
Adding the constraint of gradient domain thereof
Figure BDA0003448401500000032
And adding the L of the potentially sharp image s in the gradient domain0A norm constraint term; approximating the aerodynamic thermoluminescence effect map b by the product Wa of the row vector W containing all chebyshev orthogonal polynomials and the column vector a of all its corresponding coefficients, thus adding the L of the gradient domain2Norm constraint term
Figure BDA0003448401500000033
The following energy function is thus constructed:
Figure BDA0003448401500000034
wherein, alpha, beta, gamma is weight, | | · | | non-phosphor0Represents L0Norm, representing the number of non-0 elements, | · (| non-conducting phosphor)2Is represented by L2The norm of the number of the first-order-of-arrival,
Figure BDA0003448401500000035
a gradient operator is represented.
Further, step S6 specifically includes:
separately obtaining thermal radiance effect map estimates by alternately solving
Figure BDA0003448401500000036
And potentially sharp images
Figure BDA0003448401500000037
Figure BDA0003448401500000038
Figure BDA0003448401500000039
For solving the b sub-problem, given an s, equation (10) is rewritten as the following least squares problem:
Figure BDA00034484015000000310
wherein
Figure BDA00034484015000000311
Representing the gradient in the horizontal and vertical directions, respectively;
a is iteratively updated by:
a＝(WTW)-1WTb ⒀
solving equation (12) to obtain equation (14), and iteratively updating b by equation (14):
Figure BDA0003448401500000041
wherein F (-) represents a Fourier transform, F-1(. represents an inverse Fourier transform, D)1、D2Representing the derivative operation matrices in the horizontal and vertical directions, respectively;
for solving the s-sub-problem, given a b, equation (11) is rewritten as:
Figure BDA0003448401500000042
using an alternative iterative solution method, introducing a variable ur、ucTo perform a constraint, formula (15) is rewrittenComprises the following steps:
Figure BDA0003448401500000043
by enforcing the constraints using Split Bregman iteration, equation (16) is rewritten as:
Figure BDA0003448401500000044
wherein t isr、tcIs the Bregman variable;
an iterative update is performed by the following equation:
Figure BDA0003448401500000045
Figure BDA0003448401500000046
Figure BDA0003448401500000047
Figure BDA0003448401500000048
Figure BDA0003448401500000049
wherein
Figure BDA00034484015000000410
Figure BDA00034484015000000411
It is meant a conjugate operation of the two,
Figure BDA00034484015000000412
representing component multiplication or division.
Further, step S7 specifically includes:
and (3) processing the degraded image with the minimum scale in steps S4-S6 to obtain a potential clear image and a thermal radiation effect image, then sampling the degraded image to obtain an initial estimation of an upper-layer scale, repeating the steps S4-S6 to update the potential clear image and the thermal radiation effect image with the scale in an iteration mode, and finally obtaining the clear image and the thermal radiation effect image which are consistent with the original resolution.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the pneumatic thermal radiation effect correction method based on multi-scale chebyshev polynomial fitting can provide a thermal radiation effect correction method for infrared images generating thermal radiation effect, can obtain a high-precision residue-free pneumatic thermal radiation effect correction image under the condition of less iterative optimization times, can meet the requirements of high-quality imaging detection and navigation positioning, and has the advantages of less iterative optimization times, high robustness, high precision, no residue of pneumatic thermal radiation effect correction image and the like.
