Image blind restoration method based on COS function and Wiener filtering

Abstract

The invention relates to the technical field of image processing, and particularly provides an image blind restoration method based on a COS function and Wiener filtering, comprising: acquiring a blurred image to be processed, constructing a blind deblurring model under a variational framework, an objective function of the blind deblurring model being used for synchronously estimating a low-rank clear image and a blurring kernel; solving the target function in the multi-scale Gaussian space through an alternating iteration optimization strategy, and estimating to obtain a low-rank clear image and a blurring kernel; and performing Wiener filtering on the blurred image by using the solved blurred kernel to obtain an initial restored image, and performing COS filtering on the initial restored image to obtain a final restored image. Wiener filtering and the COS filter are combined, smooth transition is carried out through the COS filter, and the ringing artifact problem existing in traditional Wiener filtering is effectively solved.

Description

Technical Field

[0001] This invention belongs to the field of image processing technology, and in particular relates to a blind image restoration method based on the COS function and Wiener filtering. Background Technology

[0002] During remote sensing imaging, images are often blurred and noisy due to various factors such as environmental interference, platform vibration, and atmospheric turbulence, severely affecting image quality and the accuracy of subsequent analysis. Currently, the main methods for refining and restoring remote sensing images can be categorized into three types: first, deconvolution methods based on on-orbit target testing; second, restoration methods based on traditional variational models; and third, restoration methods based on deep learning.

[0003] Image degradation is typically modeled as a convolution operation between the original sharp image and a blur kernel, with noise added, thus establishing a regularized restoration framework model. Based on this model, a two-step process is used for image restoration: first, the blur kernel is estimated under a blind restoration framework; then, the estimated blur kernel is used for non-blind deblurring to achieve ringing suppression and further restore the sharp image.

[0004] In the process of non-blind deblurring, Wiener filtering is currently widely used. Wiener filtering is a special case based on the traditional variational model. Although this method can achieve non-blind deblurring, Wiener filtering still has obvious defects in actual restoration, especially in the image edge area where it is easy to introduce ringing artifacts, which affects the restoration effect. Summary of the Invention

[0005] In view of this, the present invention aims to provide a blind image restoration method based on the COS function and Wiener filtering. It improves the traditional Wiener filtering method by introducing the COS filtering method, which effectively suppresses the ringing effect in the edge region while maintaining the deblurring ability of Wiener filtering, thereby improving the overall image restoration quality.

[0006] To achieve the above objectives, the technical solution created by this invention is implemented as follows: This invention provides a method for blind image ringing suppression and restoration based on the COS function and Wiener filtering, comprising: Obtain the blurred image to be processed; A blind deblurring model is constructed within a variational framework. The objective function of the blind deblurring model is used to simultaneously estimate the low-rank sharp image and the blur kernel. A multi-scale Gaussian space is constructed, and the objective function is solved by an alternating iterative optimization strategy within the multi-scale Gaussian space to estimate and obtain a low-rank sharp image and a blur kernel. Using the obtained blur kernel, Wiener filtering is applied to the blurred image to obtain the initial restored image. Then, COS filtering is applied to the initial restored image to obtain the final restored image.

[0007] Preferably, the objective function includes: a data fidelity term, an image gradient term, a blur kernel gradient term, and a Laplacian regularization term.

[0008] Preferably, the objective function is: ; in, Indicates to make When taking the minimum value and The value, For data fidelity items, Represents a low-rank sharp image. Indicates the fuzzy kernel. Represents a blurred image. This represents the convolution operation. For image gradient terms, For the fuzzy kernel gradient term, For Laplace regularization, For the Laplace operator, For image gradient operators, This represents the image gradient operator in the x-direction. , and This represents the weighting factor.

[0009] Preferred Laplace operator for: .

[0010] Preferably, a multi-scale Gaussian space is constructed, including: The blurred image is subjected to multiple Gaussian blurring and downsampling processes to generate image pyramids of different resolutions, i.e., multi-scale Gaussian spaces.

[0011] The preferred formula for estimating the fuzzy kernel is: ; in, Indicates the fuzzy kernel. Represents FFT transformation, Represents the FFT conjugate transform. Indicates the inverse FFT. Represents a low-rank sharp image. Represents a blurred image. , and Indicates the weighting factor. For image gradient operators, For the Laplace operator; The estimation formula for low-rank sharp images is: .

[0012] Preferably, Wiener filtering is performed on the blurred image, including: ; in, This represents the initial restored image. For Wiener deconvolution function, Indicates the fuzzy kernel. Represents a blurred image. This is the reciprocal of the signal-to-noise ratio of the blurred image.

