CN111311706A - Image reconstruction method and device of pore structure - Google Patents
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Abstract
The invention provides an image reconstruction method and device of a pore structure, which relate to the technical field of oil-gas exploration, and comprise the steps of obtaining CT scanning data of a target pore structure; constructing a regularized inversion model of the target pore structure; determining a gradient function of the regularized inversion model according to the CT scanning data; constructing an iterative function of the reconstructed image of the target pore structure according to the gradient function; a reconstructed image of the target pore structure is determined from the iterative function. According to the embodiment of the invention, by constructing the regularization inversion model of the pore structure, the influence of data noise can be better suppressed in the process of image reconstruction of the pore structure of the shale, and the optimal reconstructed image is obtained in an iterative manner by combining with an optimization algorithm, so that the accuracy of the reconstructed image is effectively improved.
Description
Technical Field
The invention relates to the technical field of oil-gas exploration, in particular to an image reconstruction method and device of a pore structure.
Background
The microscopic imaging technology based on X-ray can utilize an X-ray three-dimensional microscopic imaging system to obtain observation data of a shale microporous structure, and then an inversion method is combined to image a pore structure in the shale, so that the method is a nondestructive detection method, and has important practical significance for exploration and development of unconventional oil and gas resources.
Currently, Filtered Backprojection (FBP) is the traditional algorithm for computing CT images, and in addition to this, there are several variations of filtered backprojection algorithms. All these conventional algorithms are based on the fourier slice theorem and combine a (linear) filtering operation with a back-projection operation. The disadvantages of these conventional methods include:
(1) selecting a proper Riesz potential function;
(2) the presence of the Gibbs phenomenon;
(3) the noise suppression capability is weak, so that the calculation result is unstable;
(4) noise may annihilate micro-nano pore structures;
(5) based on the image transformation, the imaging result is a gray scale map.
On the whole, in the existing method for reconstructing the image of the pore structure of the shale, the calculation process is greatly influenced by data noise, so that the accuracy of the reconstructed image is low.
Disclosure of Invention
In view of the above, the present invention provides an image reconstruction method and an image reconstruction device for a pore structure, which can suppress the influence of data noise and improve the accuracy of a reconstructed image in the process of image reconstruction of the pore structure of shale.
In a first aspect, an embodiment of the present invention provides an image reconstruction method for a pore structure, including: acquiring CT scanning data of a target pore structure; constructing a regularized inversion model of the target pore structure; determining a gradient function of the regularized inversion model according to the CT scanning data; constructing an iterative function of the reconstructed image of the target pore structure according to the gradient function; a reconstructed image of the target pore structure is determined from the iterative function.
With reference to the first aspect, an embodiment of the present invention further provides a first possible implementation manner of the first aspect, where the step of constructing the regularized inversion model of the target pore structure includes: and constructing a regularized inversion model of the target pore structure by taking the L1 norm of the attenuation function of the energy of the CT scanning ray and a total variation function of the target pore structure as regularization terms.
With reference to the first possible implementation manner of the first aspect, an embodiment of the present invention further provides a second possible implementation manner of the first aspect, where the mathematical inverse model of the regularized target pore structure is constructed by using the L1 norm and the total variation function of the attenuation function of the CT scanning ray energy of the target pore structure as regularization termsThe function is:
wherein J (m) is the regularized inversion model, m is an attenuation function of the energy of the CT scanning ray of the target pore structure, d is the CT scanning data of the target pore structure, α and β are both regularized parameters, TV (m) represents a total variation function related to m, Lm represents simulation data obtained by Radon transformation of line integral L, J (m) represents a simulation data obtained by Radon transformation of line integral L1Fitting degree of the CT scanning data and the simulation data; j. the design is a square2Is the sparsity of the target pore structure; j. the design is a square3Is the sparsity of spatial variation of the target pore structure; l1Represents a 1 norm of m; l22 norm representing m; s is a set of non-negative constraint functions on m.
With reference to the first aspect, an embodiment of the present invention further provides a third possible implementation manner of the first aspect, where the regularized inversion model is a sparse non-smooth regularized inversion model, and the step of determining a gradient function of the regularized inversion model according to the CT scan data includes: performing non-smooth approximation processing on the regularized inversion model to obtain a corresponding guidable function of the regularized inversion model; a gradient function of the regularized inversion model is determined based on the CT scan data and a first derivative of the derivable function.
