A Blind Image Restoration Method Based on COS Function and Wiener Filtering

Abstract

This invention relates to the field of image processing technology, specifically providing a blind image restoration method based on the COS function and Wiener filtering. The method includes: acquiring a blurred image to be processed; constructing a blind deblurring model within a variational framework; the objective function of the blind deblurring model being used to simultaneously estimate a low-rank sharp image and a blur kernel; solving the objective function in a multi-scale Gaussian space using an alternating iterative optimization strategy to estimate and obtain the low-rank sharp image and blur kernel; using the obtained blur kernel to perform Wiener filtering on the blurred image to obtain an initial restored image; and then performing COS filtering on the initial restored image to obtain the final restored image. This invention combines Wiener filtering with a COS filter, utilizing the COS filter for smooth transitions, effectively solving the ringing artifact problem present in traditional Wiener filtering.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of image processing, and particularly relates to an image blind restoration method based on a COS function and Wiener filtering. BACKGROUND

[0002] In the process of remote sensing imaging, due to the influence of environmental interference, platform vibration, atmospheric turbulence and other factors, the obtained remote sensing image often has blur and noise, which seriously affects the image quality and the accuracy of subsequent analysis. At present, the main methods for remote sensing image sharpening restoration can be summarized into three categories: one is the deconvolution method based on on-orbit target testing; the other is the restoration method based on traditional variational model; the third is the restoration method based on deep learning.

[0003] The image degradation process is usually modeled as the convolution operation of the original clear image and the blur kernel and the superposition of noise, and a regularized restoration framework model is established. Based on this model, a two-step process is used for image restoration: first, the blur kernel is estimated under the blind restoration framework; then, the estimated blur kernel is used for non-blind deblurring to realize ringing suppression and further restore the clear image.

[0004] In the non-blind deblurring process, the Wiener filtering method is widely used. The Wiener filtering method is a special case based on the traditional variational model. Although this method can realize non-blind deblurring, the Wiener filtering method still has obvious defects in actual restoration, especially in the image edge area, which is easy to introduce ringing artifacts, affecting the restoration effect. SUMMARY

[0005] Therefore, the present application aims to provide a blind restoration method for images based on COS function and Wiener filtering, which improves the traditional Wiener filtering method and introduces the COS filtering method to effectively suppress the ringing effect in the edge area while maintaining the deblurring ability of the Wiener filtering, thereby improving the overall restoration quality of the image.

[0006] To achieve the above-mentioned purpose, the technical scheme of the present application is as follows:

[0007] The present application provides a blind restoration method for image ringing suppression based on COS function and Wiener filtering, which comprises:

[0008] obtaining a blurred image to be processed;

[0009] constructing a blind deblurring model under a variational framework, and the objective function of the blind deblurring model is used to simultaneously estimate a low-rank clear image and a blur kernel;

[0010] constructing a multi-scale Gaussian space, and solving the objective function by an alternating iterative optimization strategy in the multi-scale Gaussian space to estimate a low-rank clear image and a blur kernel;

[0011] The obtained blur kernel is used to perform Wiener filtering on the blurred image to obtain an initial restored image, and then COS filtering is performed on the initial restored image to obtain a final restored image.

[0012] Preferably, the objective function comprises a data fidelity term, an image gradient term, a blur kernel gradient term and a Laplace regularization term.

[0013] Preferably, the objective function is:

[0014] ;

[0015] wherein, represents the minimum value of , and , is a data fidelity term, represents a low-rank clear image, represents a blur kernel, represents a blurred image, represents a convolution operation, is an image gradient term, is a blur kernel gradient term, is a Laplace regularization term, is a Laplace operator, is an image gradient operator, represents an x-direction image gradient operator, , and represent weight factors.

[0016] Preferably, the Laplace operator is:

[0017] .

[0018] Preferably, a multi-scale Gaussian space is constructed, comprising:

[0019] The blurred image is subjected to multiple Gaussian blurring and down-sampling to generate an image pyramid of different resolutions, i.e. a multi-scale Gaussian space.

[0020] Preferably, the estimation formula of the blur kernel is:

[0021] ;

[0022] wherein, represents a blur kernel, represents an FFT transform, represents an FFT conjugate transform, represents an inverse FFT transform, represents a low-rank clear image, denotes a blurred image, , and denotes a weight factor, is an image gradient operator, is a Laplace operator;

[0023] The estimation of the low-rank sharp image is given by:

[0024] .

[0025] Preferably, the blurred image is Wiener filtered, comprising:

[0026] ;

[0027] wherein, denotes an initial restored image, is a Wiener deconvolution function, denotes a blur kernel, denotes a blurred image, is an inverse signal-to-noise ratio of the blurred image.

[0028] Preferably, the initial restored image is COS filtered, comprising:

[0029] generating a matrix of pixel frequency coordinates on the initial restored image according to the size of the initial restored image, the size of the initial restored image being:

[0030] ;

[0031] wherein, are the length and width of the initial restored image, respectively, is an image size measurement function;

[0032] Any pixel frequency domain coordinate on the initial restored image is:

[0033] ;

[0034] wherein, is any pixel frequency domain coordinate on the initial restored image, is a pixel frequency domain coordinate conversion function;

[0035] The final restored image is obtained by COS filtering is:

[0036] ;

[0037] wherein, denotes taking the real part, denotes an inverse FFT transform, denotes an FFT transform, Indicates the convolution operation;

[0038] ;

[0039] 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.