[0013] Preferably, COS filtering is applied to the initial restored image, including: Generate a pixel frequency coordinate matrix on the initial restored image based on the size of the initial restored image. The size of the initial restored image is: ; in, These are the length and width of the initial restored image, respectively. This is a function for measuring image size. The frequency domain coordinates of any pixel in the initial restored image are: ; in, For any pixel frequency domain coordinates on the initial restored image, For pixel frequency domain coordinate transformation function; The final restored image is obtained through COS filtering. for: ; in, Indicates taking the real part, Indicates the inverse FFT. Represents FFT transformation, Indicates the convolution operation; ; in, Optimize parameters for grayscale values. This represents the distance between the frequency domain coordinates of any pixel and the frequency center. Indicates an adjustable parameter. , This represents the square root operation.

[0014] Compared with the prior art, the present invention can achieve the following beneficial effects: This invention creatively combines Wiener filtering with a custom COS filter. Wiener filtering is responsible for the initial strong deblurring, while the COS filter, as a smooth-transition frequency domain filter, can effectively filter out unnatural high-frequency oscillations generated by Wiener filtering near strong edges. While maintaining high definition, the visual quality is significantly improved, and the ringing artifacts generated after Wiener filtering are eliminated.

[0015] This invention introduces the Laplacian operator as a regularization term for the blur kernel to suppress noise and minor fluctuations within the blur kernel, making the estimated blur kernel more consistent with physical reality. Furthermore, by combining multi-scale Gaussian space and an alternating iterative optimization strategy, it solves for clear images and blur kernels from coarse to fine, providing stable initial values ​​for each scale solution step by step, effectively avoiding the problem of getting trapped in local optima. Attached Figure Description

[0016] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of an image blind restoration method based on the COS function and Wiener filtering provided in an embodiment of the present invention; Figure 2 The image to be processed is a blurred image provided according to an embodiment of the present invention; Figure 3 This is a schematic diagram of iterative estimation of fuzzy kernel in multi-scale Gaussian space according to an embodiment of the present invention; Figure 4 This is the final restored image provided according to an embodiment of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and do not constitute a limitation thereof. Similar elements in different embodiments are referred to by associated similar element reference numerals. In the following embodiments, many details are described to facilitate a better understanding of the invention. However, those skilled in the art will readily recognize that some features may be omitted in different situations, or may be replaced by other elements, materials, or methods. In some cases, some operations related to the invention are not shown or described in the specification. This is to avoid obscuring the core parts of the invention with excessive description. For those skilled in the art, detailed description of these related operations is not necessary; they can fully understand the related operations based on the description in the specification and general technical knowledge in the art.

[0018] It should be noted that, unless otherwise specified, the embodiments and features described in this invention can be combined to form various implementations. Furthermore, the order of the steps or actions in the method description can be changed or adjusted in a manner readily apparent to those skilled in the art. Therefore, the various orders in the specification and drawings are merely for the clear description of a particular embodiment and do not imply a mandatory order, unless otherwise stated that a particular order must be followed.

[0019] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0020] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0021] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0022] Please see Figure 1 In one embodiment of the present invention, a blind image restoration method based on COS function and Wiener filtering is provided. Based on the traditional Wiener filtering method, a custom COS filter is introduced, which effectively suppresses the ringing effect in edge regions while maintaining the deblurring capability of Wiener filtering, greatly improving the quality of the restored image. The method specifically includes the following steps: S1: Obtain the blurred image to be processed. In this embodiment of the invention, specifically as follows: Figure 2 The infrared blurred image shown is used as an example to serve as the target image for subsequent restoration.

[0023] S2: Construct a blind deblurring model within a variational framework. The objective function of the blind deblurring model is used to simultaneously estimate the low-rank sharp image and the blur kernel.

