Image reconstruction method based on g matrix and fourier transform

Abstract

The application discloses an image reconstruction method based on G matrix and Fourier transform. The overall mean of image information is inversed by a regularized G matrix inversion method, and the fluctuation component of the image information is inversed by a Fourier transform inversion method, and then the obtained inversion information is combined to obtain a high-resolution inversion reconstructed image. The G matrix inversion method is innovatively increased with a double regularization parameter term based on multiple constraint conditions, and different algorithms are used for different image information. For uniform scenes, point sources, land and sea and other prior scenes, multiple scale information can be combined to realize high-resolution image reconstruction. The application greatly reduces the calculation scale, reduces error transmission pollution, improves the resolution and accuracy of the inversion image, and is more consistent with the brightness temperature distribution characteristics of the measurement scene, and can be widely applied to the brightness temperature image inversion reconstruction process of a synthetic aperture microwave radiometer system.

Description

Technical Field

[0001] This invention belongs to the category of integrated aperture radiometer imaging systems for passive microwave remote sensing, specifically involving an image reconstruction method based on the G matrix and Fourier transform. Background Technology

[0002] Synthetic aperture radiometers are commonly used to detect extended source targets, generating a visibility function. The corrected brightness temperature of the measurement scene and the visibility function are a Fourier transform relationship. In actual measurements, the visibility function always contains azimuth-independent multiplicative errors, azimuth-dependent multiplicative errors, and additive errors. Therefore, the forward problem of obtaining the visibility space from the brightness temperature distribution can be described by a first-kind Freholm linear integral equation, while its inverse problem, after considering systematic errors, is an ill-posed equation. Ill-posed equations are characterized by susceptibility to perturbations, accompanied by unsolvable or physically meaningless incorrect solutions, and extremely high computational complexity.

[0003] Fourier inversion can easily and simply solve for the corrected brightness temperature under ideal conditions where there are no errors such as antenna coupling or channel differences. However, in practical scenarios, it can only serve as an approximate solution. The G-matrix inversion method can obtain an exact solution to the inversion equation under constraints, but the array size is large, error propagation during matrix operations is difficult to control, and the computational load is very high. Therefore, when designing a brightness temperature image inversion algorithm, it is necessary to consider the accuracy requirements of solving the equation, as well as the time constraints when processing data on platforms such as spaceborne radiometers, and to consider the controllability of computational scale and error propagation. Summary of the Invention

[0004] This invention addresses the problem of brightness temperature image inversion based on integrated aperture system in passive microwave remote sensing. It proposes an image reconstruction method based on the G matrix and Fourier transform to solve the problems of insufficient accuracy, susceptibility to systematic error contamination, or excessive computational resource consumption of traditional image reconstruction algorithms.

[0005] To solve the above problems, the specific content of the present invention is as follows:

[0006] Under ideal conditions, ignoring system errors such as channel differences and antenna coupling, the brightness temperature distribution and visibility function of the measurement scene satisfy a Fourier transform relationship, i.e., (x i ,y i ) and (x k ,y k ) represent the coordinates of antenna i and k, respectively; ξ and η represent the direction cosines; u and v represent the spatial frequencies; T mod (ξ,η) is the corrected brightness temperature. In actual measurements, the Fourier inversion method can also obtain an approximate solution to the image inversion problem based on this relationship.

[0007] For imaging systems with complex sources of actual error and a limited number of system baselines, the relationship between visibility and brightness temperature can also be established using the G matrix: V(u) = GT(u) + w(u), where w(u) represents noise. By setting regularization parameters and adding constraints with practical physical meaning, this complex matrix solution problem can be transformed into a semi-convergent optimization problem, yielding a solution with a certain accuracy.

[0008] This invention combines these two algorithms in a certain way, which reduces the high computational cost of the G matrix inversion method and reduces the fluctuations of the solution under FFT inversion.

[0009] Specifically, since the number of element antennas in a synthetic aperture radiometer is limited, the bandwidth of the resulting visibility sampling space is also limited. Therefore, for the brightness temperature information of the measurement scene, the scene can be set as prior mean information and fluctuation value information, and two algorithms can be used to solve for low-frequency information and unobservable high-frequency information, respectively. In particular, for scenes with prior models, the corresponding pattern data can be used to equivalently replace the mean information.