With reference to the third possible implementation manner of the first aspect, an embodiment of the present invention further provides a fourth possible implementation manner of the first aspect, where an expression of a gradient function of the regularized inversion model is:
wherein M (m) is htTTdiag(φ′(m))T， ht＝1/N，
In the formula,
a gradient function for the regularized inversion model; m is CT scan of the target pore structureThe attenuation function of ray energy, d is CT scanning data of the target pore structure, α and β are regular parameters, Lm represents analog data obtained by Radon transformation of line integral L;
a gradient of a function of m for the degree of fit of the CT scan data to the simulated data;
a gradient that is a function of sparsity of the target pore structure with respect to m;
a gradient that is a function of m of the sparsity of the spatial variation of the target pore structure; diag (φ '(m)) represents an N diagonal matrix with the ith diagonal element φ' ((T)im)2) N is a positive integer; t is a matrix of N × (N +1), the ith action of which is Ti(ii) a M (m) and K (m) both represent functions with respect to m.
With reference to the first aspect, an embodiment of the present invention further provides a fifth possible implementation manner of the first aspect, where the constructing an iterative function of a reconstructed image of the target pore structure according to the gradient function includes: and constructing an iterative function of the reconstructed image of the target pore structure by a gradient projection method according to the gradient function.
With reference to the fifth possible implementation manner of the first aspect, an embodiment of the present invention further provides a sixth possible implementation manner of the first aspect, where an iterative function of the reconstructed image of the target pore structure, which is constructed by using the gradient projection method, is as follows: m isk+1＝PS(mk-τkgk) (ii) a Wherein,
yk＝gk+1-gk，sk＝mk+1-mk(ii) a And, PS(·)＝(·)+＝max{0,·}；
γ ∈ (0,1) and approaches 1/2; where k is the number of iterations, mkFor the reconstructed image of the target pore structure corresponding to the kth iteration, mk+1For the reconstructed image of the target pore structure corresponding to the (k +1) th iteration, τkFor the search step size, PS(. h) is a projection operator, T is a matrix of N x (N +1) with the ith action TiN is a positive integer;
a gradient function for the regularized inversion model; gamma is a constant.
With reference to the first aspect, an embodiment of the present invention further provides a seventh possible implementation manner of the first aspect, where the step of determining a reconstructed image of the target pore structure according to the iterative function includes: calculating the optimal solution of the iterative function according to a preset iteration termination condition; the optimal solution is determined as a reconstructed image of the target pore structure.
With reference to the first aspect, an embodiment of the present invention further provides an eighth possible implementation manner of the first aspect, where the target pore structure is a pore structure of a preset shale sample, and the step of acquiring CT scan data of the target pore structure includes: and scanning the shale sample by an X-ray three-dimensional microscopic imaging system to obtain CT scanning data of the pore structure of the shale sample.
In a second aspect, an embodiment of the present invention further provides an image reconstruction apparatus with a pore structure, including: the CT scanning data acquisition module is used for acquiring CT scanning data of a target pore structure; the regularization inversion model building module is used for building a regularization inversion model of the target pore structure; a gradient function determination module for determining a gradient function of the regularized inversion model according to the CT scan data; the iterative function construction module is used for constructing an iterative function of the reconstructed image of the target pore structure according to the gradient function; and the reconstructed image determining module is used for determining a reconstructed image of the target pore structure according to the iteration function.
The embodiment of the invention has the following beneficial effects:
the embodiment of the invention provides an image reconstruction method and device of a pore structure, which are used for acquiring CT scanning data of a target pore structure; constructing a regularized inversion model of the target pore structure; determining a gradient function of the regularized inversion model according to the CT scanning data; constructing an iterative function of the reconstructed image of the target pore structure according to the gradient function; a reconstructed image of the target pore structure is determined from the iterative function. In the method, the influence of data noise can be better suppressed in the process of image reconstruction of the pore structure of the shale by constructing the regularized inversion model of the pore structure, and the optimal reconstructed image is obtained in an iterative mode by combining with an optimization algorithm, so that the accuracy of the reconstructed image is effectively improved.
Additional features and advantages of the disclosure will be set forth in the description which follows, or in part may be learned by the practice of the above-described techniques of the disclosure, or may be learned by practice of the disclosure.
