Low-rank decomposition image non-uniformity stripe correction method and system

Abstract

The invention discloses a low-rank decomposition image non-uniformity stripe correction method and system, and belongs to the technical field of digital image processing. In the process of correcting an image to be corrected, an energy functional optimization model with the purpose of minimizing the sum of a data fidelity term, an image priori term and a stripe priori term is constructed, and on the basis of the discovery that a non-uniform stripe has consistency on each column, after a rank-one constraint is applied to a stripe matrix, the non-uniform stripe is corrected, so that the correction precision of the image to be corrected is improved. The model is decomposed and solved to realize reconstruction of stripe noise and image correction, so that an image with a non-uniform stripe can be accurately corrected, and the quality of the reconstructed image is improved; meanwhile, the method can accurately correct images containing different types of non-uniform stripe noise, and is wide in application range.

Description

Technical Field

[0001] The present invention belongs to the technical field of digital image processing, and more specifically, relates to a method and system for correcting non-uniform stripes of a low-rank decomposition image. Background Art

[0002] Due to reasons such as inconsistent detector response, in imaging systems such as multispectral remote sensing push-broom, swing-broom, and infrared focal plane arrays, there will inevitably be unevenly distributed horizontal or vertical stripes during the imaging process, i.e., non-uniform banding. The banding phenomenon will disrupt the qualitative analysis of the image and introduce strong deviations in subsequent processing. Therefore, under the condition of preserving image information and image structure as much as possible, eliminating the banding in the image is of great significance to the subsequent image application. Banding image correction can effectively improve image quality.

[0003] Most of the existing image stripe correction methods use filtering or statistical methods. Existing research results have proposed to use interpolation methods (CN118279171A) and joint filtering methods (CN116993631A) to remove stripe noise. The above stripe noise correction methods have the following problems: 1) The filtering method is mainly used to remove periodic stripes, but since the filtering method usually relies on removing specific frequency components of the stripes in the frequency domain, the filter may mistakenly filter out useful image structure information, resulting in the loss of image details. In addition, filtering may cause image blurring and artifacts at the edges. At the same time, since the frequency of the stripes may not be fixed and the shape and amplitude are complex, the filtering method may not be able to remove all stripes on non-periodic strips, making it difficult to effectively restore the image. 2) The interpolation method also has its simple and efficient performance in processing periodic strips, but the interpolation method usually relies on the assumption that the distribution and amplitude in the image are smooth or predictable. It cannot be effectively processed in the case of large noise, and may also cause the loss and blurring of image detail information when smoothing and reconstructing the image. The effect may be poor on nonlinear, irregular or high-frequency stripes, and the interpolation method may have high computational costs on large-size images, affecting processing efficiency. Therefore, existing technologies cannot accurately correct images with non-uniform stripes. Summary of the invention

[0004] In view of the above defects or improvement needs of the prior art, the present invention provides a method and system for correcting non-uniform stripes of a low-rank decomposition image, which is used to solve the technical problem that the prior art cannot accurately correct images with non-uniform stripes.

[0005] In order to achieve the above object, in a first aspect, the present invention provides a method for correcting non-uniform stripes of a low-rank decomposition image, comprising:

[0006] When the non-uniform stripes are additive noise, the image containing the non-uniform stripes is used as the image to be corrected to obtain the original clear image;

[0007] When the non-uniform stripes are multiplicative noises, the image containing the non-uniform stripes is logarithmized, and the obtained logarithmized image is used as the image to be corrected for correction; the clear image obtained by correction is indexed to obtain the original clear image;

[0008] The method for correcting the image to be corrected includes:

[0009] An energy functional optimization model is constructed with the goal of minimizing the sum of data fidelity terms, image prior terms and strip prior terms; wherein the data fidelity term is used to measure the difference between the image to be corrected and the sum of the clear image to be solved and the strip matrix; the image prior term is the regularization term of the gradient of the clear image to be solved; and the strip prior term is the regularization term of the strip matrix;

[0010] After imposing a rank-one constraint on the strip matrix, the energy functional optimization model with the rank-one constraint is decomposed into a first sub-model and a second sub-model, so as to perform multiple alternating iterative solutions to the clear image and the strip matrix to be solved; the first sub-model is a model whose goal is to minimize the sum of the data fidelity term and the image prior term; the second sub-model is a model with a rank-one constraint on the strip matrix, and whose goal is to minimize the sum of the data fidelity term and the strip prior term.