Drawings
FIG. 1 is a flow chart of the pneumatic thermal radiation effect correction;
FIG. 2 is a schematic diagram of a multi-scale iteration;
FIG. 3 is an original degraded image;
FIG. 4 is a thermal emission map estimate;
FIG. 5 is a calibration chart for the effect of thermal radiation;
FIG. 6(a) is a minimum dimension bolometric effect map estimate b4(ii) a FIG. 6(b) is a thermal emission effect map estimation b3(ii) a FIG. 6(c) is a thermal emission effect map estimation b2(ii) a FIG. 6(d) is a bolometric map estimation b1(ii) a FIG. 6(e) is a thermal emission effect map estimation b consistent with the original resolution0；
FIG. 7(a) is a minimum scale latent sharp image s4(ii) a FIG. 7(b) is a latent sharp image s3(ii) a FIG. 7(c) is a latent sharp image s2(ii) a FIG. 7(d) is a latent sharp image s1(ii) a FIG. 7(e) is a graph ofLatent sharp image s with uniform original resolution0。
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention discloses a pneumatic heat radiation effect correction method based on multi-scale chebyshev polynomial fitting, which can correct the pneumatic heat radiation effect through multi-scale chebyshev orthogonal polynomial fitting. Specifically, an initial thermal radiation effect low-frequency image is obtained through filtering processing, chebyshev orthogonal polynomial surface fitting is carried out, and the fitted image is used as an initial value of multi-scale iterative optimization to reduce the number of iterative optimization; in addition, the invention uses the chebyshev orthogonal polynomial to fit the curved surface, and the orthogonality can effectively avoid the problem that a binary polynomial has a sick coefficient matrix due to the increase of the polynomial order, so that the algorithm in the invention has robustness; in addition, the invention firstly unifies the multi-scale optimization iteration and the chebyshev orthogonal polynomial surface fitting into the correction model, thereby improving the precision and obtaining the correction graph without residual aerodynamic heat radiation effect.
The method for correcting the aerodynamic thermal radiation effect based on multi-scale chebyshev polynomial fitting, disclosed by the embodiment of the invention, as shown in fig. 1, specifically comprises the following steps:
and S1, in order to reduce the adverse effect of noise and high-frequency information on the result, performing two times of filtering preprocessing on the degraded image by using non-local mean filtering (NLM) to obtain a preprocessed low-frequency smooth degraded image.
And S2, determining a symmetrical coordinate system by taking the central point of the degradation graph as a coordinate origin, wherein (i, j) is the coordinate of any point in the original coordinate system, and (r, c) is the coordinate of the corresponding point in the new coordinate system, and the image size of the degradation graph is M multiplied by N. ThenThe 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:
Figure BDA0003448401500000061
wherein
Figure BDA0003448401500000062
Is a lower integer function.
And S3, establishing a multi-scale image pyramid by adopting a bilinear interpolation downsampling method.
Assuming that g is a degraded image with an image size of M × N, as shown in FIG. 2, an image pyramid [ g ] of the degraded image g is established0,g1,g2,g3,g4]Wherein g is0To the original resolution [ M, N]，g1-g4As a result of downsampling by bilinear interpolation for g, the image resolution is [0.8 XM, 0.8 XN ] in this order]、[0.6×M,0.6×N]、[0.4×M,0.4×N]、[0.2×N,0.2×N]。
S4, selecting a chebyshev orthogonal polynomial as a base to obtain an orthogonal polynomial system.
Selecting a chebyshev orthogonal polynomial as a basis function, and setting Pz(r) is a z-th order polynomial in terms of coordinates in the r direction of
Figure BDA0003448401500000063
Set of points of { r1,r2,…,rMConstructing a corresponding orthogonal polynomial system { P }0(r),P1(r),…,Pn(r) }. Orthogonal polynomial { P) with coefficient of the highest order of 1 from polynomial trinomial recursion relationshipk(r) } (k ═ 0, 1.., n) has the following recurrence relation:
Figure BDA0003448401500000064
wherein P isk(r) is a polynomial of degree k with a coefficient of the highest term of 1, from { P }k(r) } orthogonality indicates:
Figure BDA0003448401500000071
Figure BDA0003448401500000072
from the equations (1), (2) and (3), an orthogonal polynomial system { P in the r direction can be obtained0(r),…,Pn(r)}：
{1,r-α,…,(r-αk)Pk-1(r)-βk-1Pk-2(r)}k＝2,3,…,n ⑷
Since the image is symmetrical, an orthogonal polynomial system { Q ] in the c-direction can be obtained in the same way0(c),…,Qn(c)}：
{1,c-α,…,(c-αk')Qk'-1(c)-βk'-1Qk'-2(c)}k'＝2,3,…,n ⑸
Therefore, the chebyshev orthogonal polynomial system { P ] for fitting a curved surface on a two-dimensional plane can be obtained from the equations (4), (5)0(r)Q0(c),P0(r)Q1(c)…,Pn(r)Qn(c)}：
{1,r-α,c-α,…,((r-αk)Pk-1(r)-βk-1Pk-2(r))((c-αk')Qk'-1(c)-βk'-1Qk'-2(c))} ⑹
And S5, constructing a regularization constraint term by using a chebyshev orthogonal polynomial surface fitting and modeling.