In order to make the aforementioned objects, features and advantages of the present disclosure more comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
Fig. 1 is a schematic flowchart of an image reconstruction method for a pore structure according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of CT scan data of a shale pore structure according to an embodiment of the present invention;
fig. 3 is a schematic diagram of an apparatus for acquiring CT scan data of a pore structure of a shale sample according to an embodiment of the present invention;
fig. 4 is a schematic diagram of an imaging result of image reconstruction by an FBP algorithm according to an embodiment of the present invention;
fig. 5 is a schematic diagram of an imaging result of image reconstruction performed by the image reconstruction method for a pore structure according to the present invention;
fig. 6 is a schematic structural diagram of an image reconstructing apparatus with a pore structure according to an embodiment of the present invention.
Icon: 61-CT scanning data acquisition module; 62-a regularization inversion model construction module; 63-a gradient function determination module; 64-an iterative function construction module; 65-reconstructed image determination Module.
Detailed Description
To make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Shale gas is generated in small unconnected shale cracks and is difficult to extract. With the emergence of energy crisis and the development of hydraulic fracturing technology, hydraulic fracturing technology has received increasing attention over the last decade. Shale gas is considered one of the unconventional sources of natural gas, and shale gas exploration is becoming one of the hottest areas of research. In order to successfully estimate the shale gas distribution, the shale microstructure must be obtained, which is of great significance for natural gas exploration and production. Conventional surface observation methods, such as optical and scanning electron microscopy, are not sufficient to obtain three-dimensional information about shale samples, thereby destroying the shale samples. Thus, these methods are not ideal because shale samples are difficult to develop and valuable.
Since the invention of the 20 th century 70 s, the X-ray Computed Tomography (X-ray CT) technology was successfully applied in the fields of medicine, biology, industry and science, and is a non-invasive method for visualizing the internal structure, so we try to reconstruct the shale microstructure by using the X-ray CT (Computed Tomography) technology, and the technology is non-destructive to shale.
The method is a nondestructive detection method by researching an X-ray-based microscopic imaging technology, acquiring observation data of a shale microporous structure by using an X-ray three-dimensional microscopic imaging system and then imaging by using an inversion method, and has important practical significance for exploration and development of unconventional oil and gas resources. The interior of the shale is of a micro-nano pore structure, and different structural body components have different absorption energy spectrums for X-rays. This results in the observation data being composed of different shale components attenuating X-rays of different wavebands, which cannot directly reflect the internal space structure of shale, and must go through an image reconstruction process to obtain an image of the microporous structure of shale, especially to obtain the pore type, shape, size, spatial distribution, connectivity characteristics in organic matter and the correlation between the pore type, shape, size, spatial distribution and connectivity characteristics with inorganic matter. By developing image reconstruction research of the micro-nano pore structure, particularly research based on an optimization and regularization image reconstruction algorithm, a shale micro three-dimensional structure model is provided, and theoretical support can be provided for resource reserve evaluation and exploration and development of shale gas.
In view of the problems that the calculation process of the conventional method for reconstructing the image of the pore structure of the shale is greatly influenced by data noise and the accuracy of the reconstructed image is low, the embodiment of the invention provides the method and the device for reconstructing the image of the pore structure. For the understanding of the present embodiment, a detailed description will be given first of all of the image reconstruction method of a pore structure disclosed in the embodiments of the present invention.
Referring to fig. 1, there is shown a schematic flow chart of an image reconstruction method of a pore structure according to an embodiment of the present invention, as shown in fig. 1, the method includes the following steps:
step S102: CT scan data of the target pore structure is acquired.
Here, the pore structure is a structure inside a substance, and by analyzing the pore structure of the substance, data such as the type, shape, size, spatial distribution, and communication characteristics of pores can be obtained. In this embodiment, the target pore structure may be the pore structure of any material having pores, including rocks of different lithologies, such as shale, granite, marble, and the like; and pore structures of other material objects such as wood, plastic, metal, etc. Taking shale as an example, the method is helpful for resource reserve assessment and exploration and development of shale gas by analyzing the pore structure of the shale.
The CT scanning data is obtained by CT scanning of a target pore structure, wherein CT is electronic computer tomography, and the CT scanning data and a detector with extremely high sensitivity are used for carrying out section scanning one by one around a certain part of a scanned object together by utilizing an X-ray beam, a gamma ray, ultrasonic waves and the like which are accurately collimated. The following can be classified according to the radiation used: x-ray CT (X-CT), and gamma-ray CT (gamma-CT).
Taking the target pore structure as the pore structure of the preset shale sample as an example, in one possible implementation, the shale sample may be scanned by an X-ray three-dimensional microscopic imaging system to obtain CT scan data of the pore structure of the shale sample. Referring to fig. 2, a schematic diagram of CT scan data of a shale pore structure is shown, wherein the scan data (i.e., projection data) is obtained by scanning a shale sample with an X-ray having an energy of 20 keV.
