Blind restoration method and system of ultrasonic logging images based on fuzzy factor estimation variation

Abstract

The present invention discloses a method and system for ultrasonic logging image blind restoration based on fuzzy factor estimation variation, which estimates the radius of the fuzzy factor by analyzing the logarithmic spectrum of the ultrasonic logging fuzzy image, thereby improving the stability of the subsequent iterative optimization algorithm, and at the same time, by constructing a variational blind restoration model based on the L1 norm, fully utilizing the sparse characteristics of the ultrasonic logging image, effectively improving the quality of the restored image. Compared with the existing ultrasonic logging image blind restoration method, it can effectively improve the clarity and contrast of the ultrasonic logging image, provide high-quality images for subsequent logging exploration, and has very good practicality.

Description

Technical Field

[0001] The invention relates to the technical field of petroleum logging, and in particular to a blind restoration method and system of ultrasonic logging images based on fuzzy factor estimation variation. Background Art

[0002] Ultrasonic imaging logging is an important technology in oil well logging. In recent years, with the development of downhole ultrasonic imaging, it is now possible to obtain a large number of intuitive images of the well wall and the vicinity of the well wall. Through ultrasonic logging images, the size, orientation, inclination of fractures, and the size and distribution of holes can be understood, providing the necessary geological data for subsequent exploration and development of fractured reservoirs.

[0003] However, due to factors such as the attenuation of sound waves in the medium and the non-ideal imaging characteristics of the ultrasonic transducer, the ultrasonic logging images have varying degrees of blur. Therefore, how to improve the clarity and contrast of ultrasonic logging images has become an urgent problem to be solved. Due to the complexity of the ultrasonic logging imaging environment, the fuzzy factor is often unknown. In order to obtain further information from the ultrasonic logging images (including fracture conditions, formation structure, pore structure, etc.), it is necessary to blindly restore the obtained ultrasonic blurred images.

[0004] At present, the research on blind restoration methods focuses on common visible light images, mainly focusing on motion blur, defocus blur, and Gaussian blur in visible light imaging. Various types of blind restoration methods have been proposed, and certain restoration effects have been achieved. However, the above methods do not take into account special types of images. If they are used in ultrasonic logging images, the restoration results are very unstable. In recent years, some scholars have proposed restoration methods specifically for ultrasonic logging images. However, most of these methods require the fuzzy factor to be known. There are few studies on blind restoration of ultrasonic logging images. At present, there are mainly blind restoration methods based on contrast enhancement and blind restoration methods based on APEX fuzzy factor estimation. On the one hand, these methods do not make full use of the prior information of ultrasonic logging images. On the other hand, the estimation of fuzzy factors is relatively rough and no further optimization is done. Therefore, their restoration effect is not ideal and cannot provide high-quality images for subsequent logging exploration. Summary of the invention

[0005] The present invention proposes a blind restoration method and system for ultrasonic logging images based on fuzzy factor estimation variation, which can effectively improve the clarity and contrast of ultrasonic logging images to overcome the above technical deficiencies.

[0006] In order to achieve the above technical objectives, the present invention provides a blind restoration method of ultrasonic logging images based on fuzzy factor estimation variation, which comprises the following steps:

[0007] Obtaining the logarithmic spectrum of the ultrasonic logging fuzzy image;

[0008] Based on the logarithmic spectrum of the ultrasonic logging image, a curve of the logarithmic spectrum relative to the image radius is obtained, and the radius value of the minimum ring in the fuzzy image spectrum is estimated by the curve of the logarithmic spectrum relative to the image radius;

[0009] According to the properties of Bessel function, the initial radius of the fuzzy factor is calculated by the radius value of the minimum ring in the fuzzy image spectrum;

[0010] The fuzzy factor is constructed by the initial radius of the fuzzy factor, and a variational blind restoration model based on the L1 norm is constructed for the ultrasonic logging image to obtain the optimal iterative solution of the fuzzy factor.