The degradation model of the degraded image can be expressed as:
g＝s+b+n ⑺
wherein g represents a degraded image, and fig. 3 is an original degraded image; s represents a potentially sharp image, and fig. 5 is a thermal emission effect correction chart; b represents the aerodynamic thermoluminescence effect diagram, and fig. 4 is a bolometry effect diagram estimate; n represents noise.
In data item
Figure BDA0003448401500000073
Adding the constraint of gradient domain thereof
Figure BDA0003448401500000074
And adds the L of the potential sharp image s in the gradient domain0A norm constraint term. It is desirable to approximate the aerodynamic thermoluminescence effect map b by the product Wa of the row vector W containing all chebyshev orthogonal polynomials and the column vector a of all its corresponding coefficients, thus adding the L of the gradient domain2Norm constraint term
Figure BDA0003448401500000075
The following energy function is thus constructed:
Figure BDA0003448401500000076
wherein, alpha, beta, gamma is weight, | | · | | non-phosphor0Represents L0Norm, representing the number of non-0 elements, | · (| non-conducting phosphor)2Is represented by L2The norm of the number of the first-order-of-arrival,
Figure BDA0003448401500000077
a gradient operator is represented.
Taking the chebyshev orthogonal polynomial with the highest order of 4 as an example, W can be obtained by equation (6):
W＝{P0(r)Q0(c),P0(r)Q1(c),…,P4(r)Q4(c)} ⑼
and S6, updating corresponding coefficients in the estimated chebyshev orthogonal polynomial function and the heat radiation effect diagram b and the potential clear image S by an alternate iteration method.
Due to L in the formula (8)0The existence of norm, the minimum solution is very difficult, so the estimation of the thermal radiation effect chart is respectively obtained by alternately solving the following formula
Figure BDA0003448401500000081
And potentially sharp images
Figure BDA0003448401500000082
Figure BDA0003448401500000083
Figure BDA0003448401500000084
For solving the b sub-problem, given an s, equation (10) can be written as the following least squares problem:
Figure BDA0003448401500000085
wherein
Figure BDA0003448401500000086
Representing the gradient in the horizontal and vertical directions, respectively.
a is iteratively updated by:
a＝(WTW)-1WTb ⒀
solving equation (12) yields equation (14), and iteratively updating b by equation (14):
Figure BDA0003448401500000087
wherein F (-) represents a Fourier transform, F-1(. represents an inverse Fourier transform, D)1、D2Representing the derivative operation matrix in the horizontal and vertical directions, respectively.
For solving the s-sub-problem, given a b, equation (11) can be rewritten as follows:
Figure BDA0003448401500000088
since equation (15) has L0The norm exists, the solution is very difficult, so the alternative iterative solution method is used, and the variable u is introducedr、ucTo make a constraint, equation (15) can be rewritten as:
Figure BDA0003448401500000089
by enforcing the constraints using Split Bregman iteration, equation (16) is rewritten as:
Figure BDA00034484015000000810
wherein t isr、tcIs the Bregman variable.
An iterative update is performed by the following equation:
Figure BDA0003448401500000091
Figure BDA0003448401500000092
Figure BDA0003448401500000093
Figure BDA0003448401500000094
Figure BDA0003448401500000095
wherein
Figure BDA0003448401500000096
Figure BDA0003448401500000097
It is meant a conjugate operation of the two,
Figure BDA0003448401500000098
representing component multiplication or division.
And S7, upsampling the obtained thermal radiation effect graph b and the potential clear image S to an upper scale for iteration again, and finally obtaining the thermal radiation effect graph and the potential clear image with the same resolution as the input.
