CN109584323A - The information constrained coeliac disease electrical impedance images method for reconstructing of ultrasonic reflection - Google Patents
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Abstract
The present invention relates to a kind of coeliac disease electrical impedance images algorithm for reconstructing that ultrasonic reflection is information constrained, suitable for electrical impedance tomography image reconstruction, lesion boundary profile point position is determined by ultrasonic reflection mode and is converted into gradient constraint equation, construction Lagrangian simultaneously solves reconstruction distribution of conductivity, steps are as follows: according to tested field domain, boundary voltage needed for obtaining image reconstruction measures difference；Jacobian matrix is built according to the reciprocity texture of electromagnetic field, reverse temperature intensity objective function is provided based on neighborhood total variation regularization method；Lesion boundary profile point position is obtained using ultrasonic reflection mode and constructs constraint equation；The electrical impedance tomography objective function under the guidance of ultrasonic constraint equation is optimized based on method of Lagrange multipliers；Residual error is repeated up to meet the requirements.
Description
Technical Field
The invention belongs to the technical field of electrical impedance tomography, and relates to a total variation regularization electrical impedance tomography method which uses inclusion boundary information provided by ultrasonic reflection as constraint and is used for realizing accurate reconstruction of lesions in human abdominal organs.
Background
Electrical Impedance Tomography (EIT) is a functional imaging technique that reconstructs the conductivity distribution inside the field to be measured by arranging an electrode array on the surface of the field to be measured and applying a certain current excitation and obtaining boundary voltage data. Compared with structural imaging technologies such as Computed Tomography (CT) and Magnetic Resonance Imaging (MRI), the EIT technology has lower resolution of reconstructed images but greatly accelerates the imaging speed, and can meet the requirements of real-time imaging. As a novel medical imaging technology, the electrical impedance tomography has the advantages of no invasion, no radiation, small volume, low cost and the like, and is an ideal real-time disease monitoring means. Meanwhile, EIT as a real-time monitoring tool has wide development prospect in the fields of medical imaging, flow monitoring, geological exploration, building structure detection and the like.
The main reason for the lower resolution of EIT imaging is that the process of its inverse problem (i.e. reconstructing the intra-field conductivity distribution from the boundary measurements) is severely ill-conditioned, meaning that small perturbations of the boundary measurements can lead to large variations in the solution. Meanwhile, the non-linearity problem of the electrical imaging itself causes the reconstructed image to have more artifacts and noises. In order to overcome the ill-posed and non-linear problems of the EIT inverse, expert scholars have proposed many image reconstruction algorithms, of which regularization is an effective means to overcome the ill-posed. The method fuses certain prior information into the solving process of the inverse problem in a mode of constructing a regularized penalty term, constrains the search space of the solution, and guides the optimization direction of the solution so as to achieve the purpose of improving the ill-conditioned performance. Typical regularization methods are the L2 regularization method mentioned in the article by IEEE medical Imaging journal (IEEE Transmission on medical Imaging) Vol.17, pages 285-93, by Vauhkonen et al, entitled "Tikhonov regularization and prior information in Electrical impedance Imaging" (Tikhonov regularization and prior information), the sparse regularization method for Imaging small objects in Electrical impedance tomography (sparse regularization method 1), by J.Zhao et al, IEEE International Imaging Systems and Techniques Conference (IEEE International Conference on Imaging Systems and Techniques), pp.25-30, borsic et al, 2007, in an article entitled Total variation regularization method in Electrical impedance tomography (Totalvanizing regularization Electrorequirements regularization), Vol.99, Invers Problems, pages A12-A12, et al, Total variation regularization (TV) method, et al. Different regularization terms can introduce different types of prior information, such as the uniform distribution of Tikhonov prior, the smoothness of laplacian prior, and "NOSER" published by m.cheney et al in 1990 in international journal of imaging Systems and Technology, vol 2, pages 66-75: a non-uniform distribution information corresponding to NOSER prior proposed in an algorithm for solving inverse conductivity problem (NOSER).