[0011] Further preferably, the method for correcting the image to be corrected further comprises: subtracting the solved strip matrix from the image to be corrected to obtain a final clear image.

[0012] Further preferably, the image priori term is the L0 norm of the gradient of the clear image to be solved.

[0013] Further preferably, the strip prior term is the L2 norm of the strip matrix.

[0014] Further preferably, a semi-quadratic variable separation algorithm is used to perform multiple alternating iterations on the clear image and the strip matrix to be solved.

[0015] Further preferably, the energy functional optimization model is:

[0016]

[0017] Among them, X is the clear image to be solved; G is the strip matrix; is the data fidelity term; Y is the image to be corrected; Pr1(X) is the image prior term; Pr2(G) is the strip prior term; Pr1(·) and Pr2(·) are both regularization expressions; β and λ are the corresponding regularization hyperparameters.

[0018] Further preferably, the energy functional optimization model with rank-one constraint is:

[0019]

[0020] Among them, x r is the rth row of the clear image to be solved; g r is the rth row of the strip matrix; M is the height of the image to be corrected; y r is the rth row of the image to be corrected; G is the strip matrix; Pr1(·) and Pr2(·) are both regularization expressions; β and λ are the corresponding regularization hyperparameters.

[0021] In a second aspect, the present invention provides a system for correcting non-uniform stripes of a low-rank decomposition image, comprising: a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the method for correcting non-uniform stripes of a low-rank decomposition image provided by the first aspect of the present invention is executed.

[0022] In a third aspect, the present invention also provides a computer-readable storage medium, which includes a stored computer program, wherein when the computer program is executed by a processor, the device where the storage medium is located is controlled to execute the method for correcting non-uniform stripes of a low-rank decomposition image provided in the first aspect of the present invention.

[0023] In a fourth aspect, the invention further provides a computer program product, comprising a computer program / instruction, characterized in that when the computer program / instruction is executed by a processor, the method for correcting non-uniform stripes of a low-rank decomposition image provided in the first aspect of the invention is implemented.

[0024] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

[0025] 1. The present invention provides a method for correcting non-uniform stripes in a low-rank decomposition image. In the process of correcting the image to be corrected, an energy functional optimization model is constructed with the goal of minimizing the sum of data fidelity terms, image prior terms and stripe prior terms. Based on the discovery that non-uniform strips are consistent in each column, after applying a rank-one constraint to the strip matrix, the model is decomposed and solved to achieve reconstruction of stripe noise and image correction. The present invention can maintain the image structure and accurately separate the stripe noise. By utilizing the fact that the image gradient in a natural image usually has a sparse characteristic and only has significant changes at the edge or in an area with rich texture, an image priori term is introduced. By constraining the sparsity of the image gradient, the influence of the stripe noise can be significantly weakened, and the stripe noise in the smooth area can be removed. At the same time, the structural characteristics of the image can be retained, which plays an important role in maintaining the visual quality and structure of the image after stripe correction. By utilizing the structural property of the stripe and the characteristics of the stripe component, a stripe priori term is introduced, which can be distinguished from the image information, reduce the interference of the stripe noise on the image structure, and suppress the propagation of the stripe noise in iteration, so that the corrected image is closer to a clear image without stripes, and the stability of strip removal is improved without destroying the normal details of the image. Therefore, the present invention can accurately correct an image with non-uniform stripes, and improve the quality of the reconstructed image. At the same time, the present invention can accurately correct an image containing different types of non-uniform stripe noise, and has a wide range of applications.