As shown in fig. 2, 6 and 7, for the degraded image g of the minimum scale4The potentially sharp image S is obtained after the processing of the steps S4-S64And thermal radiation effect diagram b4Then the upsampling is carried out to obtain an initial estimation of an upper scale, and the steps S4-S6 are repeated to update the potential clear image S of the scale in an iteration mode3And thermal radiation effect diagram b3(ii) a By the same token, s can be obtained2、b2，s1、b1Finally, s consistent with the original resolution is obtained0、b0。
In summary, the invention discloses a pneumatic thermal radiation effect correction method based on multi-scale chebyshev (chebyshev) polynomial fitting, which comprises the following steps: carrying out filtering processing twice on the degraded image by using non-local mean filtering (NLM) to obtain a low-frequency smooth degraded image after preprocessing; taking the center of the image as a coordinate origin, and determining a symmetrical coordinate system by using the coordinate origin; establishing a multi-scale image pyramid by adopting a bilinear interpolation downsampling method; selecting a chebyshev orthogonal polynomial as a substrate to obtain an orthogonal polynomial system; constructing a regularization constraint term by using a chebyshev orthogonal polynomial surface fitting and modeling; updating and estimating coefficients, a heat radiation effect graph and a potential clear image in the chebyshev orthogonal polynomial function by an alternate iteration method; and upsampling the obtained thermal radiation effect graph and the potential clear image to an upper scale for iteration again, and finally obtaining the thermal radiation effect graph and the potential clear image with the same resolution as the input resolution. The invention can correct the pneumatic heat radiation effect by multi-scale chebyshev orthogonal polynomial fitting.
It should be noted that, according to the implementation requirement, each step/component described in the present application can be divided into more steps/components, and two or more steps/components or partial operations of the steps/components can be combined into new steps/components to achieve the purpose of the present invention.
It will be understood by those skilled in the art that the foregoing is merely a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included within the scope of the present invention.

Claims (8)

1. A pneumatic thermal radiation effect correction method based on multi-scale chebyshev polynomial fitting is characterized by comprising the following steps:
s2, taking the center of the degraded image as a coordinate origin, and determining a symmetrical coordinate system by using the coordinate origin;
s3, establishing a multi-scale image pyramid of the degraded image by adopting a down-sampling method;
s4, selecting a chebyshev orthogonal polynomial as a base to obtain an orthogonal polynomial system;
s5, constructing a regularization constraint term by using chebyshev orthogonal polynomial surface fitting and modeling;
s6, updating and estimating corresponding coefficients in the chebyshev orthogonal polynomial function, a heat radiation effect graph b and a potential clear image S by an alternate iteration method;
and S7, upsampling the obtained thermal radiation effect graph b and the potential clear image S to an upper scale for iteration again, and finally obtaining the thermal radiation effect graph and the potential clear image with the same resolution as the input.
2. The method for correcting the aerodynamic thermal radiation effect based on multi-scale chebyshev polynomial fitting according to claim 1, further comprising:
and S1, performing filtering preprocessing on the degraded image.
3. The method of claim 2, wherein the degraded image is pre-processed by two filtering operations using non-local mean filtering.
4. The multi-scale chebyshev polynomial fit-based method for correcting the effect of aerodynamic thermal radiation according to claim 1, characterized in that a bilinear interpolation down-sampling method is used.
5. The method for correcting the aerodynamic thermal radiation effect based on the multi-scale chebyshev polynomial fitting according to claim 1, wherein the step S4 is specifically as follows:
let the image size of the degraded image be M × N, (r, c) be the coordinates of the midpoint of the coordinate system;
selecting a chebyshev orthogonal polynomial as a basis function, and setting Pz(r) is a z-th order polynomial in terms of coordinates in the r direction of
Figure FDA0003448401490000011
Set of points of { r1,r2,…,rMConstructing a corresponding orthogonal polynomial system { P }0(r),P1(r),…,Pn(r) }; wherein
Figure FDA0003448401490000012
Is a lower integer function;
orthogonal polynomial { P) with coefficient of the highest order of 1 from polynomial trinomial recursion relationshipk(r) } (k ═ 0, 1.., n) has the following recurrence relation:
Figure FDA0003448401490000013
wherein P isk(r) is a polynomial of degree k with a coefficient of the highest term of 1, from { P }k(r) } orthogonality indicates:
Figure FDA0003448401490000021
Figure FDA0003448401490000022
from the equations (1), (2) and (3), an orthogonal polynomial system { P in the r direction can be obtained0(r),…,Pn(r) } is:
{1,r-α,…,(r-αk)Pk-1(r)-βk-1Pk-2(r)}k＝2,3,…,n ⑷
since the image is symmetrical, an orthogonal polynomial system { Q ] in the c-direction can be obtained in the same way0(c),…,Qn(c) The method is as follows:
{1,c-α,…,(c-αk')Qk'-1(c)-βk'-1Qk'-2(c)}k'＝2,3,…,n ⑸
thus, the chebyshev orthogonal polynomial system { P ] for fitting a curved surface on a two-dimensional plane is obtained from the equations (4), (5)0(r)Q0(c),P0(r)Q1(c)…,Pn(r)Qn(c)}：
{1,r-α,c-α,…,((r-αk)Pk-1(r)-βk-1Pk-2(r))((c-αk')Qk'-1(c)-βk'-1Qk'-2(c))} ⑹
Thereby establishing a row vector W of the chebyshev orthogonal polynomial.
