CN114947802A - Particle swarm optimization electrical impedance imaging method based on density and density two mesh generation models - Google Patents
Particle swarm optimization electrical impedance imaging method based on density and density two mesh generation models Download PDFInfo
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Abstract
The invention discloses a particle swarm optimization electrical impedance imaging method based on two density grid subdivision models, which relates to the technical field of electrical impedance imaging, and adopts the technical scheme that: the method specifically comprises the following steps: s1: constructing an original model, marking as model 0, and generating an initial conductivity distribution sigma 0 (ii) a S2: carrying out mesh fine division on the region of interest ROI on the basis of the model 0, constructing a model I in the unchanged other regions, and constructing a model II in the combined meshes of the other regions; s3: constructing a conductivity conversion matrix from the model 0 to the model I and from the model I to the model II; s4: obtaining the electrical conductivity conversion matrix from the obtained sigma 0 Mapping to model I and model II corresponding conductivitiesDistribution value σ I And σ II (ii) a S5: solving the positive problem and the inverse problem in the electrical impedance tomography by adopting a particle swarm optimization algorithm based on the model I and the model II. The method solves the problem of dimension disaster in the particle swarm algorithm, thereby improving the positioning accuracy and the imaging speed of the target.
Description
Technical Field
The invention relates to the technical field of electrical impedance imaging, in particular to a particle swarm optimization electrical impedance imaging method based on two sparse and dense mesh generation models.
Background
Electrical Impedance Tomography (EIT) is a non-invasive, non-radiative, convenient to use, and low-cost functional imaging technique, which measures the boundary voltage of a measured region by injecting a safe excitation current to the body surface of a human body, reconstructs the Electrical Impedance distribution inside the measured region according to the measured boundary voltage value, and presents the Electrical Impedance distribution as an image on a computer. The technology does not use nuclide or ray, is harmless to human body, can be used repeatedly for multiple times of measurement, and is suitable for long-term and continuous monitoring of patients, thereby becoming a research hotspot at home and abroad and having attractive application prospect.
The solution of the EIT problem includes two parts, a positive problem and an inverse problem. The positive problem refers to that the conductivity distribution of the measured field is known to obtain the boundary voltage, and the inverse problem refers to that the conductivity distribution of the measured field is obtained by knowing the excitation current and the boundary voltage. The forward problem solving is the basis of the inverse problem solving, and a common algorithm is a finite Element fem (finite Element method) method. Experiments show that increasing the number of the subdivision units can improve the calculation accuracy, but also can increase the calculation amount, and can cause great increase of the calculation amount of the inverse problem. In addition, when the number of the subdivision units reaches a certain number, simply increasing the density of subdivision is very limited to improve the calculation accuracy of the positive problem.
EIT image reconstruction belongs to the non-linear inverse problem. The traditional algorithms include a back projection method, a Newton-Raphson method, a Gaussian-Newton method and the like. The equipotential line back projection method is a dynamic EIT technology, is simple to realize, has high imaging speed and better anti-noise performance, but has low spatial resolution of image reconstruction and more artifacts. The Newton method approximately converts a nonlinear problem into a linear problem, a lot of important information is lost in the linearization process, the distortion of a reconstructed image is easy to be serious, a Jacobian matrix and a Heisen matrix need to be solved in the calculation process, the calculation amount is greatly increased along with the increase of the number of subdivision units, and the ill-conditioned performance of the subdivision units is aggravated. Although the regularization technology is introduced to reduce the ill-posed property of the algorithm, the problems of low spatial resolution of a reconstructed image, unclear boundary and the like are still not well solved.
The EIT inverse problem can be regarded as an optimization problem, so that a heuristic optimization algorithm is adopted to minimize the difference between the measured voltage and the calculated voltage through continuous iterative optimization, and genetic algorithms GA, particle swarm optimization PSO, differential evolution algorithm DE and the like are introduced into EIT image reconstruction research in recent years. Compared with the traditional algorithm, the optimization algorithm avoids the derivation problem of the Jacobian matrix and the inverse matrix thereof, and does not depend on the mathematical expression of the field to be measured. Experiments show that the optimization effect is good when the number of the subdivision units is small, but with the increase of the number of the subdivision units, the optimization algorithm is easy to fall into stagnation and the operation speed is slow, which is called as a 'dimension disaster' problem. The "dimensional disaster" problem of the optimization algorithm is mainly embodied in two aspects: firstly, the calculated amount of the algorithm increases exponentially along with the increase of the dimensionality, and secondly, the algorithm which is well represented in the low-dimensional space may not obtain a good convergence effect in the high-dimensional space.