[0011] The ultrasonic logging image is restored according to the optimal iterative solution of the fuzzy factor to obtain the final restored image.

[0012] The present invention also provides an ultrasonic logging image blind restoration system based on fuzzy factor estimation variation, which includes the following functional modules:

[0013] A logarithmic spectrum acquisition module, used to acquire the logarithmic spectrum of the ultrasonic logging fuzzy image;

[0014] A radius estimation module is used to obtain a curve of logarithmic spectrum relative to image radius based on the logarithmic spectrum of the ultrasonic logging image, and obtain the radius value of the minimum ring in the fuzzy image spectrum through the curve estimation of the logarithmic spectrum relative to the image radius;

[0015] A radius calculation module is used to calculate the initial radius of the fuzzy factor by the radius value of the minimum ring in the fuzzy image spectrum according to the properties of the Bessel function;

[0016] The modeling and solving module is used to construct the fuzzy factor through the initial radius of the fuzzy factor, and to construct a variational blind restoration model based on the L1 norm for the ultrasonic logging image to obtain the optimal iterative solution of the fuzzy factor;

[0017] The optimized restoration module is used to restore the ultrasonic logging image according to the optimal iterative solution of the fuzzy factor to obtain the final restored image.

[0018] Compared with the prior art, the ultrasonic logging image blind restoration method and system based on fuzzy factor estimation variation described in the present invention estimates the radius of the fuzzy factor by analyzing the logarithmic spectrum of the ultrasonic logging fuzzy image, thereby improving the stability of the subsequent iterative optimization algorithm. At the same time, by constructing a variational blind restoration model based on the L1 norm, it fully utilizes the sparse characteristics of the ultrasonic logging image and effectively improves the quality of the restored image.

[0019] The ultrasonic logging image blind restoration method and system based on fuzzy factor estimation variation described in the present invention can effectively improve the clarity and contrast of ultrasonic logging images compared with existing ultrasonic logging image blind restoration methods, provide high-quality images for subsequent logging exploration, and have very good practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a flowchart of a method for blind restoration of ultrasonic logging images based on fuzzy factor estimation variation according to an embodiment of the present invention;

[0021] Figure 2 is an example diagram of the horizontal and vertical coordinates of the logarithmic spectrum-radius curve in the logarithmic spectrum image according to the embodiment of the present invention;

[0022] Figure 3 is an example diagram of the ultrasonic logging fuzzy image and the corresponding logarithmic spectrum according to the embodiment of the present invention; wherein, Figure 3 (a) is an example of a fuzzy image of ultrasonic logging; Figure 3 (b) is the corresponding log spectrum example;

[0023] Figure 4 yes Figure 3 An example of the logarithmic spectrum-radius curve of ;

[0024] Figure 5 is a comparison of the ultrasonic logging fuzzy image before and after restoration; Figure 5 (a) is an example image before restoration of the blurred ultrasonic logging image; Figure 5 (b) is an example of the restored ultrasonic logging blurred image;

[0025] Figure 6 It is a module block diagram of the ultrasonic logging image blind restoration system based on fuzzy factor estimation variation described in an embodiment of the present invention. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solution 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.

[0027] Based on the above content, an embodiment of the present invention provides a blind restoration method of ultrasonic logging images based on fuzzy factor estimation variation, such as Figure 1 As shown, it includes the following steps:

[0028] S1. Obtain the logarithmic spectrum of the ultrasonic logging fuzzy image.

[0029] Specifically, Fourier transform is performed on the ultrasonic logging fuzzy image to obtain its spectrum, and the logarithm of the spectrum is calculated to obtain the logarithmic spectrum of the fuzzy image.

[0030] S2. A curve of the logarithmic spectrum relative to the image radius is obtained based on the logarithmic spectrum of the ultrasonic logging image, and the radius value of the minimum value ring in the fuzzy image spectrum is estimated by the curve of the logarithmic spectrum relative to the image radius.