Step S104: and constructing a regularized inversion model of the target pore structure.
In order to reconstruct a real image of a target pore structure from CT scan data of the target pore structure, an inverse model needs to be established. Among them, the regularization method is a common technique to deal with the ill-posed problem, and the regularization method is generally modeled as the following minimization problem:
arg minm∈C{D(Lm,d)+αψ(m)}, (1)
where ψ is a convex function (called the regularization term), C is a convex set representing a priori knowledge of m, D (-) is a distance function (called the fidelity term) that measures how Lm approximates the projection data D, α is the regularization parameter, and α > 0.
There are many choices for the regularization term, for example, the selection based on total variation, the sparse representation method based on wavelet, the X-ray CT image reconstruction method based on tight frame and dictionary, and so on. In this embodiment, a priori regularization parameter selection method is adopted, and specifically, an L1 norm and a total variation function of an attenuation function of CT scanning ray energy about a target pore structure are used as regularization terms to construct a regularized inversion model of the target pore structure. Here, the purpose of the L1 norm regularization term and the TV total variation function regularization term is to impose an a priori constraint on the solution in order to best approximate the simulated data to the observed data, and therefore, the solution can be made using a non-monotonic gradient descent method.
Here, taking shale as an example, shale is generally composed of incompatible components such as pores, clay minerals, quartz particles, and the like, and therefore, it can be assumed that the attenuation function m is a piecewise constant function, with individual sparsity. On the other hand, the total variation minimization method forces the image (i.e., the function) to be a piecewise constant approximation. For the fidelity term, it may be used assuming that the noise in the X-ray CT projection data follows a gaussian distribution2Norm as a function of distance D, i.e.
Wherein, the above-mentioned L1 norm and total variation function of the attenuation function of the CT scanning ray energy related to the target pore structure are used as regularization terms, and the mathematical function for constructing the regularized inverse model of the target pore structure is:
wherein J (m) is the regularized inverse model and m is the CT scan of the target pore structureAttenuation function of ray energy, d CT scan data of target pore structure, α and β both being regular parameters, TV (m) representing total variation function about m, Lm representing analog data obtained by Radon transform of line integral L, J1Fitting degree of the CT scanning data and the simulation data; j. the design is a square2Is the sparsity of the target pore structure; j. the design is a square3Is the sparsity of spatial variation of the target pore structure; l1Represents a 1 norm of m; l22 norm representing m; s is a set of non-negative constraint functions on m.
Step S106: determining a gradient function of the regularized inversion model according to the CT scan data.
In actual practice, the gradient function of the regularized inversion model may be determined by the following steps 21-22:
(21) and carrying out non-smooth approximation processing on the regularized inversion model to obtain a corresponding guidable function of the regularized inversion model.
For l in the above formula (2)1Norm, approximated by a Huber function, defined as:
obviously, when δ → 0, mδ(x) Approaches to l1And (6) approaching.
In other possible embodiments, the above l1The norm may also be achieved by approximation of other functions, such as the function:
where e is a small constant. It is clear that when ∈ → 0, the norm characterized by the non-smooth functional Ω (x) can be approximated by l1And (4) norm.
To approximate the TV function in equation (2), here, a smooth function is defined:
wherein M isζ(x) Can be discretized by setting ht1/N, then the parameter m may be discretized into
TiAn N (N +1) matrix is formed for all i.
(22) A gradient function of the regularized inversion model is determined based on the CT scan data and a first derivative of the derivable function.
Here, Mζ(m) can be varied by applying a gradient to any
Obtaining, namely:
therefore, the temperature of the molten metal is controlled,
wherein diag (φ '(m)) represents an N × N diagonal matrix having an ith diagonal element of φ' ((T)im)2) T is a matrix of N × (N +1), the ith action of which is TiAnd is and
M(m)＝htTTdiag(φ′(m))T. (7)
as can be seen from equation (2), the gradient of the objective function j (m) consists of three parts, namely:
wherein,
and J3The gradients of (m) ═ tv (m) are:
wherein，
p'Huber(m) is the derivative of the function p (m) of equation (3). The gradient of the objective function j (m) can thus be explicitly expressed as:
in the formula,
the normalized inversion model is a gradient function of the normalized inversion model, m is an attenuation function of the energy of the CT scanning ray of the target pore structure, d is CT scanning data of the target pore structure, α and β are both regular parameters, Lm represents simulation data obtained by Radon transformation of a line integral L;
a gradient of a function of m for the degree of fit of the CT scan data to the simulated data;
a gradient that is a function of sparsity of the target pore structure with respect to m;
a gradient that is a function of m of the sparsity of the spatial variation of the target pore structure; m (m) and K (m) both represent functions with respect to m.