The PSO of the particle swarm has the characteristics of simple algorithm, high convergence rate, easiness in implementation, few parameters and the like, and can be applied to EIT image reconstruction. If the initial value of the PSO is preset by the priori knowledge, the particle searching has guidance, and the global optimal value can be searched in a short time. The positions of the PSO particles show the conductivity distribution of a measured field, the dimension of the particles is equal to the number of subdivision triangle units, the PSO algorithm needs to calculate the positive problem of EIT in each iteration optimization process, and obviously, the performance of the PSO algorithm is closely related to the scale of mesh subdivision in a finite element model. The adoption of the sparse grid can increase the calculation error of the positive problem, and the adoption of the fine grid can bring about 'dimension disaster', so that the PSO algorithm is early-maturing, and a good convergence effect is difficult to obtain, thereby influencing the image reconstruction effect.
The PSO algorithm mainly has the following problems in the process of realizing electrical impedance imaging:
1. the initial value of the particles has a great influence on the optimization result, and the random generation of the population brings great randomness, which is not beneficial to expanding the search space and converging to the global optimum point, so that the iterative optimization process is relatively long;
2. the dimension of the particles is equal to the number of grid splitting units in the finite element model, and the splitting fineness can cause the dimension of the PSO algorithm to be too high, so that the problem of dimension disaster is caused;
3. each iteration process needs to carry out positive problem calculation, the calculation precision of the positive problem calculation is closely related to the subdivision density of the grids, the calculation precision is high when the grid is dense, and the error is large when the grid is sparse.
Disclosure of Invention
The invention aims to provide a particle swarm optimization electrical impedance imaging method based on two density grid division models, which solves the problem of dimension disaster caused by the number of grid division units in the electrical impedance imaging process of a particle swarm optimization algorithm, can ensure the calculation precision, can improve the particle swarm optimization speed, and avoids getting into precocity, thereby improving the electrical impedance imaging spatial resolution and the imaging speed.
The technical purpose of the invention is realized by the following technical scheme: the particle swarm optimization electrical impedance imaging method based on the density mesh generation model specifically comprises the following steps:
s1: constructing an original model, marking as a model 0, and generating initial conductivity distribution;
s2: performing mesh subdivision on the ROI on the basis of the model 0, constructing a model I in other regions without changing, and constructing a model II in other regions by mesh merging;
s3: constructing a conductivity conversion matrix from the model 0 to the model I and from the model I to the model II;
s4: from the conductivity conversion matrix obtained in S3, the value of σ is obtained 0 Conductivity distribution values σ mapped to model I and model II I And σ II ；
S5: solving the positive problem and the inverse problem in the electrical impedance tomography by adopting a particle swarm optimization algorithm based on the model I and the model II.
The invention is further configured to: the specific steps of S1 are as follows:
1) applying safe current to a field to be measured through electrodes for excitation, and acquiring boundary voltage U of the field to be measured by adopting an adjacent excitation adjacent measurement method;
2) discretizing the field to be measured, carrying out mesh sparse subdivision by taking the triangle as a subdivision unit to establish a finite element model, and recording the finite element model as a model 0;
3) based on the model 0, image reconstruction is carried out by adopting a one-step Gauss Newton method to obtain initial conductivity distribution of the measured field, and the initial conductivity distribution is marked as sigma 0 ＝(σ 1 ，σ 2 ，σ 3 …σ N )；
Wherein N represents the number of the subdivision triangle units;
4) from the generated initial conductivity distribution σ 0 Reconstructing an image, wherein the image can display a region with changed electrical impedance, the region is an ROI region, and the ROI region is automatically divided by manually dividing or setting a threshold value through detecting a conductivity change gradient;
5) extracting coordinates of each node of the ROI, and subdividing a topological structure of a triangular unit and a conductivity value of the unit;
the coordinates of all nodes are recorded as H, and the network topology structure of the subdivision triangle unit is recorded as G.