[0024] Specifically, a blind deblurring model is first constructed within a variational framework. To suppress noise and minor fluctuations within the blur kernel and make the estimated blur kernel more consistent with physical reality, this embodiment of the invention incorporates a Laplacian operator into the objective function of the blind deblurring model, embedding a Laplacian regularization term within the objective function. The objective function specifically includes a data fidelity term, an image gradient term, a blur kernel gradient term, and a Laplacian regularization term, and its expression is: ; in, Represents a low-rank sharp image. Indicates the fuzzy kernel. Represents a blurred image. This represents the convolution operation. For the Laplace operator, For image gradient operators, , This represents the image gradient operator in the x-direction. This represents the image gradient operator in the y-direction. , and This represents the weighting factor, all of which are initially assigned a value of 1. Indicates to make When taking the minimum value and The value, This is a data fidelity term used to ensure the clarity of the estimated low-rank image. With fuzzy kernel The convolution result should be as close as possible to the blurry image obtained from actual observation. , The image gradient term is used to constrain the image gradient, ensuring a sharp low-rank image after deblurring. Blurred image at the edges To maintain consistent gradient changes and reduce edge artifacts, For the fuzzy kernel gradient term, for the fuzzy kernel Apply smoothness constraints. This is a Laplace regularization term used to further suppress the fuzzy kernel. Internal noise and high-frequency artifacts, Laplace operator Specifically set as follows: .

[0025] S3: Construct a multi-scale Gaussian space, solve the objective function in the multi-scale Gaussian space through an alternating iterative optimization strategy, and estimate the low-rank sharp image and blur kernel.

[0026] Specifically, such as Figure 3 As shown, in the process of solving the fuzzy kernel, a multi-scale Gaussian space is first constructed, and a coarse-to-fine strategy is adopted for solving the fuzzy kernel. The construction process of the multi-scale Gaussian space is as follows: for the fuzzy image... Multiple Gaussian blurring and downsampling processes are performed to generate image processing layers at multiple scales, resulting in image pyramids of different resolutions, i.e., multi-scale Gaussian spaces.

[0027] Further, low-rank sharp images are solved simultaneously at each scale. With fuzzy kernel The solution results of the upper scale are used as the initial values ​​of the next scale, that is, the solution results of the coarse scale are used as the initial values ​​of the fine scale. The objective function is optimized by alternating and iteratively solving at multiple scales to estimate and obtain the low-rank sharp image and blur kernel.

[0028] In the alternating iterative optimization process, regarding the fuzzy kernel The solution process is designed as follows: To accelerate convergence and obtain more accurate results, embodiments of the present invention utilize a fuzzy kernel... In the solution process, only the image gradient in the x-direction is considered, and a blur kernel is generated in the frequency domain using Fast Fourier Transform (FFT). Solve for the estimation formula: ; in, Indicates the fuzzy kernel. Represents FFT transformation, Represents the FFT conjugate transform. This represents the inverse FFT.

[0029] Regarding low-rank clear images The solution process is designed as follows: In each iteration, the previously obtained blur kernel is fixed and used to obtain a low-rank sharp image. The solution to this problem is given by the estimation formula: .

[0030] In short, during the iterative solution process, the low-resolution solution results are used as the initial values ​​for the high-resolution solution, by fixing the low-rank clear image. Solving the fuzzy kernel Then solve the fuzzy kernel Fix the image and re-solve for the low-rank sharp image. This is done through alternating iterative optimization to determine the weight factors in the objective function and obtain the final fuzzy kernel. .

[0031] S4: Using the obtained blur kernel, Wiener filtering is applied to the blurred image to obtain the initial restored image. Then, COS filtering is applied to the initial restored image to obtain the final restored image.

[0032] Specifically, the fuzzy kernel is obtained in S3 estimation. Subsequently, image sharpening is achieved through a combination of Wiener filtering and COS filtering, effectively suppressing ringing artifacts while retaining the powerful deblurring capabilities of Wiener filtering. The estimated blur kernel is then used... For blurry images The initial restored image is obtained by performing Wiener filtering. The Wiener filtering function is as follows: ; in, This represents the initial restored image. For Wiener deconvolution function, This is the reciprocal of the signal-to-noise ratio of the blurred image, specifically 0.01 in this case.

[0033] After obtaining the initial restored image, a custom frequency-domain COS filter is used to suppress ringing artifacts in the Wiener filtering result, and the initial restored image is then subjected to COS filtering. The specific process of constructing the COS filter is as follows: First, using built-in Matlab functions, the initial dimensions of the restored image are obtained as follows: ; in, These represent the length and width of the initial restored image, expressed here using the number of pixel rows and columns. This is a built-in image size measurement function in Matlab.

[0034] Further call Matlab's built-in pixel frequency domain coordinate transformation function The arbitrary pixel frequency domain coordinates are further obtained from the size of the initial restored image, specifically: ; in, The frequency domain coordinates of any pixel on the initial restored image.

[0035] The above formula can be used to generate a grid matrix with the same size as the initial restored image.

[0036] The distance between the frequency domain coordinates of any pixel and the frequency center is calculated as follows: ; in, This represents the square root operation.