[0031] That is, the logarithmic spectrum of the ultrasonic logging image is analyzed to obtain a logarithmic spectrum-radius curve, the abscissa of which is the radius d with the center of the image as the center of the circle, such as Figure 2 As shown in the figure, the ordinate is the logarithmic spectrum average value of all coordinate points on the radius. The radius value d0 of the minimum ring in the blurred image spectrum is obtained through the logarithmic spectrum-radius curve.

[0032] S3. According to the properties of the Bessel function, the initial radius of the fuzzy factor is calculated by the radius value of the minimum ring in the fuzzy image spectrum.

[0033] According to the properties of the Bessel function, the relationship between the radius of the fuzzy factor and the radius of the minimum ring in the fuzzy image spectrum can be expressed as:

[0034]

[0035] In formula (1), r0 is the initial radius of the blur factor; L╳L is the size of the image; and d is the radius of the minimum ring in the blurred image spectrum.

[0036] S4. The fuzzy factor is constructed through the initial radius of the fuzzy factor, and a variational blind restoration model based on the L1 norm is constructed for the ultrasonic logging image to obtain the optimal iterative solution of the fuzzy factor.

[0037] The fuzzy factor is constructed by the initial radius of the fuzzy factor, as shown in formula (2):

[0038]

[0039] In formula (2), (x, y) represents the pixel coordinates with the center of the image as the origin, r 2 =x 2 +y 2 , r0 is the initial radius of the fuzzy factor estimated in equation (1).

[0040] For ultrasonic logging images, a variational blind restoration model based on L1 norm is constructed, as shown in formula (3):

[0041]

[0042] In formula (3), J represents the cost function, u represents the blind restored image, k represents the fuzzy factor, and g represents the fuzzy image. represents the convolution operation, represents the gradient operator, l represents the Laplace operator, Ω represents the image space, L1 represents the L1 norm, L 2 represents the L2 norm, a1 and a2 represent the regularization parameters. On this basis, auxiliary variables are introduced to transform it into a form that is easy to optimize and solve, as shown in formula (4):

[0043]

[0044] When β1, β2→∞ (4)

[0045] In formula (4), w and z represent the introduced auxiliary variables, and β1 and β2 represent the newly introduced parameters. When β1, β2→∞, formula (3) and formula (4) are equivalent.

[0046] After constructing the variational blind restoration model based on the L1 norm, the parameters need to be initialized, that is, the fuzzy factor constructed by the initial radius of the fuzzy factor is used as the initial fuzzy factor, and the ultrasonic logging fuzzy image is used as the initial restoration image. The auxiliary variables β1 and β2 are initialized to 1, and their maximum values ​​are set to 10. 6 , n, n+1 in the following equations (5) to (8) represent the results of the nth and n+1th iterations.

[0047] The process of solving the optimal iterative solution of the fuzzy factor is as follows:

[0048] Fix k, u, and z, optimize w, and obtain the iterative solution of the auxiliary variable w.

[0049]

[0050] Fix k, u, and w, optimize z, and obtain the iterative solution of the auxiliary variable z.

[0051]

[0052] Fix k, z, w, optimize u, and obtain the iterative solution of the restored image u.

[0053]

[0054] In the formula, F -1 represents inverse Fourier transform, superscript * represents conjugate, K, G, Z, D, and W represent k, g, and z, respectively. The Fourier transform of w.

[0055] Fix u, z, w, optimize k, and obtain the iterative solution of the fuzzy factor k.

[0056]

[0057] In formula (8), L represents the Fourier transform of the Laplace operator l.

[0058] In the above iterative optimization process, each time an iterative optimization is performed, the values ​​of β1 and β2 will increase by 3 times compared with the previous iterative optimization. 6 When , it is necessary to continue iterative optimization until the iterative change of the fuzzy factor k is less than the set threshold, then the iterative optimization is terminated to obtain the optimal iterative solution of the fuzzy factor k.

[0059] S5. Restoring the ultrasonic logging image according to the optimal iterative solution of the fuzzy factor to obtain a final restored image.