[0010] The actual measurement system processing is a linear process. The equivalent prior mean information is used to calculate the visibility function using the G matrix, and a linear transformation is used to obtain the background brightness temperature of the measurement scene, i.e., V0 = GT0. However, in actual calculations, this equation is ill-posed. Therefore, this invention, taking into account the characteristics of a synthetic aperture radiometer, introduces a double regularization parameter, an energy constraint term, and a band-limited constraint term to more accurately obtain multi-scale information on the scene brightness temperature distribution. This is transformed into a minimization problem with regularization parameters, where L1 is the gradient operator, L2 is the Laplace operator, 0 < λ < 1, and the minimization objective function is:

[0011] For the fluctuation information of scene brightness temperature, the original brightness temperature data of the measured scene is used as input. The visibility function corresponding to each pixel is used for difference operation to obtain the fluctuation information ΔV=V2-V1, and then processed by Fourier transform relationship T2(ξ,η). ＝ F -1 [W(u,v)ΔV(u,v)]. The mean and fluctuation values ​​can be directly inverted using the superposition property of a linear system to obtain the brightness temperature image T = T1 + T2.

[0012] This invention solves for the fluctuation components of the brightness temperature image by Fourier transform, effectively eliminating the interference of background brightness temperature measurement errors and systematic errors. It uses the G matrix to calculate the equivalent mean information of the brightness temperature data, ensuring the overall accuracy requirements of the reconstructed image and reducing the overall computational load. It is suitable for image inversion requirements of various integrated aperture radiometer systems. Attached Figure Description

[0013] Figure 1This is a basic flowchart for image reconstruction from a synthetic aperture radiometer.

[0014] Figure 2 This is a schematic diagram of solving the regularized G matrix inversion in the constraint space;

[0015] Figure 3 It is a high-resolution image reconstruction method based on the G matrix and FFT transform;

[0016] Figure 4a This is a schematic diagram of the original image;

[0017] Figure 4b This is a schematic diagram of reconstructing the original image using the FFT algorithm;

[0018] Figure 4c This is a schematic diagram of reconstructing the original image using the FFT algorithm combined with the G matrix;

[0019] Figure 5a This is a schematic diagram illustrating the quantitative evaluation of image quality inversion using the FFT algorithm.

[0020] Figure 5b This is a schematic diagram illustrating the quantitative evaluation of image quality obtained by combining the FFT algorithm with the G matrix. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and embodiments, and specific implementation methods for some application scenarios will be introduced, describing the process of obtaining this algorithm. For those skilled in the art, these examples can be used to obtain high-resolution reconstructed images in other similar scenarios.

[0022] This invention provides an image reconstruction method based on the G matrix and Fourier transform, comprising:

[0023] Step S1: In the integrated aperture detection mechanism of the passive remote sensing microwave radiometer, for brightness and temperature scenes with certain characteristics, the overall mean of the image information is inverted using the regularized G matrix method. The objective function of the G matrix optimization is enhanced with regularization parameters, constraints, a first-order gradient operator, and a second-order Laplace operator. The fluctuation components of the image information are inverted using the Fourier transform method. The process of obtaining the visibility function using the integrated aperture radiometer system is a linear process. By combining the obtained inversion information, a high-resolution inversion reconstructed image is obtained.

[0024] In one embodiment of the image reconstruction method based on the G matrix and Fourier transform of the present invention, step S1 includes:

[0025] Solving the G matrix image inversion equation transforms the traditional ill-conditioned equation for finding the Moore-Penrose pseudo-inverse into solving an optimization problem with energy constraints, least squares conditions, and minimum norm conditions through band-limited regularization and minimum regularization.

[0026] Among them, the two regularization methods introduced modify the objective function of the minimization problem through double regularization parameter terms, gradient operators and Laplace operators. The regularization term corresponding to the energy constraint condition adds the L operator to better reflect the image texture information, and the regularization term corresponding to the band-limited constraint condition adds the gradient operator to better highlight the image edge information of the finite bandwidth sampling values ​​of the synthetic aperture radiometer.

[0027] In one embodiment of the image reconstruction method based on the G matrix and Fourier transform of the present invention, step S1 includes:

[0028] When measuring a uniform scene with good brightness temperature consistency on the sea surface or snow, if the redundancy and compressibility of the mean information of the brightness temperature image are greater than the preset threshold, and the computational load is less than the preset threshold, then a regularized G matrix is ​​used for high-precision solution; if the fluctuation of the image's undulation component is less than the preset threshold, then the FFT inversion method is used to maintain high accuracy and eliminate error interference from background brightness temperature error and system error.

[0029] In one embodiment of the image reconstruction method based on the G matrix and Fourier transform of the present invention, step S1 includes:

[0030] When measuring the source scene of point interference sources, the sun, or the moon, based on the method of solving the mean scene, a regularized G matrix inversion method is applied to the point source and its surrounding area. The inversion information obtained by combining the composite algorithm is used to further highlight and sharpen the brightness temperature information near the point source, resulting in a high-resolution inversion image.