[0026] 2. Furthermore, in the low-rank decomposition image non-uniform stripe correction method provided by the present invention, the image prior term is the L0 norm of the gradient of the clear image to be solved, which can effectively maintain the structural characteristics of the image, avoid detail loss, and constrain the smoothness of the image.

[0027] 3. Furthermore, the method for correcting non-uniform stripes in low-rank decomposition images provided by the present invention, after performing multiple alternating iterative solutions to the clear image and the strip matrix to be solved, also subtracts the solved strip matrix from the image to be corrected to obtain a final clear image. Through this operation, the rich information carried in the image to be corrected can be fully utilized without losing the image structure information, thereby further improving the accuracy of the correction.

[0028] 4. Furthermore, the low-rank decomposition image non-uniform strip correction method provided by the present invention adopts a semi-quadratic variable separation algorithm to perform multiple alternating iterations on the clear image and strip matrix to be solved, and decomposes the original problem into a series of simpler quadratic optimization problems, thereby simplifying the calculation and approximating the solution of the original problem. The solution efficiency can be effectively improved while ensuring the solution accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 A flowchart of correcting an image to be corrected provided by an embodiment of the present invention;

[0030] Figure 2 A block diagram of correcting an image to be corrected provided by an embodiment of the present invention;

[0031] Figure 3 A schematic diagram of the image correction effect provided by an embodiment of the present invention; wherein (a) is an original clear image after correction of a degraded image; and (b) is an original clear image after correction of another degraded image. DETAILED DESCRIPTION

[0032] In order to make the purpose, technical solutions 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.

[0033] In order to solve the technical problems that the prior art processes images containing non-uniform stripe noise, resulting in missing image information after correction and incomplete removal of stripe noise in the corrected image, the present invention provides a method for correcting non-uniform stripes in low-rank decomposition images. The overall concept is to conduct an in-depth analysis of the mechanism of the occurrence of related problems, and based on the analysis results, impose a rank-one constraint on the stripe matrix accordingly, so that the image structural information is not lost on the basis of removing the stripe noise from the finally reconstructed image.

[0034] In order to achieve the above object, in a first aspect, the present invention provides a method for correcting non-uniform stripes of a low-rank decomposition image, comprising:

[0035] When the non-uniform stripes are additive noise, the image containing the non-uniform stripes is used as the image to be corrected to obtain the original clear image;

[0036] When the non-uniform stripes are multiplicative noise, the image containing the non-uniform stripes is logarithmized, and the obtained logarithmic image is used as the image to be corrected for correction; the clear image obtained by correction is exponentialized to obtain the original clear image. It should be noted that the logarithmization here can use a logarithmic function with any positive integer a as the base to process each pixel in the image, and correspondingly, the base of the exponentialization is also a. In an optional implementation, the logarithmic function uses the ln function, and the base of the exponential function is a constant e.

[0037] It should be noted that the image in the present invention may be an infrared image, a hyperspectral image, a multispectral remote sensing image, etc., which is not limited here.

[0038] Specifically, Figure 1As shown, the method for correcting the image to be corrected includes:

[0039] 1) Construct an energy functional optimization model with the goal of minimizing the sum of data fidelity terms, image prior terms and strip prior terms; wherein the data fidelity term is used to measure the difference between the image to be corrected and the sum of the clear image to be solved and the strip matrix; the image prior term is the regularization term of the gradient of the clear image to be solved; and the strip prior term is the regularization term of the strip matrix;

[0040] In an optional implementation mode, starting from the above technical concept, the setting of relevant constraints and the establishment of the overall model in the present invention are analyzed as follows:

[0041] The degradation mechanism model of stripe noise can be expressed as:

[0042] Y=G+X

[0043] Among them, Y is the image to be corrected; X is the clear image to be solved; G is the stripe noise.