[0060] The present invention will be further described below in conjunction with examples:

[0061] The blurred image and the corresponding log spectrum are as follows Figure 3 As shown, the logarithmic spectrum is obtained according to the blurred image and the corresponding logarithmic spectrum - the radius curve is as follows Figure 4 As shown;

[0062] Figure 4 The circled point in is the minimum value, which indicates the radius point of the minimum ring. Its corresponding horizontal coordinate is the radius value d of the minimum ring, and d=14 in the figure. Therefore, the radius of the fuzzy factor is estimated to be

[0063]

[0064] By iteratively optimizing the fuzzy factor, the final blind restored image is obtained, such as Figure 5 As shown in the figure, compared with the blurred image, it is obvious that the blind restored image has higher contrast and richer details in terms of visual effect. In addition, the contrast of cracks and holes in the logging image is higher and their edges are clearer. Some cracks hidden in the blurred image can be identified in the blind restored image.

[0065] The present invention discloses a blind restoration method for ultrasonic logging images based on fuzzy factor estimation variation. The method estimates the radius of the fuzzy factor by analyzing the logarithmic spectrum of the ultrasonic logging fuzzy image, thereby improving the stability of the subsequent iterative optimization algorithm. At the same time, by constructing a variational blind restoration model based on the L1 norm, the sparse characteristics of the ultrasonic logging image are fully utilized, thereby effectively improving the quality of the restored image.

[0066] The ultrasonic logging image blind restoration method based on fuzzy factor estimation variation described in the present invention can effectively improve the clarity and contrast of ultrasonic logging images compared with existing ultrasonic logging image blind restoration methods, provide high-quality images for subsequent logging exploration, and has very good practicality.

[0067] Based on the above-mentioned ultrasonic logging image blind restoration method based on fuzzy factor estimation variation, the present invention also provides an ultrasonic logging image blind restoration system based on fuzzy factor estimation variation, such as Figure 6 As shown, it includes the following functional modules:

[0068] The logarithmic spectrum acquisition module 10 is used to acquire the logarithmic spectrum of the ultrasonic logging fuzzy image;

[0069] The radius estimation module 20 is used to obtain a curve of logarithmic spectrum relative to image radius based on the logarithmic spectrum of the ultrasonic logging image, and obtain the radius value of the minimum ring in the fuzzy image spectrum through the curve estimation of the logarithmic spectrum relative to the image radius;

[0070] A radius calculation module 30, for calculating an initial radius of a fuzzy factor by using a radius value of a minimum ring in a fuzzy image spectrum according to the properties of a Bessel function;

[0071] The modeling and solving module 40 is used to construct a fuzzy factor through the initial radius of the fuzzy factor, and to construct a variational blind restoration model based on the L1 norm for the ultrasonic logging image, so as to solve and obtain the optimal iterative solution of the fuzzy factor;

[0072] The optimization restoration module 50 is used to restore the ultrasonic logging image according to the optimal iterative solution of the fuzzy factor to obtain the final restored image.

[0073] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and modules described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0074] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A blind restoration method for ultrasonic logging images based on fuzzy factor estimation variation, characterized in that: The steps include: Obtaining the logarithmic spectrum of the ultrasonic logging fuzzy image; Based on the logarithmic spectrum of the ultrasonic logging image, a curve of the logarithmic spectrum relative to the image radius is obtained, and the radius value of the minimum ring in the fuzzy image spectrum is estimated by the curve of the logarithmic spectrum relative to the image radius; According to the properties of Bessel function, the initial radius of the fuzzy factor is calculated by the radius value of the minimum ring in the fuzzy image spectrum; The fuzzy factor is constructed by the initial radius of the fuzzy factor, and a variational blind restoration model based on the L1 norm is constructed for the ultrasonic logging image to obtain the optimal iterative solution of the fuzzy factor. The ultrasonic logging image is restored according to the optimal iterative solution of the fuzzy factor to obtain the final restored image; The formula of the L1-norm variational blind restoration model is as follows: When β1, β2→∞ In the formula, J represents the cost function, u represents the blind restored image, k represents the fuzzy factor, and g represents the fuzzy image. represents the convolution operation, represents the gradient operator, l represents the Laplace operator, Ω represents the image space, L 1 represents the L1 norm, L 2 represents the L2 norm, a1 and a2 represent regularization parameters, w and z represent the introduced auxiliary variables, and β1 and β2 represent the newly introduced parameters.