[0040] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0041] 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.

[0042] 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

[0043] 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:

[0044] 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;

[0045] Figure 2 The image to be processed is a blurred image provided according to an embodiment of the present invention;

[0046] 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;

[0047] Figure 4 This is the final restored image provided according to an embodiment of the present invention. Detailed Implementation

[0048] For the purpose of making the object, technical solutions and advantages of the present application more clear, the present application is further described in detail below in combination with the drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and do not constitute a limitation on the present application. In different embodiments, similar elements are associated with similar element labels. In the following embodiments, many details are described in order to make the present application better understood. However, those skilled in the art can easily recognize that some features can be omitted in different cases, or can be replaced by other elements, materials, methods. In some cases, some operations related to the present application are not shown or described in the specification in order to avoid the core part of the present application being overwhelmed by too much description, and it is not necessary for those skilled in the art to describe these related operations in detail according to the description in the specification and general technical knowledge in the art.

[0049] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other to form various embodiments without conflict. At the same time, each step or action in the method description can also be sequentially adjusted or adjusted in a manner obvious to those skilled in the art. Therefore, the various sequences in the specification and drawings are only for the purpose of clearly describing a certain embodiment, and do not mean a necessary sequence, unless otherwise stated that a certain sequence must be followed.

[0050] In the description of the present application, it should be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the purpose of facilitating the description of the present application and simplifying the description, and do not indicate or imply that the device or element indicated must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application. In addition, the terms "first", "second" and the like are only for the purpose of description, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features limited by "first", "second" and the like can explicitly or implicitly include one or more features. In the description of the present application, unless otherwise stated, the meaning of "a plurality of" is two or more.

[0051] 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.

[0052] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0053] 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:

[0054] 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.

[0055] 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.

[0056] 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:

[0057] ;

[0058] 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:

[0059] .

[0060] 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.

[0061] 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.

[0062] 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.

[0063] In the alternating iterative optimization process, regarding the fuzzy kernel The solution process is designed as follows:

[0064] To accelerate convergence and obtain more accurate results, embodiments of the present invention utilize a fuzzy kernel... In the solving process, only the image gradient in the x direction is considered, and the blur kernel is solved in the frequency domain by fast Fourier transform (FFT) The solving estimation formula is:

[0065] ;

[0066] wherein, represents the blur kernel, represents the FFT transform, represents the FFT conjugate transform, represents the inverse FFT transform.

[0067] The solving process of the low-rank clear image is designed as follows:

[0068] In each iteration process, the previously obtained blur kernel is fixed, and the low-rank clear image is solved by using the blur kernel, and the estimation formula is:

[0069] .

[0070] In short, in the iterative solving process, the low-resolution solving result is used as the initial value of the high-resolution solving, the blur kernel is solved by fixing the low-rank clear image , the solved blur kernel is fixed, and the low-rank clear image is re-solved to realize alternating iterative optimization, determine the weight factor in the objective function, and obtain the final blur kernel . .

[0071] S4: The blur kernel obtained by solving is used to perform Wiener filtering on the blurred image to obtain an initial restored image, and then COS filtering is performed on the initial restored image to obtain a final restored image.

[0072] Specifically, after the blur kernel is estimated in S3, Wiener filtering and COS filtering are combined to perform image sharpening processing, which retains the strong deblurring ability of Wiener filtering while effectively suppressing the ringing artifacts caused by Wiener filtering. The blur kernel estimated is used to perform Wiener filtering on the blurred image to obtain an initial restored image, and the processing function of the Wiener filtering is:

[0073] ;

[0074] wherein, represents the initial restored image, is a Wiener deconvolution function, The reciprocal of the signal-to-noise ratio of the blurred image is 0.01.

[0075] After obtaining the initial restored image, a frequency domain COS filter is defined to suppress the ringing artifact in the Wiener filtering result, and the initial restored image is subjected to COS filtering. The specific process of constructing the COS filter is as follows:

[0076] Firstly, the size of the initial restored image is obtained by using the function provided by Matlab:

[0077] ;

[0078] Wherein, L and W are the length and width of the initial restored image respectively, and in this case, the number of rows and columns of pixels are used to represent, is the image size measurement function provided by Matlab.

[0079] Further call the pixel frequency domain coordinate conversion function provided by Matlab , and further obtain the arbitrary pixel frequency domain coordinates from the size of the initial restored image, which is:

[0080] ;

[0081] Wherein, is the arbitrary pixel frequency domain coordinate of the initial restored image.

[0082] Through the above formula, a grid matrix with the same size as the initial restored image can be generated.

[0083] Further, the distance between the arbitrary pixel frequency domain coordinate and the frequency center is calculated, and the calculation formula is:

[0084] ;

[0085] Wherein, represents the square root operation.

