Method and system for correcting non-uniform stripes in low-rank decomposition images

Abstract

The present invention discloses a method and system for correcting non-uniform stripes in low-rank decomposition images, belonging to the technical field of digital image processing. In the process of correcting the image to be corrected, an energy functional optimization model with the goal of minimizing the sum of data fidelity terms, image prior terms and stripe prior terms is constructed, and based on the discovery that non-uniform strips are consistent in each column, after applying a rank-one constraint to the stripe matrix, the model is decomposed and solved to achieve reconstruction of stripe noise and image correction. This method can accurately correct images with non-uniform stripes, thereby improving the quality of the reconstructed image. At the same time, the present invention can accurately correct images containing different types of non-uniform stripe noise, and has a wide range of applications.

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 in a low-rank decomposition image. Background Art

[0002] Due to inconsistent detector response and other factors, uneven distribution of light and dark in horizontal or vertical streaks, a phenomenon known as non-uniform banding, is unavoidable in imaging systems such as multispectral remote sensing push-broom, swing-broom, and infrared focal plane arrays. Banding can disrupt qualitative image analysis and introduce significant bias in subsequent processing. Therefore, eliminating banding while preserving image information and structure as much as possible is crucial for subsequent image applications. Banding correction effectively improves image quality.

[0003] Most existing image striping correction methods use filtering or statistical methods. Existing research results have proposed using interpolation methods (CN118279171A) and joint filtering methods (CN116993631A) to remove striping noise. These striping noise correction methods have the following problems: 1) Filtering methods are mainly used to remove periodic striping. However, because filtering methods generally rely on removing specific frequency components of the striping in the frequency domain, the filter may mistakenly filter out useful image structural information, resulting in a loss of image details. In addition, filtering may cause image blurring and artifacts at edges. Furthermore, because the frequency of the striping may not be fixed and the shape and amplitude are complex, filtering methods may not be able to remove all the striping in non-periodic striping, making it difficult to effectively restore the image. 2) Interpolation methods also have their own simple and efficient performance in processing periodic striping, but interpolation methods generally rely on the assumption that the distribution and amplitude of the image are smooth or predictable. They cannot effectively handle the situation with large noise. They may also cause loss of image details and blurring when smoothing and reconstructing the image. The effect may be poor on nonlinear, irregular, or high-frequency stripes, and interpolation methods for large images may be computationally expensive, affecting processing efficiency. Therefore, existing technologies are unable to accurately correct images with non-uniform stripes. Summary of the Invention

[0004] In response to the above defects or improvement needs of the prior art, the present invention provides a method and system for correcting non-uniform stripes in low-rank decomposition images, which are 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 objectives, in a first aspect, the present invention provides a method for correcting non-uniform stripes in 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 noise, 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 exponentially converted 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 the data fidelity term, the image prior term, and the stripe 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 stripe matrix. The image prior term is a regularization term for the gradient of the clear image to be solved. The stripe prior term is a regularization term for the stripe 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 to perform multiple alternating iterative solutions to the clear image and 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 includes: 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 stripe prior term is the L2 norm of the stripe 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] Where 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 stripe 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 low-rank decomposition image non-uniform stripe correction system, comprising: a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it executes the low-rank decomposition image non-uniform stripe correction method provided by the first aspect of the present invention.

[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 low-rank decomposition image non-uniform strip correction method provided in the first aspect of the present invention.

[0023] In a fourth aspect, the invention also 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 low-rank decomposition images. 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 stripe matrix, the model is decomposed and solved to achieve stripe noise reconstruction and image correction. The present invention can maintain image structure and accurately separate stripe noise. By utilizing the fact that image gradients in natural images are usually sparse and only have significant changes at the edges or in areas with rich textures, an image prior term is introduced. By constraining the sparsity of the image gradient, the influence of stripe noise can be significantly weakened, stripe noise in smooth areas can be removed, and the structural features of the image can be retained. This plays an important role in maintaining the visual quality and structure of the image after stripe correction. By utilizing the structural properties of the stripes and the characteristics of the stripe components, a stripe prior term is introduced, which can be distinguished from image information, reducing the interference of stripe noise on the image structure, and suppressing the propagation of stripe noise in iterations, making the corrected image closer to a clear image without stripes, and improving the stability of striping without destroying the normal details of the image. Therefore, the present invention can accurately correct images with non-uniform stripes, thereby improving the quality of the reconstructed image. At the same time, the present invention can accurately correct images containing different types of non-uniform stripe noise, and has a wide range of applications.

[0026] 2. Furthermore, the low-rank decomposition image non-uniform stripe correction method provided by the present invention has an image prior term which 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 the final clear image. This operation can fully utilize the rich information carried in the image to be corrected without losing the image structure information, thereby further improving the accuracy of the correction.

[0028] 4. Furthermore, the low-rank decomposition image non-uniform banding correction method provided by this invention employs a semi-quadratic variable separation algorithm to perform multiple alternating iterations on the target image and the banding matrix. By decomposing the original problem into a series of simpler quadratic optimization problems, the computation is simplified and the solution to the original problem is approximated. This effectively improves solution efficiency while maintaining 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 according to an embodiment of the present invention;

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

[0032] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining 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 may 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 existing technology of image processing containing non-uniform stripe noise results 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 relevant problems. Based on the analysis results, a rank-one constraint is imposed on the stripe matrix accordingly, so that the image structural information is not lost on the basis of removing the stripe noise from the final reconstructed image.