The invention is further configured to: the specific steps of S2 are as follows:
1) establishing initialization arrays GG and HH;
2) extracting the topology and the node coordinates of the ith triangular node of the ROI area, and respectively assigning HH and GG;
3) taking the midpoints of 1-3 triangle sides on the ith triangle to obtain a midpoint coordinate, and storing the midpoint coordinate into GG;
4) numbering the newly generated midpoint coordinates, and putting a topological structure of a plurality of small triangular subdivision units formed between the newly generated midpoint coordinates and the node coordinates into HH;
5) repeatedly executing the step 3) and the step 4) until all the triangles in the ROI area are refined and subdivided;
6) carrying out merging optimization on the nodes and topological structures of the thinned ROI area and other areas to obtain a network topological structure of the model I;
7) and carrying out mesh merging on the regions outside the ROI to obtain a model II, and updating the topological structure and the node number of the subdivision unit of the model.
The invention is further configured to: the specific steps of S3 are as follows:
1) let the number of mesh generation units of the sparse mesh generation model 0 be N, and the conductivity distribution matrix be A ═ σ [ σ ] 1 σ 2 σ 3 … σ N ] T A column vector of nx 1; setting the number of mesh generation units of the fine mesh generation model I to be N 1 The conductivity distribution matrix is B ═ sigma' 1 σ' 2 σ' 3 … σ' N1 ]T is N 1 A column vector of x 1;
2) constructing a conversion matrix C1 of unit characteristics from a fine to sparse subdivision model by utilizing correlation, wherein row elements correspond to sparse subdivision units, column elements correspond to encrypted subdivision units, and rows and columns where the matrix elements are located are 1 if the rows and the columns are related to the sparse and dense subdivision units, otherwise, the values are 0;
3) tong (Chinese character of 'tong')C1 T Obtaining the conductivity distribution value sigma of the subdivision unit of the model I 1 ；
4) Similarly, a model I to model II conductivity conversion matrix C2 is constructed and then passed
The conductivity distribution value sigma of the model II is obtained II ；
Wherein epsilon is the number of the small triangle subdivision units.
The invention is further configured to: the specific steps of S5 are as follows:
1) establishing a particle group with the size of m and limiting the number m, the dimension D and the position of the particles [ x min ，x max ]Iteration number, variation rate P c Initializing a limited range and an initial value of the speed, wherein the dimension D represents the number N of the triangular subdivision units in the sparse grid model II 2 、x max And x min Maximum values σ representing the electrical conductivity of the measured region, respectively max And minimum value G min ；
2) Initializing the position x of each particle in the population i ＝(x i1 ，x i2 ，x i3 ，…，x iD ) Converting the initial electrical impedance distribution of the measured region obtained by the one-step Gauss-Newton method into the electrical conductivity distribution [ sigma ] corresponding to the sparse grid model II 1 σ 2 σ 3 … σ N2 ] T As an initial value of the particle;
3) calculating to obtain a calculated voltage through a positive problem, and calculating the fitness value of each particle;
4) taking the fitness value of the initial particle as an individual extreme value pbest, and taking the minimum value of the individual extreme values as a group extreme value gbest;
5) by updating the formula:
v ij (t+1)＝w·v ij (t)+c 1 ·r 1 ·(pbest ij (t)-x ij (t))+c 2 ·r 2 ·(gbest j (t)-x ij (t))
x ij (t+1)＝v ij (t+1)+x i (t)
updating the speed and the position of the particles, and performing boundary limitation;
wherein w represents an inertial weight, c 1 And c 2 Is an acceleration constant with a value ranging from 0 to 2, r 1 And r 2 The random numbers are uniformly distributed between 0 and 1, i is 1, 2, …, m, j is 1, 2, …, D, t is iteration times;
6) subdividing the particle position x of a sparse mesh model ij Converting the mapping matrix into a conductivity distribution value of a fine model grid subdivision unit, then performing positive problem calculation, and then performing fitness value calculation;
7) when the particle fitness is smaller than pbest, updating pbest to the new position of the particle, and when the particle fitness is smaller than gbest, updating gbest to the new position of the particle;
8) if the generated random number r < P m If yes, executing mutation operation, otherwise, entering step 9);
9) when the maximum iteration times are reached or the fitness value reaches a set error value, ending iteration to output a group extreme value gbest, otherwise, returning to the step 5) to carry out the next iteration cycle process; and the output population extreme value gbest is the electrical impedance distribution of the optimized measured area, and an EIT image is reconstructed according to the electrical impedance distribution.