[0031] In one embodiment of the image reconstruction method based on the G matrix and Fourier transform of the present invention, step S1 includes:

[0032] When measuring land and ocean scenes, land areas are classified into one category and ocean areas into another. A composite inversion algorithm based on a regularized G matrix and Fourier transform is applied to each region to eliminate mutual error interference between the two significantly different measurement scenes during the inversion process.

[0033] In one embodiment of the image reconstruction method based on the G matrix and Fourier transform of the present invention, step S1 includes:

[0034] When measuring a priori scene with a known brightness temperature model, such as when there is already annual or seasonal average brightness temperature data of the actual scene, the brightness temperature data and the pattern data with the same magnitude as the actual brightness temperature are solved by the regularized G matrix inversion method with reference to the image mean data processing method. The difference between the actual measured data and the pattern data is solved by the Fourier inversion method with reference to the image fluctuation value data processing method. The information obtained by combining the composite inversion algorithm is used to obtain a high-resolution reconstructed image.

[0035] refer to Figure 1 In the actual image reconstruction process of a synthetic aperture radiometer system, a binary interferometer composed of a group of unit antennas receives brightness temperature radiation information. This information is then filtered, orthogonalized, and subjected to digital complex correlation operations on the orthogonal components via their respective receiver channels to obtain the corresponding visibility function. Ignoring errors such as differences in receiver transmission characteristics, the corrected brightness temperature and the visibility function obtained after mathematical processing are the results of Fourier transforms of each other. However, after introducing errors, the visibility function is expressed as V(u)=∫K(u,ξ)c(u)T ideal The first kind of Fredholm linear integral equation is ill-posed, with an excessively large condition number, making it difficult to find an exact solution. Although the Fourier transform method is computationally simple and fast, it can only obtain an approximate solution to this problem.

[0036] To obtain a definitive solution, the image reconstruction problem can also be equivalent to a matrix problem, V = GT. Since synthetic aperture radiometers often measure large extended sources, the number of brightness temperature pixels is often greater than the number of non-redundant visibility sample points. The analytical solution is expressed as T = G. H (GG H ) -1 V. Given a visibility error constraint of ε and a brightness temperature radiation energy constraint of E, like Figure 2 As shown, numerical computation can solve for the regularization parameter μ. opt and optimal objective function A high-precision solution is obtained. Furthermore, to reduce the loss of high-frequency information due to the limited bandwidth of the synthetic aperture radiometer, a new regularization parameter is introduced into this objective function to obtain multi-scale information on the scene brightness temperature distribution. L1 is the gradient operator, L2 is the Laplace operator, 0 < λ < 1, and the objective function is minimized as follows: Based on the characteristics of linear systems, the regularization terms corresponding to both energy constraints and band-limited constraints can be equivalently represented by brightness-temperature residual terms. Adding the L operator to the former better reflects image texture information, while adding the gradient operator to the latter better characterizes image edge information from the finite bandwidth samples of the synthetic aperture radiometer. The regularization parameter λ can be determined empirically first, and then the minimization problem can be solved graphically using a single-parameter (μ) regularization method. Alternatively, all regularization parameters μ and λ can be directly determined using a two-dimensional generalized cross-validation method.

[0037] Although the numerical solution obtained by the regularized G matrix inversion method approximates the exact solution with high accuracy, the computational complexity of solving the G operator, analyzing generalized solutions, and solving semi-convergent optimization problems is substantial, and the intermediate results are easily contaminated by error propagation. Therefore, an inversion algorithm is needed that can eliminate interference from systematic errors and background brightness temperature errors, while maintaining high accuracy (resolution) and a suitable computational load. (Reference) Figure 3 The process, combined with the claims and the description in the above invention content, ensures the high accuracy of the overall image by solving the mean part of the brightness temperature information using the regularized G matrix inversion method, minimizing system errors and background interference, and reduces the amount of computation and storage by solving the fluctuation part of the brightness temperature information using the Fourier inversion method.

[0038] In Example 1, for uniform brightness temperature scenes, such as calm sea surfaces and snowfields, the scene brightness temperature is directly averaged by pixels. The mean value is inverted using a regularized G matrix. The difference between the original brightness temperature information and the mean value is used for Fourier inversion. The inversion results are then superimposed to obtain a high-resolution reconstructed image.

[0039] Example 2: For a uniform brightness temperature scene containing point sources, such as the sun and moon, after obtaining the background reconstruction image using Example 1 for the uniform scene, the original brightness temperature information of the point sources and nearby small areas is directly inverted using the regularized G matrix method. Since the computational area is very small and the radiation energy source is singular, even the regularized G matrix inversion method has a relatively small computational load. The inversion results are then superimposed to obtain a high-resolution reconstructed image.