In addition to being ill-conditioned and non-linear, EIT suffers from both low sensitivity in the center of the field and blurring of reconstructed inclusion boundaries. Due to the distributed nature of the electric field and the limitations of the excitation current in electrical tomography, the sensitivity profile of EIT techniques is relatively low in the center of the field area and does not effectively reconstruct the content far from the boundary electrodes. The shape of an object is often important information in an image, the boundary of the object is an important feature of an image, and due to the soft field characteristic of the electrical tomography, the gradient of the boundary of an inclusion in an EIT reconstruction result is low, the conductivity value is in smooth transition, and the outline of the object cannot be effectively distinguished. Liu et al, 2017, IEEE Medical Imaging Collection, volume 9, page 1, parameterized level set method for Electrical impedance tomography, boundary-based Electrical impedance Imaging algorithms may be established to reconstruct inclusion boundaries. However, in an EIT image of reconstructed pixel values, the boundaries of low-resolution objects due to EIT tend to be rather blurred. By utilizing shape prior information of the inclusion, a shape constraint regularization term is constructed, and the obvious inclusion boundary can be hopefully reserved in an EIT reconstruction image.
The human tissue structure is complicated, the conductivity distribution difference between different tissues and organs is different, and the change of the size and the shape of a focus needs to be clearly judged and understood in the process of postoperative monitoring or long-term detection of the focus. In the field of medical imaging, provision of shape prior information is mostly achieved by multi-modality imaging method fusion, such as the curvilinear wave transform-based CT-MRI fusion algorithm proposed in the book 57 of modern optical Journal (Journal of model Optics), page 273 of 286 by ali.f.m. in current transform approach for the fusion of MR and CT images (a curvelet transform approach for the fusion of MR and CT images); in 2008 of Guo et al, a non-sampling contourlet transform-based MRI-SPECT image fusion method was proposed in multi-modal medical image fusion based on multi-scale geometric analysis and contourlet transform (Multimodality medical image fusion based on multi-scale geometric analysis and contourlet transform) published in Neurocomputing 72, page 203-211. The ultrasonic imaging technology is widely applied to medical image diagnosis and postoperative monitoring as an imaging method with no invasion, no radiation, small volume and low cost, and the using environment of the ultrasonic imaging technology is similar to that of electrical tomography and has similar characteristics; meanwhile, the ultrasonic tomography technology has a hard field characteristic and is relatively sensitive to the change of an organization structure, the reflection mode of the ultrasonic tomography technology can clearly judge the shape and the geometric size of a focus, the focus boundary information is obtained through the ultrasonic reflection mode and the reconstruction process of electrical impedance imaging is restrained, the structural imaging advantage of ultrasonic imaging and the functional imaging advantage of electrical imaging can be combined, and the size and the conductivity change of the detected focus can be completely and clearly represented. At present, most of ultrasonic/electrical dual-mode methods adopt respective mode to respectively image and perform image fusion, the fusion result is relatively poor, and structural prior information of the ultrasonic cannot be fully utilized. Therefore, there is a need for a lesion boundary constraint information based on ultrasound reflections to more accurately guide the reconstruction process of EIT.
Disclosure of Invention
The invention provides an electrical impedance tomography image reconstruction algorithm based on ultrasonic reflection boundary constraint information, aiming at the problem that the traditional electrical impedance tomography method can not effectively reconstruct the size and the boundary contour of a focus in the electrical impedance tomography image reconstruction of the abdominal focus of a human body.
An electrical impedance tomography image reconstruction method based on ultrasonic reflection boundary constraint information comprises the following steps:
the method comprises the following steps: obtaining a boundary voltage measurement difference value delta V required by image reconstruction according to a field to be measured, wherein the specific calculation mode is
ΔV＝Vmea-Vref
In the formula VrefRepresenting the measured value of the boundary voltage of the reference field, V, obtained by simulation calculationmeaIs a measured actual field boundary voltage measurement in the presence of inclusions.
Step two: constructing a Jacobian matrix according to the reciprocity property of an electromagnetic field, and providing an inverse problem solving objective function based on a neighborhood total variation regularization method
[1] The acquisition of the Jacobian matrix refers to the calculation of a sensitivity matrix according to a reference field boundary voltage measured value obtained by simulation calculation and in combination with a reciprocity theorem theory, and the calculation formula is as follows:
in the formula, SijThe sensitivity coefficient of the ith electrode pair relative to the jth electrode pair is represented by the ith row and jth column elements of the Jacobian matrix Si，φjRespectively indicates that the ith electrode pair and the jth electrode pair respectively have I excitation currentiAnd IjThe distribution of the field potential at the time of operation,represents a gradient operator ^ nx∫ydxdy represents the integration of the length and width of each pixel element within the field.