In conclusion, the invention has the following beneficial effects: the method adopts a one-step Gauss-Newton method of the traditional classical algorithm, and the solved conductivity distribution result is used as an initial value of the PSO particles, so that the particle search has guidance, the particles can be prompted to search a global optimal solution in a short time and adopt a sparse mesh subdivision model, the reduction of subdivision units is favorable for reducing the dimensionality of the particles, and the iteration speed of the algorithm is greatly improved; the abnormal area is subjected to grid encryption, and the grid density of other areas is unchanged, so that the reconstruction precision of the abnormal area can be improved, and higher reconstruction efficiency is ensured; by establishing conversion between the two models, the conductivity distribution value solved under the sparse grid model is converted and mapped under the fine grid model so as to carry out positive problem calculation; the method comprises the steps that a group extreme value generated after each iterative optimization of particles is mapped to a conductivity distribution value of a fine mesh generation model through a conductivity conversion matrix between a sparse mesh model and a fine mesh model, and then positive problem calculation is carried out, so that the updating of an individual extreme value and the group extreme value is realized, and the optimization of particle swarm is completed; variation operation is introduced into the electrical impedance imaging algorithm, namely variation probability factors are introduced into the whole population position, so that the diversity of the population is kept, the local optimal position can be skipped, and the capability of the population to search the global optimal solution is improved.
Drawings
FIG. 1 is a flow chart of a particle swarm optimization electrical impedance imaging method based on two density mesh generation models in the embodiment of the invention;
FIG. 2 is a schematic diagram of a mesh subdivision structure in an embodiment of the present invention;
FIG. 3 is a flow chart of a partially subdivided mesh model in an embodiment of the present invention;
fig. 4 is a flowchart of the particle swarm algorithm in the embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to figures 1-4.
Example (b): the particle swarm optimization electrical impedance imaging method based on the density mesh generation model comprises the following steps of:
s1: constructing an original model, marking as a model 0, and generating initial conductivity distribution;
s2: carrying out mesh fine division on the region of interest ROI on the basis of the model 0, constructing a model I in the unchanged other regions, and constructing a model II in the combined meshes of the other regions;
s3: constructing conductivity conversion matrixes from the model 0 to the model I and from the model I to the model II;
s4: from the conductivity conversion matrix obtained at S3, the value of σ is obtained 0 Conductivity distribution values σ mapped to model I and model II I And σ II ；
S5: solving the positive problem and the inverse problem in the electrical impedance tomography by adopting a particle swarm optimization algorithm based on the model I and the model II.
The specific steps of S1 are:
1) applying safe current to a field to be measured through electrodes for excitation, and acquiring boundary voltage U of the field to be measured by adopting an adjacent excitation adjacent measurement method;
2) discretizing the field to be measured, carrying out mesh sparse subdivision by taking the triangle as a subdivision unit to establish a finite element model, and recording the finite element model as a model 0;
3) based on the model 0, image reconstruction is carried out by adopting a one-step Gauss Newton method to obtain initial conductivity distribution of the measured field, and the initial conductivity distribution is marked as sigma 0 ＝(σ 1 ，σ 2 ，σ 3 …σ N )；
Wherein N represents the number of the subdivision triangle units;
4) from the generated initial conductivity distribution σ 0 Reconstructing an image, wherein the image can display a region with changed electrical impedance, the region is an ROI region, and the ROI region is automatically divided by manually dividing or setting a threshold value through detecting a conductivity change gradient;
5) extracting coordinates of each node of the ROI, and subdividing a topological structure of a triangular unit and a conductivity value of the unit;
the coordinates of all nodes are recorded as H, and the network topology structure of the subdivision triangle unit is recorded as G.
The specific steps of S2 are:
1) establishing initialization arrays GG and HH;
2) extracting the topology and the node coordinates of the ith triangular node of the ROI area, and respectively assigning HH and GG;
3) taking the midpoints of 1-3 triangle sides on the ith triangle to obtain a midpoint coordinate, and storing the midpoint coordinate into GG;
4) numbering the newly generated midpoint coordinates, and putting a topological structure of a plurality of small triangular subdivision units formed between the newly generated midpoint coordinates and the node coordinates into HH;
5) repeatedly executing the step 3) and the step 4) until all the triangles in the ROI area are refined and subdivided;
6) carrying out merging optimization on the nodes and topological structures of the thinned ROI area and other areas to obtain a network topological structure of the model I;
7) and carrying out mesh merging on the regions outside the ROI to obtain a model II, and updating the topological structure and the node number of the subdivision unit of the model.