[0040] Example 3: When retrieving a wide-swath image that mixes land and ocean areas, the background brightness temperature model data of the two regions differ significantly, easily causing interference during the inversion process. Therefore, when multiple regions exist within the image sheet with marked differences in their brightness temperature models, these regions are classified and processed separately using the composite algorithm described in Example 1. This eliminates mutual background brightness temperature interference and effectively obtains a high-resolution reconstructed image. For such measurement scenarios with significant differences, it is possible to obtain... Figure 4a , 4b 4c and Figure 5a , 5bBy comparing the reconstruction results of different algorithms, it can be found that the composite algorithm has smaller mean error and standard root mean square error in the reconstructed image, and a higher degree of fit with the brightness and temperature of the original scene.

[0041] Example 4: For some prior scenarios, i.e., the brightness temperature models of these scenarios are known or there is partial brightness temperature data of these scenarios, such as the annual average brightness temperature data of a certain region in a certain year, these model values ​​that are consistent with the magnitude of the actual measurement state can be used as equivalent mean components. The mean information is obtained by regularizing the G matrix inversion method. The difference component between the actual brightness temperature data and the model value is used as equivalent fluctuation value component. The fluctuation value information is obtained by Fourier transform inversion method. The two are superimposed to obtain an effective high-resolution inversion image.

Claims

1. An image reconstruction method based on the G matrix and Fourier transform, characterized in that, include: Step S1: In the integrated aperture detection mechanism of the passive remote sensing microwave radiometer, for brightness and temperature scenes with certain characteristics, the overall mean of the image information is inverted using the regularized G matrix method. The objective function of the G matrix optimization is enhanced with regularization parameters, constraints, a first-order gradient operator, and a second-order Laplace operator. The fluctuation components of the image information are inverted using the Fourier transform method. The process of obtaining the visibility function using the integrated aperture radiometer system is a linear process. By combining the obtained inversion information, a high-resolution inversion reconstructed image is obtained.

2. The image reconstruction method based on the G matrix and Fourier transform as described in claim 1, characterized in that, Step S1 includes: Solving the G matrix image inversion equation transforms the traditional ill-conditioned equation for finding the Moore-Penrose pseudo-inverse into solving an optimization problem with energy constraints, least squares conditions, and minimum norm conditions through band-limited regularization and minimum regularization. Among them, the two regularization methods introduced modify the objective function of the minimization problem through double regularization parameter terms, gradient operators and Laplace operators. The regularization term corresponding to the energy constraint condition adds the Laplace operator to better reflect the image texture information, and the regularization term corresponding to the band-limited constraint condition adds the gradient operator to better highlight the image edge information of the finite bandwidth sampling values ​​of the synthetic aperture radiometer.

3. The image reconstruction method based on the G matrix and Fourier transform as described in claim 1, characterized in that, Step S1 includes: When measuring a uniform scene with good brightness temperature consistency on the sea surface or snow, if the redundancy and compressibility of the mean information of the brightness temperature image are greater than the preset threshold, and the computational load is less than the preset threshold, then a regularized G matrix is ​​used for high-precision solution; if the fluctuation of the image's undulation component is less than the preset threshold, then the FFT inversion method is used to maintain high accuracy and eliminate error interference from background brightness temperature error and system error.

4. The image reconstruction method based on the G matrix and Fourier transform as described in claim 1, characterized in that, Step S1 includes: When measuring the source scene of point interference sources, the sun, or the moon, based on the method of solving the mean scene, a regularized G matrix inversion method is applied to the point source and its surrounding area. The inversion information obtained by combining the composite algorithm is used to further highlight and sharpen the brightness temperature information near the point source, resulting in a high-resolution inversion image.

5. The image reconstruction method based on the G matrix and Fourier transform as described in claim 1, characterized in that, Step S1 includes: When measuring land and ocean scenes, land areas are classified into one category and ocean areas into another. A composite inversion algorithm based on a regularized G matrix and Fourier transform is applied to each region to eliminate mutual error interference between the two significantly different measurement scenes during the inversion process.

6. The image reconstruction method based on the G matrix and Fourier transform as described in claim 1, characterized in that, Step S1 includes: When measuring a prior scene with a known brightness temperature model, where the prior scene with a known brightness temperature model is the annual average or seasonal average brightness temperature data of an existing actual scene, the brightness temperature data and the pattern data with the same magnitude as the actual brightness temperature are solved by the regularized G matrix inversion method with reference to the image mean data processing method. The difference between the actual measured data and the pattern data is solved by the Fourier inversion method with reference to the fluctuation component data processing method of the image information. The information obtained by combining the composite inversion algorithm is used to obtain a high-resolution reconstructed image.

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