[0037] Define the COS filter function as follows: ; in, The parameter is optimized for grayscale values; here, the parameter value is specifically set to 100. This indicates an adjustable parameter.

[0038] The preliminary restored image obtained by Wiener filtering is further converted to the frequency domain and multiplied with the COS filter to suppress the high-frequency components that cause ringing. The filtered frequency domain result is then subjected to inverse Fourier transform to obtain, as shown below. Figure 4 The final restored image shows that the ringing effect has been significantly suppressed. for: ; in, Indicates taking the real part, Indicates the inverse FFT. Represents FFT transformation, This represents the convolution operation. This is the COS filter function.

[0039] In summary, the above description is merely a preferred embodiment of this specification and is not intended to limit the scope of protection of this specification. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this specification should be included within the scope of protection of this specification.

[0040] The systems, apparatuses, modules, or units described in one or more of the above embodiments may be implemented by a computer chip or entity, or by a product having a certain function. A typical implementation device is a computer. Specifically, a computer may be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smartphone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or any combination of these devices.

[0041] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0042] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments.

Claims

1. A blind image restoration method based on the COS function and Wiener filtering, characterized in that, include: Obtain the blurred image to be processed; A blind deblurring model is constructed within a variational framework, wherein the objective function of the blind deblurring model is used to simultaneously estimate a low-rank sharp image and a blur kernel. A multi-scale Gaussian space is constructed, and the objective function is solved in the multi-scale Gaussian space through an alternating iterative optimization strategy to estimate and obtain the low-rank sharp image and the blur kernel; Using the obtained blur kernel, Wiener filtering is applied to the blurred image to obtain an initial restored image, and then COS filtering is applied to the initial restored image to obtain the final restored image.

2. The image blind restoration method based on COS function and Wiener filtering according to claim 1, characterized in that, The objective function includes: a data fidelity term, an image gradient term, a blur kernel gradient term, and a Laplacian regularization term.

3. The image blind restoration method based on COS function and Wiener filtering according to claim 1, characterized in that, The objective function is: ； in, Indicates to make When taking the minimum value and The value, For data fidelity items, Represents a low-rank sharp image. Indicates the fuzzy kernel. Represents a blurred image. This represents the convolution operation. For image gradient terms, For the fuzzy kernel gradient term, For Laplace regularization, For the Laplace operator, For image gradient operators, This represents the image gradient operator in the x-direction. , and This represents the weighting factor.

4. The image blind restoration method based on COS function and Wiener filtering according to claim 3, characterized in that, The Laplace operator for: 。 5. The image blind restoration method based on COS function and Wiener filtering according to claim 1, characterized in that, The construction of the multi-scale Gaussian space includes: The blurred image is subjected to multiple Gaussian blurring and downsampling processes to generate image pyramids of different resolutions, i.e., the multi-scale Gaussian space.

6. The image blind restoration method based on COS function and Wiener filtering according to claim 1, characterized in that, The estimation formula for the fuzzy kernel is: ； in, Indicates the fuzzy kernel. Represents FFT transformation, Represents the FFT conjugate transform. Indicates the inverse FFT. Represents a low-rank sharp image. Represents a blurred image. , and Indicates the weighting factor. For image gradient operators, For the Laplace operator; The estimation formula for the low-rank sharp image is: 。 7. The image blind restoration method based on COS function and Wiener filtering according to claim 1, characterized in that, Performing Wiener filtering on the blurred image includes: ； in, This represents the initial restored image. For Wiener deconvolution function, Indicates the fuzzy kernel. Represents a blurred image. This is the reciprocal of the signal-to-noise ratio of the blurred image.

8. The image blind restoration method based on COS function and Wiener filtering according to claim 7, characterized in that, COS filtering is applied to the initial restored image, including: A pixel frequency coordinate matrix is ​​generated on the initial restored image based on the size of the initial restored image. The size of the initial restored image is: ； in, These are the length and width of the initial restored image, respectively. This is a function for measuring image size. The frequency domain coordinates of any pixel in the initial restored image are: ； in, The frequency domain coordinates of any pixel on the initial restored image. For pixel frequency domain coordinate transformation function; The final restored image is obtained through COS filtering. for: ； in, Indicates taking the real part, Indicates the inverse FFT. Represents FFT transformation, This represents the convolution operation. For COS filtering function; ； in, Optimize parameters for grayscale values. This represents the distance between the frequency domain coordinates of any pixel and the frequency center. Indicates an adjustable parameter. , This represents the square root operation.

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