In this embodiment, as shown in fig. 2, mesh subdivision may adopt 1:2, 1:3, 1:4 refinements, for example, 1:4 refinements, where 1:4 refinements are that a new point is introduced into each of three side centers of a subdivided small triangle, and the points are connected to change from one triangle into four small triangles; when calculating the coordinate, the middle point of the ith triangle side is taken to obtain a new coordinate and the new coordinate is stored in GG, and the coordinates of the original three vertexes are respectively set as (u) 11 ,v 11 )、(u 22 ，v 22 )、(u 33 ,v 33 ) And taking the middle point of the connecting line of every two vertexes, wherein the coordinates are as follows:
numbering the newly generated three middle points, and putting the newly generated topological structures of the four small triangle subdivision units into HH; in the sparse meshing model, 4:1 or 2:1 merging can be adopted.
The specific steps of S3 are:
1) let the number of mesh generation units of the sparse mesh generation model 0 be N, and the conductivity distribution matrix be A ═ σ [ σ ] 1 σ 2 σ 3 … σ N ] T A column vector of nx 1; setting the number of mesh generation units of the fine mesh generation model I to be N 1 The conductivity distribution matrix is B ═ sigma' 1 σ′ 2 σ′ 3 … σ′ N1 ] T Is N 1 A column vector of x 1;
2) constructing a conversion matrix C1 of unit characteristics from a fine to sparse subdivision model by utilizing correlation, wherein row elements correspond to sparse subdivision units, column elements correspond to encrypted subdivision units, and rows and columns where the matrix elements are located are 1 if the rows and the columns are related to the sparse and dense subdivision units, otherwise, the values are 0;
in this embodiment, the transformation matrix is used to realize mutual transformation between cell characteristics of the sparse mesh generation model and the dense mesh generation model. For 1:4 grid refinement, the unit characteristics of the refined 4 subdivision units are the same as those of the original sparse subdivision unit, the original unit is divided into 4 units in a geometric form, and the conversion matrix obtained by adopting the method is as follows:
3) by B ═ C1 T Obtaining the conductivity distribution value sigma of the subdivision unit of the model I I ；
4) Similarly, a model I to model II conductivity conversion matrix C2 is constructed and then passed
Obtaining the conductivity distribution value sigma of the model II II ；
Wherein epsilon is the number of the small triangle subdivision units.
The specific steps of S5 are:
1) establishing a particle group with the size of m and limiting the number m, the dimension D and the position of the particles [ x min ，x max ]Iteration number, variation rate P m Initializing a limited range and an initial value of the speed, wherein the dimension D represents the number D, x of the triangle subdivision units in the sparse grid model II max And x min Maximum values σ representing the electrical conductivity of the measured region, respectively max And minimum value σ min ；
2) Initializing the position x of each particle in the population i ＝(x i1 ，x i2 ，x i3 ，…，x iD ) Converting the initial electrical impedance distribution of the measured region obtained by the one-step Gauss-Newton method into the electrical conductivity distribution [ sigma ] corresponding to the sparse grid model II 1 σ 2 σ 3 … σ N2 ] T As an initial value of the particle;
3) calculating to obtain a calculated voltage through a positive problem, and calculating the fitness value of each particle;
4) taking the fitness value of the initial particle as an individual extreme value pbest, and taking the minimum value of the individual extreme values as a group extreme value gbest;
5) by updating the formula:
v ij (t+1)＝w·v ij (t)+c 1 ·r 1 ·(pbest ij (t)-x ij (t))+c 2 ·r 2 ·(gbest j (t)-x ij (t))
x ij (t+1)＝v ij (t+1)+x i (t)
updating the speed and the position of the particles, and performing boundary limitation;
wherein w represents an inertial weight, c 1 And c 2 Is an acceleration constant with a value ranging from 0 to 2, r 1 And r 2 The random numbers are uniformly distributed between 0 and 1, i is 1, 2, …, m, j is 1, 2, …, D, t is the iteration number;
6) dividing the particle position x of the sparse grid model ij Converting the mapping matrix into a conductivity distribution value of a fine model grid subdivision unit, then performing positive problem calculation, and then performing fitness value calculation;
7) when the particle fitness is smaller than pbest, updating pbest to the new position of the particle, and when the particle fitness is smaller than gbest, updating gbest to the new position of the particle;
8) if the generated random number r < P m If yes, executing mutation operation, otherwise, entering step 9);
9) and when the maximum iteration times are reached or the fitness value reaches a set error value, finishing iteration and outputting the population extreme value gbest, otherwise, returning to the step 5) to output the population extreme value gbest in the next iteration cycle process, namely the electrical impedance distribution of the optimized measured region, and reconstructing an EIT image according to the electrical impedance distribution.