[0086] The COS filtering function is defined as:

[0087] ;

[0088] Wherein, is the gray value optimization parameter, and the parameter is specifically 100, represents an adjustable parameter.

[0089] Further, the preliminary restored image obtained by Wiener filtering is converted to the frequency domain, multiplied by the COS filter, so as to suppress the high frequency component leading to ringing, and the filtered frequency domain result is subjected to inverse Fourier transform to obtain Figure 4 ​The final recovered image in which the ringing effect is significantly suppressed is:

[0090] ;

[0091] wherein, represents taking the real part, represents an inverse FFT transform, represents an FFT transform, represents a convolution operation, is a COS filter function.

[0092] In conclusion, the above merely describes preferred embodiments of the present specification, and is not intended to limit the protection scope of the present specification. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present specification shall be included in the protection scope of the present specification.

[0093] The system, apparatus, module or unit illustrated by one or more embodiments described above can be specifically implemented by a computer chip or entity, or by a product with certain functions. A typical implementation device is a computer. Specifically, the computer may, for example, be a personal computer, a laptop computer, a cellular phone, a camera phone, a smart phone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.

[0094] It should also be noted that the terms "comprising", "including", or any other variant thereof are intended to cover non-exclusive inclusions, such that processes, methods, articles, or devices that comprise a list of elements do not exclude other elements not expressly listed, or do not exclude other elements inherent to such processes, methods, articles, or devices. Without more limitations, an element defined by the phrase "comprising a" does not exclude the presence of additional identical elements in the process, method, article, or device that includes the element.

[0095] Each of the embodiments in the present specification is described in a progressive manner, and the same or similar parts between each embodiment can be referred to each other, and each embodiment focuses on the difference from other embodiments. In particular, for system embodiments, since they are basically similar to method embodiments, the description is relatively simple, and the relevant parts can be referred to the part of the method embodiment.

Claims

1. A blind image restoration method based on COS function and Wiener filtering, characterized in that, The method comprises the following steps: acquiring a blurred image to be processed; constructing a blind deblurring model under a variational framework, a target function of the blind deblurring model being used for synchronously estimating a low-rank clear image and a blur kernel; the target function being: ； wherein denotes a convolution operation, denotes a blur kernel, denotes a blurred image, denotes a value of the minimum, is a data fidelity term, denotes a low-rank clear image, denotes a blur kernel, denotes a blurred image, denotes a convolution operation, is an image gradient term, is a blur kernel gradient term, is a Laplace regularization term, is a Laplace operator, is an image gradient operator, denotes an x-direction image gradient operator, , and denote weight factors; constructing a multi-scale Gaussian space, and solving the target function by an alternating iterative optimization strategy in the multi-scale Gaussian space to obtain the low-rank clear image and the blur kernel; performing Wiener filtering on the blurred image by using the solved blur kernel to obtain an initial restored image, and performing COS filtering on the initial restored image to obtain a final restored image.

2. The COS function and Wiener filter based image blind restoration method according to claim 1, wherein, The target function comprises a data fidelity term, an image gradient term, a blur kernel gradient term and a Laplace regularization term. 3.The COS function and Wiener filter based image blind restoration method of claim 1, wherein, the laplacian is: 。 4. The COS function and Wiener filter based image blind restoration method of claim 1, wherein, The multi-scale Gaussian space is constructed by: performing Gaussian blurring and down-sampling on the blurred image for multiple times to generate an image pyramid of different resolutions, i.e., the multi-scale Gaussian space.

5. The COS function and Wiener filter based image blind restoration method of claim 1, wherein, The estimation formula of the blur kernel is: ； wherein denotes a blur kernel, denotes an FFT transform, denotes an FFT conjugate transform, denotes an FFT inverse transform, denotes a low-rank sharp image, denotes a blurred image, , and denotes a weight factor, is an image gradient operator, is a Laplace operator; The estimation formula of the low-rank clear image is: 。 6. The COS function and Wiener filter based image blind restoration method of claim 1, wherein, The Wiener filtering on the blurred image comprises: ； wherein denotes the initial restored image, is a Wiener deconvolution function, denotes the blur kernel, denotes the blurred image, is the inverse of the signal-to-noise ratio of the blurred image.

7. The COS function and Wiener filter based image blind restoration method of claim 6, wherein, The COS filtering on the initial restored image comprises: generating a pixel frequency coordinate matrix on the initial restored image according to the size of the initial restored image, the size of the initial restored image being: ； wherein, are the length and width of the initial restored image, respectively, is an image size measurement function; any pixel frequency domain coordinate on the initial restored image being: ； wherein, is the pixel frequency domain coordinate of the initial restored image, is the pixel frequency domain coordinate conversion function; Obtaining a final restored image by COS filtering is: ； wherein, denotes taking the real part, denotes an inverse FFT transform, denotes an inverse FFT transform, denotes a convolution operation, is a COS filter function; ； wherein is a gray value optimization parameter, denotes the distance of an arbitrary pixel frequency domain coordinate from the frequency center, denotes an adjustable parameter, , denotes a square root operation.

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