Step S108: and constructing an iterative function of the reconstructed image of the target pore structure according to the gradient function.
In one possible embodiment, an iterative function of the reconstructed image of the target pore structure is constructed by gradient projection based on the gradient function.
The iterative function of the reconstructed image of the target pore structure constructed by the gradient projection method is as follows:
mk+1＝PS(mk-τkgk)； (11)
wherein,
and, PS(·)＝(·)+＝max{0,·}；
γ ∈ (0,1) and approaches 1/2;
where k is the number of iterations, mkFor the reconstructed image of the target pore structure corresponding to the kth iteration, mk+1For the reconstructed image of the target pore structure corresponding to the (k +1) th iteration, τkFor the search step size, PS(. h) is a projection operator, T is a matrix of N x (N +1) with the ith action TiN is a positive integer;
a gradient function for the regularized inversion model; gamma is a constant.
When performing an iterative solution, a search is performed along the negative gradient direction, where sk＝-gk＝-g(mk) Is the search direction, τkIs the step size; and backtracking linear search is carried out to ensure the feasibility of the iterative points, so that an optimal step size meeting the condition of non-accurate line search can be selected from a list of step size point columns.
Step S110: a reconstructed image of the target pore structure is determined from the iterative function.
Here, an optimal solution of the iterative function is calculated according to a preset iteration termination condition; and determining the optimal solution as a reconstructed image of the target pore structure.
In practice, the iterative function may be solved to obtain its optimal solution according to the following steps 31-34:
(31) and (5) initializing.
First, the maximum number of iteration steps k is selectedmaxα ∈ (0,1), let k equal 0;
secondly, an FBP (Filter Back Projection reconstruction) algorithm is used for obtaining an initial solution m of the problem0。
(32) Taking a fixed initial step length tau0。
Obtaining an iteration point m by using a formula (11)1(ii) a Then, according to the known iteration point m0And m1Calculating the step τ using equation (12)k。
(33) Executing an iterative algorithm:
wherein: (.)+＝max{0,·}。
(34) And (4) judging termination conditions: and (4) outputting when the shutdown requirement is met, otherwise, enabling k ← k +1 to return to the step (32) to continue iterative computation.
Thus, through the above steps S102-S110, a reconstructed image of the target pore structure can be obtained. The pore structure image reconstruction method, regularization modeling and optimization method provided in this embodiment may iteratively solve an optimal solution by using a nonlinear programming technique, and compared with a conventional FBP method, the method is not sensitive to noise, and the use of the technique has stronger flexibility, for example, CT scan data of a pore structure for image reconstruction may be taken from any set of row data, and projections are not necessarily taken from a series of uniformly distributed angles, and even, due to the application of the regularization technique, the data may be incomplete.
The embodiment of the invention provides an image reconstruction method of a pore structure, which comprises the steps of obtaining CT scanning data of a target pore structure; constructing a regularized inversion model of the target pore structure; determining a gradient function of the regularized inversion model according to the CT scanning data; constructing an iterative function of the reconstructed image of the target pore structure according to the gradient function; and determining a reconstructed image of the target pore structure according to the iterative function. In the method, the influence of data noise can be better suppressed in the process of image reconstruction of the pore structure of the shale by constructing the regularized inversion model of the pore structure, and the optimal reconstructed image is obtained in an iterative mode by combining with an optimization algorithm, so that the accuracy of the reconstructed image is effectively improved.
In order to more clearly understand the image reconstruction method of the pore structure provided in the above embodiment and verify the image reconstruction effect of the method, the present embodiment performs image reconstruction on the pore structure of a certain shale sample, and the process is described as follows.
In this example, a shale sample was taken from a well shale sample consisting of quartz (43%), feldspar (12%), pyrite (5%), dolomite (5%) and clay containing illite-smectite-chlorite (35%). For the experiments, the samples were first cut into small rectangular prisms by means of a cutter. Then, the small prism is polished into a small cylinder with the diameter of 1mm and the length of 5mm by using sand paper for a multi-energy X-ray computed tomography experiment.