In this embodiment, the fitness function is selected as the sum of squares of difference values between the calculated voltage and the measured voltage, and the smaller the value, the better the optimization result, wherein the calculated voltage is obtained by the positive problem calculation, and when the positive problem calculation is performed, a conversion matrix of the conductivity between the model II and the model I is first established, the conductivity distribution of the mesh division unit of the model II is mapped to the conductivity distribution value of the mesh division unit of the model I, and then the positive problem calculation is performed.
The working principle is as follows: the method adopts a one-step Gauss-Newton method of the traditional classical algorithm, the solved conductivity distribution result is used as an initial value of the PSO particles, so that the particle search has guidance, the particles can be prompted to search a global optimal solution in a short time and adopt a sparse mesh generation model, the generation of a generation unit is beneficial to reducing the dimensionality of the particles, the iteration speed of the algorithm is greatly improved, the mesh encryption is carried out on an abnormal area, the mesh density of other areas is unchanged, the reconstruction precision of the abnormal area can be improved, and the higher reconstruction efficiency is ensured; the method comprises the steps that a group extreme value generated after each iterative optimization of particles is mapped to a conductivity distribution value of a fine mesh generation model through a conductivity conversion matrix between a sparse mesh model and a fine mesh model, and then positive problem calculation is carried out, so that the updating of an individual extreme value and the group extreme value is realized, and the optimization of particle swarm is completed; variation operation is introduced into the electrical impedance imaging algorithm, namely variation probability factors are introduced into the whole population position, so that the diversity of the population is kept, the local optimal position is favorably jumped out, and the capability of the population for searching the global optimal solution is improved.
The present embodiment is only for explaining the present invention, and it is not limited to the present invention, and those skilled in the art can make modifications of the present embodiment without inventive contribution as needed after reading the present specification, but all of them are protected by patent law within the scope of the claims of the present invention.
Claims (5)
1. A particle swarm optimization electrical impedance imaging method based on density two grid generation models is characterized in that: the method specifically comprises the following steps:
s1: constructing an original model, marking as model 0, and generating an initial conductivity distribution sigma 0 ；
S2: performing mesh subdivision on the ROI on the basis of the model 0, constructing a model I in other regions without changing, and constructing a model II in other regions by mesh merging;
s3: constructing a conductivity conversion matrix from the model 0 to the model I and from the model I to the model II;
s4: from the conductivity conversion matrix obtained at S3, the value of σ is obtained 0 Conductivity distribution values σ mapped to model I and model II I And σ II ；
S5: solving the positive problem and the inverse problem in the electrical impedance tomography by adopting a particle swarm optimization algorithm based on the model I and the model II.
2. The particle swarm optimization electrical impedance imaging method based on the density mesh generation model and the density mesh generation model according to claim 1, wherein the method comprises the following steps: the specific steps of S1 are as follows:
1) applying safe current to a field to be measured through electrodes for excitation, and acquiring boundary voltage U of the field to be measured by adopting an adjacent excitation adjacent measurement method;
2) discretizing the field to be measured, carrying out mesh sparse subdivision by taking the triangle as a subdivision unit to establish a finite element model, and recording the finite element model as a model 0;
3) based on the model 0, image reconstruction is carried out by adopting a one-step Gauss Newton method to obtain initial conductivity distribution of the measured field, and the initial conductivity distribution is marked as sigma 0 ＝(σ 1 ，σ 2 ，σ 3 ...σ N )；
Wherein N represents the number of the subdivision triangle units;
4) from the generated initial conductivity distribution σ 0 Reconstructing an image, wherein the image can display a region with changed electrical impedance, the region is an ROI region, and the ROI region is automatically divided by manually dividing or setting a threshold value through detecting the change gradient of the electrical conductivity;
5) extracting coordinates of each node of the ROI, and subdividing a topological structure of a triangular unit and a conductivity value of the unit;
the coordinates of all nodes are recorded as H, and the network topology structure of the subdivision triangle unit is recorded as G.