[2] An electrical impedance tomography inverse problem solving objective function is given based on a neighborhood total variation regularization method, and the calculation formula is as follows:
wherein g represents the conductivity value of each pixel unit in the reconstructed image result,representing the value of g when the minimum value is obtained by satisfying the expression, S represents a Jacobian matrix,regularization representing the square of two norms, λ representing the total variationRegularization parameter, LpThe regularization matrix representing the total variation is obtained by calculating the position relation among different pixels, β represents a pre-selected normal number which is generally selected to be 0.01, and the regularization matrix mainly has the function of preventing the situation that a regularization item is not differentiable when the gradient of a pixel value is equal to 0, p represents the p-th pixel in a field, and the total number of pixel units of a reconstructed image is N.
[3] And (3) unfolding the objective function solved by the electrical impedance tomography inverse problem by using a least square method to obtain the objective function of the kth iterative reconstruction, wherein the calculation formula is as follows:
wherein, gk+1An objective function, g, representing the kth iterationkDenotes the value of the conductivity of the pixel, Δ g, taken at the kth iterationkRepresenting the amount of change in the optimized pixel conductivity values required for the k-th iteration.
Step three: obtaining the position of a focus boundary contour point by using an ultrasonic reflection mode and constructing a constraint equation:
[1] based on an ultrasonic reflection mode, the ultrasonic transducer emits pulse ultrasonic waves, the change of sound pressure signals received by the emitting transducer and the adjacent ultrasonic transducer along with time is recorded, the transit time between the emitting sound waves and the receiving sound waves is recorded, the vertical distance between a boundary contour point and a probe or a central connecting line of the probe is calculated, and the calculation mode can be written as follows:
d＝c·tf/2
wherein d represents the vertical distance between the focus boundary contour point and the probe or the central connecting line of the probe, c represents the average sound velocity of human abdominal tissues, and tfRepresenting the time of flight between the transmitted sound wave and the received sound wave. And obtaining the specific coordinates of the boundary contour points according to the vertical distance between the boundary contour points and the probe or the central connecting line of the probe.
[2] Generally, lesions in abdominal homogeneous organs are convex closed curves under a two-dimensional interface, and in order to quantify the shape index of the lesions, an elliptical shape is used as a fitting target of boundary contour points to obtain a closed boundary contour, which is expressed as:
where x denotes the abscissa of a point on the contour, xcTo fit the abscissa of the center point of the elliptical profile, y denotes the ordinate of the point on the profile, ycIs the ordinate of the center point of the fitted ellipse profile, a is the major axis of the fitted ellipse, and b is the minor axis of the fitted ellipse.
[3] And constructing a constraint equation of the boundary point, wherein the gradient descending value of the elliptic boundary is required to be a larger numerical value, and the gradient descending values of other areas are required to be smaller numerical values. The constraint equation is constructed in such a way that:
H(g)＝[g(pi)-α·gb,...,g(pb)-gb,…,g(po)-α-1·gb,…,g(p)-g]＝0
wherein p isiIndicating the pixel cell on the fitted contour in which the normal vector points within the pixel, pbRepresenting the pixel elements on the fitted contour, po represents the pixel elements on the fitted contour where the off-pixel normal vector points, gbThe conductivity values of the pixel units on the fitted contour are represented, other pixel units are represented by p, the conductivity values are represented by g, α is a gradient descending value, and the conductivity value is selected to be 105。
Step four: and (4) carrying out optimization solution on the electrical impedance tomography target function under the guidance of the ultrasonic constraint equation based on a Lagrange multiplier method.
[1]Constructing a Lagrangian function: electrical impedance tomography target function F (Δ g) during each iteration of the inverse problem reconstruction algorithmk) Can be expressed as:
ultrasound contour gradient constraint equation G (Δ G)k) Can be expressed as:
G(Δgk)＝H(gk)+JH(gk)·Δgk＝0
wherein JH(gk) Represents the equation H (g) during the kth iterationk) First order partial differential matrix. Constructing a new Lagrangian function L (delta g) according to a Lagrangian multiplier methodkμ), expressed as:
L(Δgk,μ)＝F(Δgk)+μG(Δgk)
where μ is the Lagrangian coefficient.