Among them, the multi-energy X-ray micro-tomography experiment was performed on the BL13W1 beam line of a synchrotron radiation apparatus (SSRF) of some markets. An X-ray source was derived using a 16-pole wobbler apparatus at a magnetic field of 1.9T and a magnetic period length of 14 cm. Wherein, the energy storage ring works under 3.5GeV, the current is 230mA, and a power-up mode is adopted. The X-ray source is a synchrotron, i.e. a system of bending magnets which emit high-frequency X-ray radiation when an electron beam accelerated in the energy storage ring passes through it.
As shown in fig. 3, which is a schematic diagram of an apparatus for acquiring CT scan data of the pore structure of a shale sample, during an experiment, a cylindrical shale sample is mounted on a rotating table, and is rotated in 0.167 degree increment steps in a continuous rotation process for a total of 180 degrees. The X-ray energy is selected from between 10keV and 24 keV. The distance from the sample to the detector is 10cm, the exposure time is 4s, the transmitted X-rays are absorbed by a thin scintillation screen, which converts the X-rays into visible light of a certain wavelength. In addition, image acquisition was performed through a 10-fold objective lens using an optical Peter CCD detector with an intrinsic pixel size of 3.3 × 3.3 μm.
After obtaining the projection data, selecting the projection data with the energy of 20keV for inversion calculation, referring to fig. 4 and fig. 5, which are respectively a schematic diagram of an imaging result of image reconstruction by an FBP algorithm and a schematic diagram of an imaging result of image reconstruction by the image reconstruction method of the pore structure according to the present invention provided in the embodiments of the present invention, it can be known that the artifact is significantly removed by the image method of the pore structure provided in the present embodiment, and the imaging effect is better and clearer by comparing the imaging effects of fig. 4 and fig. 5.
According to the image reconstruction method for the pore structure, the regularization inversion model is constructed by using the sparse L1 norm and the total variation term, the sparsity of shale components (such as pores) is considered, meanwhile, the edge-preserving structure of imaging is considered, noise and reconstruction artifacts can be successfully removed by using the method, and the image reconstruction method has a better imaging effect compared with a traditional Filtering Back Projection (FBP) algorithm.
Corresponding to the above image reconstruction method for a pore structure, the present embodiment further provides an image reconstruction device for a pore structure, as shown in fig. 6, which is a schematic structural diagram of an image reconstruction device for a pore structure, as can be seen from fig. 6, the device includes a CT scan data acquisition module 61, a regularization inversion model construction module 62, a gradient function determination module 63, an iterative function construction module 64, and a reconstructed image determination module 65, which are connected in sequence, where functions of each module are as follows:
a CT scan data acquisition module 61, configured to acquire CT scan data of a target pore structure;
a regularization inversion model construction module 62 for constructing a regularization inversion model of the target pore structure;
a gradient function determining module 63, configured to determine a gradient function of the regularized inversion model according to the CT scan data;
an iterative function construction module 64 configured to construct an iterative function of the reconstructed image of the target pore structure according to the gradient function;
a reconstructed image determination module 65 for determining a reconstructed image of the target pore structure according to the iterative function.
The image reconstruction device of the pore structure provided by the embodiment of the invention obtains CT scanning data of a target pore structure; constructing a regularized inversion model of the target pore structure; determining a gradient function of the regularized inversion model according to the CT scanning data; constructing an iterative function of the reconstructed image of the target pore structure according to the gradient function; a reconstructed image of the target pore structure is determined from the iterative function. In the device, the influence of data noise can be better suppressed in the process of image reconstruction of the pore structure of the shale by constructing the regularized inversion model of the pore structure, and the optimal reconstructed image is obtained in an iterative mode by combining with an optimization algorithm, so that the accuracy of the reconstructed image is effectively improved.
In one possible implementation, the regularized inversion model building module 62 is further configured to: and constructing a regularized inversion model of the target pore structure by taking the L1 norm of the attenuation function of the energy of the CT scanning ray and a total variation function of the target pore structure as regularization terms.