6. The method for correcting the aerodynamic thermal radiation effect based on the multi-scale chebyshev polynomial fitting according to claim 1, wherein the step S5 is specifically as follows:
the degradation model of the degraded image is represented as:
g＝s+b+n ⑺
wherein g represents a degraded image, s represents a potentially sharp image, b represents an aerodynamic thermoluminescence effect map, and n represents noise;
in data item
Figure FDA0003448401490000023
Adding the constraint of gradient domain thereof
Figure FDA0003448401490000024
And adding the L of the potentially sharp image s in the gradient domain0A norm constraint term; approximating the aerodynamic thermoluminescence effect map b by the product Wa of the row vector W containing all chebyshev orthogonal polynomials and the column vector a of all its corresponding coefficients, thus adding the L of the gradient domain2Norm constraint term
Figure FDA0003448401490000025
The following energy function is thus constructed:
Figure FDA0003448401490000026
wherein, alpha, beta, gamma is weight, | | · | | non-phosphor0Represents L0Norm, representing the number of non-0 elements, | · (| non-conducting phosphor)2Is represented by L2The norm of the number of the first-order-of-arrival,
Figure FDA0003448401490000027
a gradient operator is represented.
7. The method for correcting the aerodynamic thermal radiation effect based on the multi-scale chebyshev polynomial fitting according to claim 6, wherein the step S6 is specifically as follows:
separately obtaining thermal radiance effect map estimates by alternately solving
Figure FDA0003448401490000031
And potentially sharp images
Figure FDA0003448401490000032
Figure FDA0003448401490000033
Figure FDA0003448401490000034
For solving the b sub-problem, given an s, equation (10) is rewritten as the following least squares problem:
Figure FDA0003448401490000035
wherein
Figure FDA0003448401490000036
Representing the gradient in the horizontal and vertical directions, respectively;
a is iteratively updated by:
a＝(WTW)-1WTb ⒀
solving equation (12) to obtain equation (14), and iteratively updating b by equation (14):
Figure FDA0003448401490000037
wherein F (-) represents a Fourier transform, F-1(. represents an inverse Fourier transform, D)1、D2Representing the derivative operation matrices in the horizontal and vertical directions, respectively;
for solving the s-sub-problem, given a b, equation (11) is rewritten as:
Figure FDA0003448401490000038
using an alternative iterative solution method, introducing a variable ur、ucTo perform a constraint, equation (15) is rewritten as:
Figure FDA0003448401490000039
by enforcing the constraints using Split Bregman iteration, equation (16) is rewritten as:
Figure FDA00034484014900000310
wherein t isr、tcIs the Bregman variable;
an iterative update is performed by the following equation:
Figure FDA0003448401490000041
Figure FDA0003448401490000042
Figure FDA0003448401490000043
Figure FDA0003448401490000044
Figure FDA0003448401490000045
wherein
Figure FDA0003448401490000046
Figure FDA0003448401490000047
It is meant a conjugate operation of the two,
Figure FDA0003448401490000048
representing component multiplication or division.
8. The method for correcting the aerodynamic thermal radiation effect based on the multi-scale chebyshev polynomial fitting according to claim 7, wherein the step S7 is specifically as follows:
and (3) processing the degraded image with the minimum scale in steps S4-S6 to obtain a potential clear image and a thermal radiation effect image, then sampling the degraded image to obtain an initial estimation of an upper-layer scale, repeating the steps S4-S6 to update the potential clear image and the thermal radiation effect image with the scale in an iteration mode, and finally obtaining the clear image and the thermal radiation effect image which are consistent with the original resolution.
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