[0034] In order to achieve the above objectives, in a first aspect, the present invention provides a method for correcting non-uniform stripes in 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 resulting logarithmic image is used as the image to be corrected. The corrected clear image is then exponentially scaled to obtain the original clear image. It should be noted that the logarithmization here can be performed using a logarithmic function with an arbitrary positive integer a as the base to process each pixel in the image. Correspondingly, the base of the exponentialization is also a. In one optional embodiment, the logarithmic function is the ln function, and the base of the exponential function is the 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, if 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 the data fidelity term, the image prior term, and the stripe prior term. The data fidelity term measures the difference between the image to be corrected and the sum of the clear image to be solved and the stripe matrix. The image prior term is a regularization term for the gradient of the clear image to be solved. The stripe prior term is a regularization term for the stripe matrix.

[0040] In an optional implementation manner, 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] Where Y is the image to be corrected; X is the clear image to be solved; and 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] Where 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 stripe 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 can be L1 regularization or L2 regularization, which is not limited here. Preferably, in an optional embodiment, the image prior term is the L0 norm of the gradient of the clear image to be solved. In an optional embodiment, the stripe prior term is the L2 norm of the stripe 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 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 embodiment, it is found through research that the non-uniform stripes are consistent in each column. Based on this finding, the present invention proposes to impose a rank-one constraint on the stripe matrix. And the gradient of the image Imposing sparse constraints and using the L0 norm can effectively constrain the smoothness of the image.

[0050] At this point, 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 regularization 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 embodiment, the Half-Quadratic Splitting 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 Half-Quadratic Splitting 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 rank-one constrained energy functional optimization model, we can determine the final stripe matrix G. Subtracting the stripe matrix G from the image to be corrected yields the clear image X. This operation fully utilizes the rich information contained in the image to be corrected without losing any structural information, further improving the accuracy of the correction.

[0063] Based on the above analysis, the present invention constructs an energy functional optimization model with the goal of minimizing the sum of the data fidelity term, the image prior term, and the stripe prior term, and decomposes and solves the model while imposing a rank-one constraint on the stripe matrix to achieve stripe noise reconstruction and image correction. This can improve the correction accuracy of images containing non-uniform stripes and improve the quality of the reconstructed image. Compared with existing filtering methods, the present invention can maintain useful image structural information as much as possible without blurring image details. It can also stably and effectively restore images in the case of stripes with non-fixed frequency and complex shapes and amplitudes. Compared with existing interpolation methods, the present invention can also effectively process even in the case of large noise, can protect image details, 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, taking an infrared image containing non-uniform stripes captured by a push-broom imaging system as an example, the correction process includes:

[0066] S1. Construct an energy functional optimization model with the goal of minimizing the sum of the data fidelity term, the image prior term, and the stripe 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 stripe matrix; the image prior term is the L0 norm of the gradient of the clear image to be solved; and the stripe prior term is the L2 norm of the stripe 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 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, so as to perform multiple alternating iterative solutions to the clear image and 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, perform Fourier transform on X, then take the derivative and set the derivative to 0 to obtain the 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] Where r represents the rth row and M represents the total number of rows. The closed-form solution of g is:

[0088]

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

[0090] S3: Use the stripe expression model to reconstruct the linear system of non-uniformity, and subtract the stripe noise from the image to be corrected Y to perform correction X=YG to 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 structural information.

[0092] The following further analyzes and illustrates the beneficial effects that can be achieved by this embodiment in combination with actual calibration examples.

[0093] Figure 3 The figure shows the correction results of the non-uniform stripe correction method for low-rank decomposition images 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 achieve correction for different images.

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

[0095] The related technical solution is the same as the low-rank decomposition image non-uniform stripe correction method provided by 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 low-rank decomposition image non-uniform strip correction method provided in the first aspect of the present invention.

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

[0098] In a fourth aspect, the invention also 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 by 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 merely 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 scope of protection 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 noise, 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 exponentially converted 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 stripe 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 stripe matrix; the image prior term is a regularization term of the gradient of the clear image to be solved; and the stripe prior term is a regularization term of the stripe 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, so as to perform multiple alternating iterative solutions to the clear image to be solved and the strip matrix; the first sub-model is a model with the goal of minimizing 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 with the goal of minimizing the sum of the data fidelity term and the strip prior term; 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; x r is the rth row of the clear image to be solved; g r is the r-th row of the strip matrix; G is the strip matrix; β and λ are the corresponding regularization hyperparameters; || || 0 represents the L0 norm; || || 2 represents the L2 norm.

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

4. The method for correcting non-uniform stripes in a low-rank decomposition image according to any one of claims 1 to 3, wherein: The method for correcting the image to be corrected further includes: subtracting the strip matrix obtained by solution from the image to be corrected to obtain a final clear image.

5. 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 4 is executed.

6. 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 low-rank decomposition image non-uniform stripe correction method according to any one of claims 1 to 4.

7. A computer program product, characterized in that The method comprises computer program instructions, characterized in that when the computer program / instructions are executed by a processor, the method for correcting non-uniform stripes of a low-rank decomposition image according to any one of claims 1 to 4 is implemented.

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