[2]Solving a Lagrange function: lagrange's function inThe conditions necessary to obtain the extremum (minimum) are:
wherein,representing a partial differential solution. From the objective function and constraint equations above, the above equation can be expanded and expressed as:
wherein,
[3] constructing a new electrical imaging target equation and optimizing and solving the target function according to the extreme value condition of the Lagrange multiplier function, wherein the target equation is expressed as follows:
using the above formula Snew·Δx＝bnewExpressing, and solving the equation by using Gauss Newton iteration, wherein each step of iteration in the solution is expressed as:
Δxk+1＝Δxk-(Snew TSnew+ηI)-1·Snew T·(SnewΔxk-bnew)
where k denotes the number of iterations, I denotes the regularization matrix (here replaced by a unity matrix), and η is the regularization parameter in a gauss-newton iteration.
[4]By iteration of the above-mentioned Gauss-Newton method, Δ g is obtainedkAnd used to update the conductivity distribution of each pixel cell, the calculation is expressed as:
gk+1＝gk+ξ·Δgk
where ξ is the step size for updating the pixel cell conductivity value.
Step five: repeating the step four until the residual error meets the requirement
Wherein, Regk＝||S·gk- Δ V | | represents a residual value, and ∈ is an artificially set residual threshold.
The method provided by the invention can keep a relatively complete and accurate inclusion boundary in an electrical impedance imaging result, effectively reduces imaging artifacts while giving the accurate position and size of the inclusion position, and remarkably improves the reconstruction quality of the abdominal focus EIT image inverse problem solution.
The algorithm is based on a neighborhood total variation regularization reconstruction algorithm, focus contour boundary points obtained by ultrasonic reflection are converted into a pixel gradient constraint equation, and an optimization solving process of an image reconstruction algorithm objective function is guided. The method solves the problems of fuzzy boundary and serious artifact in the visual detection of homogeneous organ focus in human abdomen by the traditional electrical imaging algorithm, and obviously improves the resolution capability of the electrical impedance tomography technology to the focus with different sizes and different positions. The application of the total variation regularization reconstruction algorithm is expanded, and the solving precision of the electrical impedance tomography inverse problem and the image reconstruction quality are improved. The electrical impedance image reconstruction algorithm based on ultrasonic reflection boundary constraint information has the core idea that the position of a focus boundary contour point is determined through an ultrasonic reflection mode and converted into a gradient constraint equation, a Lagrangian function is constructed, and the reconstructed conductivity distribution is solved, wherein: the position of a focus boundary contour point is obtained through an ultrasonic reflection mode and is fitted, so that the information such as the position, the size and the like of the focus is effectively obtained; by constructing a Lagrange function and solving by using a Gauss Newton method, the problems of fuzzy boundary and unclear size resolution of a focus reconstruction result of the traditional electrical imaging image reconstruction algorithm are effectively solved. The algorithm can keep a clear and accurate shape structure of the inclusion in a reconstruction result, and obviously improves the electrical impedance tomography precision on the basis of ensuring the imaging speed.
Drawings
FIG. 1 is a complete flow chart of an electrical impedance tomography image reconstruction algorithm based on ultrasonic reflection boundary constraint information, which is mainly divided into two parts, namely acquisition of ultrasonic reflection boundary constraint information and solving of an electrical impedance reconstruction inverse problem under an ultrasonic constraint equation.
FIG. 2 is a block diagram of an electrical impedance tomography system used in the present invention for abdominal lesions;
FIG. 3 is five exemplary simulation models of the present invention and shows the corresponding neighborhood total variation regularization (TV) imaging results and the final imaging results of the algorithm of the present invention, respectively;
FIG. 4 is a comparison of relative error and image correlation coefficient for different imaging results of five sets of simulation models of the present invention.
Detailed Description
The electrical impedance tomography image reconstruction algorithm based on the ultrasonic reflection boundary constraint information is described with reference to the accompanying drawings and embodiments.