[0044] On the basis of the above degradation mechanism model, the optimization framework can be established based on the maximum a posteriori probability method as follows, that is, the above energy functional optimization model is:

[0045]

[0046] Among them, X is the clear image to be solved; G is the strip matrix; is the data fidelity term; Y is the image to be corrected; Pr1(X) is the image prior term; Pr2(G) is the strip prior term; Pr1(·) and Pr2(·) are both regularization expressions; β and λ are the corresponding regularization hyperparameters.

[0047] It should be noted that the regularization may be L1 regularization or L2 regularization, which is not limited here. Preferably, in an optional implementation, the image prior term is the L0 norm of the gradient of the clear image to be solved. In an optional implementation, the strip prior term is the L2 norm of the strip matrix.

[0048] 2) After imposing a rank-one constraint on the strip matrix, the energy functional optimization model with the rank-one constraint is decomposed into a first sub-model and a second sub-model, so as to perform multiple alternating iterative solutions to the clear image and the strip matrix to be solved; the first sub-model is a model whose goal is to minimize the sum of the data fidelity term and the image prior term; the second sub-model is a model with a rank-one constraint on the strip matrix, and whose goal is to minimize the sum of the data fidelity term and the strip prior term.

[0049] In an optional implementation, it is found through research that the non-uniform strips are consistent in each column. Based on this finding, the present invention proposes to impose a rank-one constraint on the strip matrix. In addition, a sparse constraint is imposed on the gradient ▽x of the image, and the L0 norm is used to effectively constrain the smoothness of the image.

[0050] At this time, the expression of the data fidelity term is as follows:

[0051]

[0052] Where M is the height of the image to be corrected; y r is the rth row of the image to be corrected; x r is the rth row of X; g r is the rth row of G.

[0053] The expression of the image prior is as follows:

[0054]

[0055] The expression of the strip prior is as follows:

[0056]

[0057] The energy functional optimization model with rank-one constraint is obtained as follows:

[0058]

[0059] Among them, Pr1(·) and Pr2(·) are regularized expressions; β and λ are the corresponding regularization hyperparameters; rank represents the rank of the matrix.

[0060] It should be noted that the Half-Quadratic Splitting (HQS) algorithm, ADMM algorithm, etc. can be used to perform multiple alternating iterations to solve the clear image and strip matrix to be solved, which is not limited here. Preferably, in an optional implementation, the semi-quadratic variable separation algorithm is used to perform multiple alternating iterations to solve the clear image and strip matrix to be solved. HQS is a method for solving optimization problems, especially when the objective function contains non-convex or difficult-to-handle terms, it can be effectively solved. By introducing auxiliary variables and alternating optimization, HQS decomposes the original problem into a series of simpler quadratic optimization problems, thereby simplifying the calculation and approximating the solution to the original problem. Using the semi-quadratic variable separation algorithm to solve the model can effectively improve the solution efficiency while ensuring the solution accuracy.

[0061] In an optional implementation manner, the method for correcting the image to be corrected further includes: subtracting the solved strip matrix from the image to be corrected to obtain a final clear image.

[0062] By solving the above rank-one constrained energy functional optimization model, the final strip matrix G can be solved, and after subtracting the strip matrix G from the image to be corrected, a clear image X is obtained. This operation can make full use of the rich information carried in the image to be corrected without losing the image structure information, further improving the accuracy of correction.

[0063] Based on the above analysis, the present invention constructs an energy functional optimization model with the goal of minimizing the sum of data fidelity terms, image prior terms, and strip prior terms, and decomposes and solves the model to achieve reconstruction and image correction of strip noise while imposing a rank-one constraint on the strip matrix. This can improve the correction accuracy of images containing non-uniform stripes and improve the quality of reconstructed images. Compared with existing filtering methods, the present invention can maintain useful image structure information as much as possible, will not blur image details, and can also stably and effectively restore images in the case of stripes with non-fixed frequencies and complex shapes and amplitudes. Compared with existing interpolation methods, the present invention can also effectively process even when there is a lot of noise, can protect image detail information, and has high computational efficiency.