2. The method for blind restoration of ultrasonic logging images based on fuzzy factor estimation variation according to claim 1 is characterized in that: Perform Fourier transform on the ultrasonic logging fuzzy image to obtain its spectrum, and then calculate the logarithm of the spectrum to obtain the logarithmic spectrum of the fuzzy image.

3. The method for blind restoration of ultrasonic logging images based on fuzzy factor estimation variation according to claim 1 is characterized in that: After constructing the variational blind restoration model based on the L1 norm, it is necessary to initialize the parameters, that is, to construct the fuzzy factor through the initial radius of the fuzzy factor as the initial fuzzy factor, and to use the ultrasonic logging fuzzy image as the initial restoration image.

4. The method for blind restoration of ultrasonic logging images based on fuzzy factor estimation variation according to claim 1 is characterized in that: The process of solving the optimal iterative solution of the fuzzy factor is as follows: Fix k, u, z, optimize w, and obtain the iterative solution of the auxiliary variable w; Fix k, u, and w, optimize z, and obtain the iterative solution of the auxiliary variable z; Fix k, z, w, optimize u, and obtain the iterative solution of the restored image u; Fix u, z, w, optimize k, and obtain the optimal iterative solution of the fuzzy factor k.

5. The method for blind restoration of ultrasonic logging images based on fuzzy factor estimation variation according to claim 1 is characterized in that: With each iterative optimization, the values ​​of β1 and β2 will increase by 3 times compared with the previous iterative optimization.

6. The method for blind restoration of ultrasonic logging images based on fuzzy factor estimation variation according to claim 1 is characterized in that: When the iterative change of the fuzzy factor k is greater than the set threshold or β1<10 6 When , it is necessary to continue iterative optimization until the iterative change of the fuzzy factor k is less than the set threshold, then the iterative optimization is terminated to obtain the optimal iterative solution of the fuzzy factor k.

7. A blind restoration system for ultrasonic logging images based on fuzzy factor estimation variation, characterized in that: Includes the following functional modules: A logarithmic spectrum acquisition module, used to acquire the logarithmic spectrum of the ultrasonic logging fuzzy image; A radius estimation module is used to obtain a curve of logarithmic spectrum relative to image radius based on the logarithmic spectrum of the ultrasonic logging image, and obtain the radius value of the minimum ring in the fuzzy image spectrum through the curve estimation of the logarithmic spectrum relative to the image radius; A radius calculation module is used to calculate the initial radius of the fuzzy factor by the radius value of the minimum ring in the fuzzy image spectrum according to the properties of the Bessel function; The modeling and solving module is used to construct the fuzzy factor through the initial radius of the fuzzy factor, and to construct a variational blind restoration model based on the L1 norm for the ultrasonic logging image to obtain the optimal iterative solution of the fuzzy factor; An optimized restoration module is used to restore the ultrasonic logging image according to the optimal iterative solution of the fuzzy factor to obtain the final restored image; The formula of the L1-norm variational blind restoration model is as follows: When β1, β2→∞ In the formula, J represents the cost function, u represents the blind restored image, k represents the fuzzy factor, and g represents the fuzzy image. represents the convolution operation, represents the gradient operator, l represents the Laplace operator, Ω represents the image space, L 1 represents the L1 norm, L 2 represents the L2 norm, a1 and a2 represent regularization parameters, w and z represent the introduced auxiliary variables, and β1 and β2 represent the newly introduced parameters.

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