The invention discloses an electrical impedance tomography image reconstruction algorithm based on ultrasonic reflection boundary constraint information, which aims at a visualization application form of focus visualization monitoring in a homogeneous organ of an upper abdomen of a human body. A positive problem model for representing electrical impedance tomography of tumors in the liver and the kidney is constructed in a priori mode by using a two-dimensional cross section structure of the upper abdomen of a human body, and boundary contour position information of a focus is determined through an ultrasonic reflection mode and converted into a constraint equation. The iterative solution process of the image reconstruction inverse problem can be decomposed into two parts, namely Lagrange function construction based on a neighborhood total variation regularization method and pixel unit conductivity iterative value solving by using a Gauss-Newton method, wherein the Lagrange function construction unifies an ultrasonic constraint equation and an electrical optimization target function under a unified solution frame, and the iterative solution of the Gauss-Newton method can quickly provide a numerical solution of the conductivity iterative value under the condition of satisfying the constraint equation and is used for updating the conductivity distribution and the Lagrange function of the pixel unit.
As shown in FIG. 1, the invention is an electrical impedance tomography image reconstruction algorithm based on ultrasonic reflection boundary constraint information. The algorithm mainly comprises five parts, namely boundary measurement value acquisition, reciprocity theorem calculation sensitivity, ultrasonic reflection constraint equation construction and Lagrange function construction, and a Gauss-Newton method is used for iterative calculation of a conductivity iterative value and updating of a Lagrange function. Fig. 2 is a basic schematic of an electrical impedance tomography test mode for lesions in the abdomen of a human body.
Fig. 3 and 4 respectively show the imaging result of the conventional electrical impedance imaging image reconstruction algorithm, the imaging result of the algorithm, and a reconstruction index, where the reconstruction index includes two types, namely a Relative Error (RE) and an image Correlation Coefficient (CC), and the calculation method may be represented as follows:
where σ denotes the reconstructed pixel cell conductivity distribution, σ*Representing the conductivity distribution, σ, in real casejAnd σj *Representing the reconstructed and true conductivity distribution of the jth pixel cell,andrepresents the average of the reconstructed and true conductivity distributions.
The embodiment of the algorithm comprises the following specific steps:
(1) for the distribution of the content in the models 1-4 in fig. 4, the boundary voltage measurement data required for the respective reconstruction are respectively obtained, and the boundary voltage measurement difference Δ V required for the image reconstruction is obtained according to the measured field, and the specific calculation method is
ΔV＝Vmea-Vref
In the formula VrefRepresenting the measured value of the boundary voltage of the reference field, V, obtained by simulation calculationmeaIn the presence of detectionActual field boundary voltage measurement values under the inclusion, as shown in fig. 2, 32 electrodes are involved in measurement and reconstruction, and according to an excitation acquisition strategy of 'adjacent current excitation, adjacent voltage measurement', Vmea、VrefContains 928 sets of voltage measurements.
(2) Constructing a Jacobian matrix according to the reciprocity property of an electromagnetic field, and providing an inverse problem solving objective function based on a neighborhood total variation regularization method
The acquisition of the Jacobian matrix refers to the calculation of a sensitivity matrix according to a reference field boundary voltage measured value obtained by simulation calculation and by combining a reciprocity theorem theory, and the calculation formula is as follows:
in the formula, SijThe sensitivity coefficient of the ith electrode pair relative to the jth electrode pair is represented by the ith row and jth column elements of the Jacobian matrix Si，φjRespectively indicates that the ith electrode pair and the jth electrode pair respectively have I excitation currentiAnd IjThe distribution of the field potential at the time of operation,represents a gradient operator ^ nx∫ydxdy represents the integration of the length and width of each pixel element within the field.
b. An electrical impedance tomography inverse problem solving objective function is given based on a neighborhood total variation regularization method, and the calculation formula is as follows:
wherein g represents the conductivity value of each pixel unit in the reconstructed image result,representing the value of g when the minimum value is obtained by satisfying the expression, S represents a Jacobian matrix,the square of a two-norm is expressed, lambda represents a regularization parameter of the total variation regularization, and an empirical value of 3 multiplied by 10 is selected-4，LpThe regularization matrix representing the total variation is obtained by calculating the position relation among different pixels, β represents a pre-selected normal number, wherein the selection is 0.01, the regularization matrix mainly has the function of preventing the situation that a regularization item is not differentiable when the gradient of a pixel value is equal to 0, p represents the p-th pixel in a field, and the total number of pixel units of a reconstructed image is N.
c. And (3) unfolding the objective function solved by the electrical impedance tomography inverse problem by using a least square method to obtain the objective function of the kth iterative reconstruction, wherein the calculation formula is as follows:
wherein, gk+1An objective function, g, representing the kth iterationkDenotes the value of the conductivity of the pixel, Δ g, taken at the kth iterationkRepresenting the amount of change in the optimized pixel conductivity values required for the k-th iteration.