[0064] In order to further illustrate the method for correcting an image to be corrected provided by the present invention, a specific embodiment is described in detail below:

[0065] like Figure 2 As shown, in this embodiment, an infrared image containing non-uniform stripes taken by a push-broom imaging system is taken as an example, and the correction process includes:

[0066] S1. Construct an energy functional optimization model with the goal of minimizing the sum of data fidelity term, image prior term and strip prior term; wherein the data fidelity term is used to measure the difference between the image to be corrected and the sum of the clear image to be solved and the strip matrix; the image prior term is the L0 norm of the gradient of the clear image to be solved; and the strip prior term is the L2 norm of the strip matrix;

[0067] In this embodiment, the energy functional optimization model is:

[0068]

[0069] Among them, 0 represents the L0 norm; 2 represents the L2 norm.

[0070] S2. After imposing a rank-one constraint on the strip matrix, the energy functional optimization model with the rank-one constraint is decomposed into a first sub-model and a second sub-model, so as to perform multiple alternating iterative solutions to the clear image and the strip matrix to be solved; the first sub-model is a model whose goal is to minimize the sum of the data fidelity term and the image prior term; the second sub-model is a model with a rank-one constraint on the strip matrix, and whose goal is to minimize the sum of the data fidelity term and the strip prior term.

[0071] In this embodiment, the energy functional optimization model with rank-one constraint is:

[0072]

[0073] In this implementation, when solving the energy functional optimization model, the energy functional optimization model with rank-one constraint is decomposed into a first sub-model (X sub-problem) and a second sub-model (G sub-problem), specifically:

[0074]

[0075] (1) For subproblem X, use variable substitution to iteratively solve subproblem X:

[0076]

[0077] Introducing auxiliary variables The equivalent energy function is obtained as follows:

[0078]

[0079] Alternate iterations are used for optimization. For the X subproblem, Fourier transform X and then take the derivative and set the derivative to 0 to obtain a closed-form solution:

[0080]

[0081] Among them, 1 is a matrix whose element values ​​are all 1. For the U subproblem, the solution is:

[0082]

[0083] (2) For the G subproblem, the rank-one property of the strip matrix is ​​used to transform the subfunction into a final solvable energy functional optimization function:

[0084]

[0085] Since the strip matrix G has a constraint rank(G) = 1, each row corresponds to g r is the same as g, and further we get:

[0086]

[0087] Among them, r represents the rth row and M represents the total number of rows. The closed-form solution of g is obtained:

[0088]

[0089] The final estimated strip matrix G is obtained.

[0090] S3: Reconstruct the linear system of non-uniformity using the stripe expression model, and subtract the stripe noise from the image to be corrected Y to perform correction X=YG, and obtain the final clear image;

[0091] In general, this embodiment imposes a rank-one constraint on the stripe matrix, which can remove stripe noise with high precision without damaging image structure information.

[0092] The beneficial effects that can be achieved by this embodiment are further analyzed and explained below in combination with actual calibration examples.

[0093] Figure 3 The figure shows the correction result of non-uniform stripe correction based on the low-rank decomposition image non-uniform stripe correction method provided by this embodiment; wherein, Figure (a) is the original clear image after correction of a degraded image; Figure (b) is the original clear image after correction of another degraded image. Figure 3 It can be seen from the results that this embodiment can effectively implement correction for different images.

[0094] In a second aspect, the present invention provides a system for correcting non-uniform stripes of a low-rank decomposition image, comprising: a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the method for correcting non-uniform stripes of a low-rank decomposition image provided by the first aspect of the present invention is executed.

[0095] The related technical solution is the same as the low-rank decomposition image non-uniform stripe correction method provided in the first aspect of the present invention, and will not be described in detail here.

[0096] In a third aspect, the present invention also provides a computer-readable storage medium, which includes a stored computer program, wherein when the computer program is executed by a processor, the device where the storage medium is located is controlled to execute the method for correcting non-uniform stripes of a low-rank decomposition image provided in the first aspect of the present invention.

[0097] The related technical solution is the same as the method for correcting non-uniform stripes of low-rank decomposition images provided in the first aspect of the present invention, and will not be described in detail here.