In another possible embodiment, the above-mentioned regularization term is the L1 norm and the total variation function of the attenuation function of the CT scan ray energy with respect to the target pore structure, and the mathematical function for constructing the regularized inverse model of the target pore structure is:
wherein J (m) is the regularized inversion model, m is an attenuation function of the energy of the CT scanning ray of the target pore structure, d is the CT scanning data of the target pore structure, α and β are both regularized parameters, TV (m) represents a total variation function related to m, Lm represents simulation data obtained by Radon transformation of line integral L, J (m) represents a simulation data obtained by Radon transformation of line integral L1Fitting degree of the CT scanning data and the simulation data; j. the design is a square2Is the sparsity of the target pore structure; j. the design is a square3Is the sparsity of spatial variation of the target pore structure; l1Represents a 1 norm of m; l22 norm representing m; s is a set of non-negative constraint functions on m.
In another possible embodiment, the regularized inversion model is a sparse non-smooth regularized inversion model, and the gradient function determining module 63 is further configured to: performing non-smooth approximation processing on the regularized inversion model to obtain a corresponding guidable function of the regularized inversion model; a gradient function of the regularized inversion model is determined based on the CT scan data and a first derivative of the derivable function.
In another possible embodiment, the expression of the gradient function of the regularized inversion model is:
wherein M (m) is htTTdiag(φ′(m))T，ht＝1/N，
In the formula,
the normalized inversion model is a gradient function of the normalized inversion model, m is an attenuation function of the energy of the CT scanning ray of the target pore structure, d is CT scanning data of the target pore structure, α and β are both regular parameters, Lm represents simulation data obtained by Radon transformation of a line integral L;
a gradient of a function of m for the degree of fit of the CT scan data to the simulated data;
a gradient that is a function of sparsity of the target pore structure with respect to m;
a gradient that is a function of m of the sparsity of the spatial variation of the target pore structure; diag (φ '(m)) represents an N diagonal matrix with the ith diagonal element φ' ((T)im)2) N is a positive integer; t is a matrix of N × (N +1), the ith action of which is Ti(ii) a M (m) and K (m) both represent functions with respect to m.
In another possible implementation, the above iterative function building module 64 is further configured to: and constructing an iterative function of the reconstructed image of the target pore structure by a gradient projection method according to the gradient function.
In another possible embodiment, the iterative function of the reconstructed image of the target pore structure constructed by the gradient projection method is: m isk+1＝PS(mk-τkgk) (ii) a Wherein,
yk＝gk+1-gk，sk＝mk+1-mk(ii) a And, PS(·)＝(·)+＝max{0,·}；
γ ∈ (0,1) and approaches 1/2; where k is the number of iterations, mkFor the reconstructed image of the target pore structure corresponding to the kth iteration, mk+1For the reconstructed image of the target pore structure corresponding to the (k +1) th iteration, τkFor the search step size, PS(. h) is a projection operator, T is a matrix of N x (N +1) with the ith action TiN is a positive integer;
a gradient function for the regularized inversion model; gamma is a constant.
In another possible implementation, the above reconstructed image determining module 65 is further configured to: calculating the optimal solution of the iterative function according to a preset iteration termination condition; the optimal solution is determined as a reconstructed image of the target pore structure.
In another possible embodiment, the target pore structure is a pore structure of a preset shale sample, and the CT scan data acquiring module 61 is further configured to: and scanning the shale sample by an X-ray three-dimensional microscopic imaging system to obtain CT scanning data of the pore structure of the shale sample.
The implementation principle and the generated technical effect of the image reconstruction apparatus with a pore structure provided by the embodiment of the present invention are the same as those of the aforementioned embodiment of the image reconstruction method with a pore structure, and for brief description, reference may be made to the corresponding contents in the aforementioned embodiment of the image reconstruction method with a pore structure where no mention is made in the embodiment of the image reconstruction apparatus with a pore structure.
The image reconstruction method of a pore structure, the image reconstruction apparatus of a pore structure, and the computer program product of an electronic device provided in the embodiments of the present invention include a computer-readable storage medium storing a program code, where instructions included in the program code may be used to execute the image reconstruction method of a pore structure described in the foregoing method embodiments, and specific implementation may refer to the method embodiments, and will not be described herein again.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a non-volatile computer-readable storage medium executable by a processor. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
In addition, in the description of the embodiments of the present invention, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (10)
1. A method of image reconstruction of a pore structure, comprising:
acquiring CT scanning data of a target pore structure;
constructing a regularized inversion model of the target pore structure;
determining a gradient function of the regularized inversion model according to the CT scanning data;
constructing an iterative function of a reconstructed image of the target pore structure according to the gradient function;
determining a reconstructed image of the target pore structure according to the iterative function.
2. The method of claim 1, wherein the step of constructing the regularized inverse model of the target pore structure comprises:
and constructing a regularized inversion model of the target pore structure by taking the L1 norm of the attenuation function of the energy of the CT scanning ray and a total variation function of the target pore structure as regularization terms.