(3) Obtaining the position of a focus boundary contour point by using an ultrasonic reflection mode and constructing a constraint equation:
a. based on an ultrasonic reflection mode, the ultrasonic transducer emits pulse ultrasonic waves, the change of sound pressure signals received by the emitting transducer and adjacent ultrasonic transducers along with time is recorded, the transit time between the emitting sound waves and the receiving sound waves is recorded, the vertical distance between a boundary contour point and a probe or a central connecting line of the probe is calculated, and the calculation mode is represented as follows:
d＝c·tf/2
wherein d represents the vertical distance between the focus boundary contour point and the probe or the central connecting line of the probe, and c represents the human bodyAverage speed of sound of abdominal tissue, tfRepresenting the time of flight between the transmitted sound wave and the received sound wave. And obtaining the specific coordinates of the boundary contour points according to the vertical distance between the boundary contour points and the probe or the central connecting line of the probe.
b. In general, lesions in organs with homogeneous abdominal regions are all convex closed curves under a two-dimensional interface, and in order to quantify the shape index of the lesions, an elliptical shape is used as a fitting target of boundary contour points to obtain a closed boundary contour, which is expressed as:
where x denotes the abscissa of a point on the contour, xcTo fit the abscissa of the center point of the elliptical profile, y denotes the ordinate of the point on the profile, ycIs the ordinate of the center point of the fitted ellipse profile, a is the major axis of the fitted ellipse, and b is the minor axis of the fitted ellipse.
c. And constructing a constraint equation of the boundary point, wherein the gradient descending value of the elliptic boundary is required to be a larger numerical value, and the gradient descending values of other areas are required to be smaller numerical values. The constraint equation is constructed in such a way that:
H(g)＝[g(pi)-α·gb,...,g(pb)-gb,…,g(po)-α-1·gb,…,g(p)-g]＝0
wherein p isiIndicating the pixel cell on the fitted contour in which the normal vector points within the pixel, pbRepresenting the pixel elements on the fitted contour, po represents the pixel elements on the fitted contour where the off-pixel normal vector points, gbThe conductivity values of the pixel units on the fitted contour are represented, other pixel units are represented by p, the conductivity values are represented by g, α is a gradient descending value, and the conductivity value is selected to be 105。
(4) And carrying out optimization solution on the electrical impedance tomography target function under the guidance of the ultrasonic constraint equation based on a Lagrange multiplier method.
a. Constructing a Lagrangian function: electrical impedance tomography target function F (Δ g) during each iteration of the inverse problem reconstruction algorithmk) Can be expressed as:
ultrasound contour gradient constraint equation G (Δ G)k) Can be expressed as:
G(Δgk)＝H(gk)+JH(gk)·Δgk＝0
wherein JH(gk) Represents the equation H (g) during the kth iterationk) First order partial differential matrix. Constructing a new Lagrangian function L (delta g) according to a Lagrangian multiplier methodkμ), expressed as:
L(Δgk,μ)＝F(Δgk)+μG(Δgk)
wherein mu is Lagrange coefficient, and the empirical value is 5 × 10-4。
b. Solving a Lagrange function: lagrange's function inThe conditions necessary to obtain the extremum (minimum) are:
wherein,representing a partial differential solution. From the objective function and constraint equations above, the above equation can be expanded and expressed as:
wherein,
c. constructing a new electrical imaging target equation and optimizing and solving the target function according to the extreme value condition of the Lagrange multiplier function, wherein the target equation is expressed as follows:
using the above formula Snew·Δx＝bnewExpressing, and solving the equation by using Gauss Newton iteration, wherein each step of iteration in the solution is expressed as:
Δxk+1＝Δxk-(Snew TSnew+ηI)-1·Snew T·(SnewΔxk-bnew)
where k denotes the number of iterations, I denotes the regularization matrix (here, the unitary matrix is used for substitution), η is the regularization parameter in gauss-newton iterations, and the empirical value is 3 × 10-4。
d. By iteration of the above-mentioned Gauss-Newton method, Δ g is obtainedkThe weight coefficient of (a) is used to update the conductivity distribution of each pixel unit, and the calculation method can be written as:
gk+1＝gk+ξ·Δgk
ξ is the step size for updating the conductivity value of pixel unit, and the empirical value is 2.5 × 10-2。