[0098] In a fourth aspect, the invention further provides a computer program product, comprising a computer program / instruction, characterized in that when the computer program / instruction is executed by a processor, the method for correcting non-uniform stripes of a low-rank decomposition image provided in the first aspect of the invention is implemented.

[0099] The related technical solution is the same as the low-rank decomposition image non-uniform stripe correction method provided in the first aspect of the present invention, and will not be described in detail here.

[0100] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is 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 non-uniform stripes in a low-rank decomposition image, characterized in that: include: When the non-uniform stripes are additive noise, the image containing the non-uniform stripes is used as the image to be corrected to obtain the original clear image; When the non-uniform stripes are multiplicative noises, the image containing the non-uniform stripes is logarithmized, and the obtained logarithmized image is used as the image to be corrected for correction; the clear image obtained by correction is indexed to obtain the original clear image; The method for correcting the image to be corrected includes: An energy functional optimization model is constructed with the goal of minimizing the sum of a data fidelity term, an image prior term, and a strip prior term; the data fidelity term is used to measure the difference between the image to be corrected and the sum of the clear image to be solved and the strip matrix; the image prior term is a regularization term of the gradient of the clear image to be solved; and the strip prior term is a regularization term of the strip matrix; After applying a rank-one constraint to the strip matrix, the energy functional optimization model with the rank-one constraint is decomposed into a first sub-model and a second sub-model to perform multiple alternating iterative solutions to the clear image to be solved and the strip matrix; the first sub-model is a model whose goal is to minimize the sum of the data fidelity term and the image prior term; the second sub-model is a model with a rank-one constraint on the strip matrix, and whose goal is to minimize the sum of the data fidelity term and the strip prior term.

2. The method for correcting non-uniform stripes of low-rank decomposition images according to claim 1, characterized in that: The energy functional optimization model is: Wherein, X is the clear image to be solved; G is the strip matrix; is the data fidelity term; Y is the image to be corrected; Pr1(X) is the image prior term; Pr2(G) is the strip prior term; Pr1(·) and Pr2(·) are both regularization expressions; β and λ are the corresponding regularization hyperparameters.

3. The method for correcting non-uniform stripes of low-rank decomposition images according to claim 1, characterized in that: The energy functional optimization model with rank-one constraint is: Wherein, M is the height of the image to be corrected; y r is the rth row of the image to be corrected; r is the rth row of the clear image to be solved; g r is the rth row of the strip matrix; G is the strip matrix; Pr1(·) and Pr2(·) are both regularized expressions; β and λ are the corresponding regularization hyperparameters.

4. The method for correcting non-uniform stripes of low-rank decomposition images according to claim 1, characterized in that: The image priori term is the L0 norm of the gradient of the clear image to be solved.

5. The method for correcting non-uniform stripes of low-rank decomposition images according to claim 1, characterized in that: The strip prior term is the L2 norm of the strip matrix.

6. The method for correcting non-uniform stripes of low-rank decomposition images according to claim 1, characterized in that: A semi-quadratic variable separation algorithm is used to perform multiple alternating iterations on the clear image to be solved and the strip matrix.

7. The method for correcting non-uniform stripes of a low-rank decomposition image according to any one of claims 1 to 6, characterized in that: The method for correcting the image to be corrected further includes: subtracting the strip matrix obtained by solving from the image to be corrected to obtain a final clear image.

8. A low-rank decomposition image non-uniform stripe correction system, characterized in that: include: A memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the method for correcting non-uniform stripes of a low-rank decomposition image according to any one of claims 1 to 7 is executed.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a stored computer program, wherein when the computer program is executed by a processor, the device where the storage medium is located is controlled to execute the method for correcting non-uniform stripes of a low-rank decomposition image as described in any one of claims 1-7.

10. A computer program product, characterized in that It includes a computer program / instruction, characterized in that when the computer program / instruction is executed by a processor, it implements the low-rank decomposition image non-uniform strip correction method described in any one of claims 1-7.

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