3. The method of claim 2, wherein the regularizing term is an L1 norm and a total variation function of an attenuation function of CT scan ray energy with respect to the target pore structure, and the mathematical function for constructing the regularized inverse model of the target pore structure is:
wherein J (m) is the regularized inversion model, m is an attenuation function of the energy of the CT scanning ray of the target pore structure, d is the CT scanning data of the target pore structure, α and β are both regularized parameters, TV (m) represents a total variation function related to m, Lm represents simulation data obtained by Radon transformation of line integral L, J (m) represents simulation data obtained by Radon transformation of line integral L1Fitting degree of the CT scanning data and the simulation data; j. the design is a square2Is the sparsity of the target pore structure; j. the design is a square3Is the sparsity of spatial variation of the target pore structure; l1Represents a 1 norm of m; l22 norm representing m; s is a set of non-negative constraint functions on m.
4. The method of claim 1, wherein the regularized inversion model is a sparse non-smooth regularized inversion model, and the step of determining a gradient function of the regularized inversion model from the CT scan data comprises:
performing non-smooth approximation processing on the regularized inversion model to obtain a corresponding guidable function of the regularized inversion model;
determining a gradient function of the regularized inversion model based on the CT scan data and a first derivative of the derivable function.
5. The method of claim 4, wherein the gradient function of the regularized inversion model is expressed as:
wherein M (m) is htTTdiag(φ′(m))T，ht＝1/N，
In the formula,
the normalized inversion model is a gradient function of the normalized inversion model, m is an attenuation function of the energy of the CT scanning ray of the target pore structure, d is CT scanning data of the target pore structure, α and β are both regular parameters, Lm represents simulation data obtained by Radon transformation of a line integral L;
a gradient which is a function of m of the degree of fit of the CT scan data to the simulated data;
as a function of the sparsity of the target pore structure with respect to mA gradient;
a gradient that is a function of m of the sparsity of the spatial variation of the target pore structure; diag (φ '(m)) represents an N diagonal matrix with the ith diagonal element φ' ((T)im)2) N is a positive integer; t is a matrix of N × (N +1), the ith action of which is Ti(ii) a M (m) and K (m) both represent functions with respect to m.
6. The method of claim 1, wherein the step of constructing an iterative function of the reconstructed image of the target pore structure according to the gradient function comprises:
and constructing an iterative function of the reconstructed image of the target pore structure by a gradient projection method according to the gradient function.
7. The method for reconstructing an image of a pore structure according to claim 6, wherein the iterative function of the reconstructed image of the target pore structure constructed by the gradient projection method is as follows:
mk+1＝PS(mk-τkgk)；
wherein,
yk＝gk+1-gk，sk＝mk+1-mk；
and, PS(·)＝(·)+＝max{0,·}；
γ ∈ (0,1) and approaches 1/2;
where k is the number of iterations, mkFor the reconstructed image of the target pore structure corresponding to the kth iteration, mk+1The weight of the target pore structure corresponding to the (k +1) th iterationConstruct an image, τkFor the search step size, PS(. h) is a projection operator, T is a matrix of N x (N +1) with the ith action TiN is a positive integer;
a gradient function that is the regularized inversion model; gamma is a constant.
8. The method for reconstructing an image of a pore structure according to claim 1, wherein said step of determining a reconstructed image of said target pore structure according to said iterative function comprises:
calculating the optimal solution of the iterative function according to a preset iteration termination condition;
determining the optimal solution as a reconstructed image of the target pore structure.
9. The method for reconstructing an image of a pore structure according to claim 1, wherein the target pore structure is a pore structure of a preset shale sample, and the step of acquiring the CT scan data of the target pore structure comprises:
and scanning the shale sample by an X-ray three-dimensional microscopic imaging system to obtain CT scanning data of the pore structure of the shale sample.
10. An apparatus for reconstructing an image of a pore structure, comprising:
the CT scanning data acquisition module is used for acquiring CT scanning data of a target pore structure;
the regularization inversion model building module is used for building a regularization inversion model of the target pore structure;
a gradient function determination module for determining a gradient function of the regularized inversion model according to the CT scan data;
the iterative function construction module is used for constructing an iterative function of the reconstructed image of the target pore structure according to the gradient function;
and the reconstructed image determining module is used for determining a reconstructed image of the target pore structure according to the iteration function.
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