(5) Updating the Lagrange function and solving by using a Gauss-Newton iteration method, and repeating the steps until the residual error meets the requirement:
wherein, Regk＝||S·gk- Δ V | | represents a residual value, epsilon is an artificially set residual threshold, and the empirical value is 1 × 10-4。
The method provided by the invention can keep a relatively complete and accurate inclusion boundary in an electrical impedance imaging result, effectively reduces imaging artifacts while giving an accurate position and focus of the inclusion, and remarkably improves the reconstruction quality of the abdominal focus EIT image inverse problem solution. The position of a focus boundary contour point is obtained through an ultrasonic reflection mode and is fitted, so that the information such as the position, the size and the like of the focus is effectively obtained; by constructing a Lagrange function and solving by using a Gauss Newton method, the problems of fuzzy boundary and unclear size resolution of a focus reconstruction result of the traditional electrical imaging image reconstruction algorithm are effectively solved. The algorithm can keep a clear and accurate shape structure of the inclusion in a reconstruction result, and obviously improves the electrical impedance tomography precision on the basis of ensuring the imaging speed.
The embodiments described above are some exemplary models of the present invention, and the present invention is not limited to the disclosure of the embodiments and the drawings. It is intended that all equivalents and modifications which come within the spirit of the disclosure be protected by the present invention.
Claims (2)
1. An ultrasonic reflection information constrained abdomen lesion electrical impedance image reconstruction method is suitable for electrical impedance tomography image reconstruction, the position of a focus boundary contour point is determined through an ultrasonic reflection mode and converted into a gradient constraint equation, a Lagrangian function is constructed, and reconstructed conductivity distribution is solved and obtained by the following steps
The method comprises the following steps: obtaining a boundary voltage measurement difference value delta V required by image reconstruction according to a field to be measured:
ΔV＝Vmea-Vref
in the formula VrefShow through simulationTrue calculated reference field boundary voltage measurement, VmeaIs a measured actual field boundary voltage measurement in the presence of inclusions.
Step two: constructing a Jacobian matrix according to the reciprocity property of an electromagnetic field, and giving an inverse problem solving objective function based on a neighborhood total variation regularization method as follows
[1] The acquisition of the Jacobian matrix refers to calculating a sensitivity matrix according to a reference field boundary voltage measured value obtained by simulation calculation and by combining a reciprocity theorem theory;
[2] an electrical impedance tomography inverse problem solving objective function is given based on a neighborhood total variation regularization method, and the calculation formula is as follows:
wherein g represents the conductivity value of each pixel unit in the reconstructed image result,representing the value of g when the minimum value is obtained by satisfying the expression, S represents a Jacobian matrix,denotes the square of the two-norm, λ denotes the regularization parameter of the total variation regularization, LpThe total variation regularization matrix is represented and obtained by calculating the position relation among different pixels, β represents a pre-selected normal number which is generally selected to be 0.01, and the regularization matrix has the main function of preventing the occurrence of the condition that regularization items are not differentiable when the gradient of a pixel value is equal to 0, p represents the p-th pixel in a field domain, and the total number of pixel units of a reconstructed image is N;
[3] and (3) unfolding the objective function solved by the electrical impedance tomography inverse problem by using a least square method to obtain the objective function of the kth iterative reconstruction, wherein the calculation formula is as follows:
wherein, gk+1An objective function, g, representing the kth iterationkDenotes the value of the conductivity of the pixel, Δ g, taken at the kth iterationkRepresenting the variation of the optimized pixel conductivity value required by the k iteration;
step three: obtaining the position of a focus boundary contour point by using an ultrasonic reflection mode and constructing a constraint equation:
[1] based on an ultrasonic reflection mode, the ultrasonic transducer emits pulse ultrasonic waves, the change of sound pressure signals received by the emitting transducer and the adjacent ultrasonic transducer along with time is recorded, the transition time between the emitting sound waves and the receiving sound waves is recorded, and the vertical distance between a boundary contour point and a probe or a central connecting line of the probe is calculated:
d＝c·tf/2
wherein d represents the vertical distance between the focus boundary contour point and the probe or the central connecting line of the probe, c represents the average sound velocity of the human abdomen soft tissue, and tfRepresenting the transit time between the transmitted sound wave and the received sound wave, and obtaining the specific coordinates of the boundary contour points according to the vertical distance between the boundary contour points and the probe or the central connecting line of the probe;
[2] regarding the focus in the abdominal mean organ as a convex closed curve under a two-dimensional interface, and adopting an elliptical shape as a fitting target of boundary contour points to obtain a closed boundary contour in order to quantify the shape index of the focus;
[3] constructing a constraint equation of boundary points, wherein the gradient descending value of the elliptic boundary is required to be a larger numerical value, and the gradient descending values of other areas are required to be smaller numerical values; the constraint equation is constructed in such a way that:
H(g)＝[g(pi)-α·gb,...,g(pb)-gb,…,g(po)-α-1·gb,…,g(p)-g]＝0
wherein p isiIndicating the pixel cell on the fitted contour in which the normal vector points within the pixel, pbPixel elements represented on the fitted contour, poIndicating the pixel cell on the fitted contour at which the pixel's outside normal vector points, gbThe conductivity values of the pixel units on the fitted contour are represented, and other pixel units are uniformly represented by p, whichThe conductivity value is expressed by g, α is a gradient descending value, and is selected to be 105；
Step four: performing optimization solution on the electrical impedance tomography target function under the guidance of an ultrasonic constraint equation based on a Lagrange multiplier method;
[1]constructing a Lagrangian function: electrical impedance tomography target function F (Δ g) during each iteration of the inverse problem reconstruction algorithmk) Expressed as:
ultrasound contour gradient constraint equation G (Δ G)k) Expressed as:
G(Δgk)＝H(gk)+JH(gk)·Δgk＝0
wherein JH(gk) Represents the equation H (g) during the kth iterationk) A first order partial differential matrix of; constructing a new Lagrangian function L (delta g) according to a Lagrangian multiplier methodk,μ)：
L(Δgk,μ)＝F(Δgk)+μG(Δgk)
Wherein μ is a Lagrangian coefficient;
[2] solving a Lagrange function: constructing a new electrical imaging target equation and optimizing and solving the target function according to the extreme value condition of the Lagrange multiplier function, wherein the target equation is expressed as follows:
wherein, represents a partial differential solution, S will be usednew·Δx＝bnewExpressing the target equation and solving it using Gauss-Newton iterationEach iteration is represented as:
Δxk+1＝Δxk-(Snew TSnew+ηI)-1·Snew T·(SnewΔxk-bnew)
wherein,a matrix of coefficients representing the objective equation,a solution to the objective equation is represented,k represents iteration times, I represents a regularization matrix (which is replaced by a unit matrix), and η is a regularization parameter in Gaussian Newton iteration;
[4]by iteration of the above-mentioned Gauss-Newton method, Δ g is obtainedkThe weight coefficient is used for updating the conductivity distribution of each pixel unit, and the calculation method is as follows:
gk+1＝gk+ξ·Δgk
ξ is the step size for updating the conductivity value of the pixel unit;
step five: repeating the step four until the residual error meets the requirement
Wherein, Regk＝||S·gk- Δ V | | represents a residual value, and ∈ is an artificially set residual threshold.
2. The ultrasound process tomography reconstruction method of claim 1, wherein: the boundary measurement value in the first step is obtained by placing a certain number of square electrodes on the surface of a two-dimensional section of the abdomen of a human body, adopting a measurement strategy of circular excitation, transmission and total reception based on the measurement mode of adjacent current excitation and adjacent voltage measurement, and obtaining a boundary voltage measurement difference value delta V required by image reconstruction, wherein the boundary voltage measurement difference value delta V is a difference value between a reference field boundary voltage measurement value obtained through simulation calculation and a measured actual field boundary voltage measurement value in the presence of inclusions.
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