3. The particle swarm optimization electrical impedance imaging method based on the density mesh generation model and the density mesh generation model as claimed in claim 2, wherein: the specific steps of S2 are as follows:
1) establishing initialization arrays GG and HH;
2) extracting the topology and the node coordinates of the ith triangular node of the ROI area, and respectively assigning HH and GG;
3) taking the midpoints of 1-3 triangle sides on the ith triangle to obtain a midpoint coordinate, and storing the midpoint coordinate into GG;
4) numbering the newly generated midpoint coordinates, and putting a topological structure of a plurality of small triangular subdivision units formed between the newly generated midpoint coordinates and the node coordinates into HH;
5) repeatedly executing the step 3) and the step 4) until all the triangles in the ROI area are refined and subdivided;
6) carrying out merging optimization on the nodes and topological structures of the thinned ROI area and other areas to obtain a network topological structure of the model I;
7) and carrying out mesh merging on the regions outside the ROI to obtain a model II, and updating the topological structure and the node number of the subdivision unit of the model.
4. The particle swarm optimization electrical impedance imaging method based on the density mesh generation model and the density mesh generation model as claimed in claim 3, wherein the method comprises the following steps: the specific steps of S3 are as follows:
1) let the number of mesh generation units of the sparse mesh generation model 0 be N, and the conductivity distribution matrix be A ═ σ [ σ ] 1 σ 2 σ 3 …σ N ] T A column vector of nx 1; setting the number of mesh generation units of the fine mesh generation model I to be N 1 The conductivity distribution matrix is B ═ sigma' 1 σ′ 2 σ′ 3 ...σ′ N1 ] T Is N 1 A column vector of x 1;
2) constructing a conversion matrix C1 of unit characteristics from a fine to sparse subdivision model by utilizing correlation, wherein row elements correspond to sparse subdivision units, column elements correspond to encrypted subdivision units, and rows and columns where the matrix elements are located are 1 if the rows and the columns are related to the sparse and dense subdivision units, otherwise, the values are 0;
3) by B ═ C1 T Obtaining the conductivity distribution value sigma of the subdivision unit of the model I I ；
4) Similarly, a model I to model II conductivity conversion matrix C2 is constructed and then passed
The conductivity distribution value sigma of the model II is obtained II ；
Wherein epsilon is the number of the small triangle subdivision units.
5. The particle swarm optimization electrical impedance imaging method based on the density mesh generation model and the density mesh generation model according to claim 4, wherein the method comprises the following steps: the specific steps of S5 are as follows:
1) establishing a particle group with the size of m and limiting the number m, the dimension D and the position of the particles [ x min ，x max ]Iteration number, variation rate P m Initializing a limited range and an initial value of the speed, wherein the dimension D represents the number N of the triangular subdivision units in the sparse grid model II 2 、x max And x min Maximum values σ representing the electrical conductivity of the measured region, respectively max And minimum value σ min ；
2) Initializing the position x of each particle in the population i ＝(x i1 ，x i2 ，x i3 ，…，x iD ) The initial impedance distribution sigma of the measured region is obtained by one-step Gauss-Newton method 0 Conversion into conductivity distribution σ corresponding to sparse grid model II II ＝[σ 1 σ 2 σ 3 …σ N2 ] T As an initial value of the particle;
3) calculating a positive problem based on the model I to obtain a calculated voltage, and calculating the fitness value of each particle;
4) taking the fitness value of the initial particle as an individual extreme value pbest, and taking the minimum value of the individual extreme values as a group extreme value gbest;
5) by updating the formula:
v ij (t+1)＝w·v ij (t)+c 1 ·r 1 ·(pbest ij (t)-x ij (t))+c 2 ·r 2 ·(gbest j (t)-x ij (t))
x ij (t+1)＝v ij (t+1)+x i (t)
updating the speed and the position of the particles, and performing boundary limitation;
where w represents the inertial weight, c 1 And c 2 Is an acceleration constant with a value ranging from 0 to 2, r 1 And r 2 The random numbers are uniformly distributed between 0 and 1, i is 1, 2, …, m, j is 1, 2, D, t is iteration times;
6) subdividing the sparse grid into the particle positions x of the model II ij Converting the mapping matrix into a conductivity distribution value of a fine model I grid subdivision unit, then performing positive problem calculation, and then performing fitness value calculation;
7) when the particle fitness is smaller than pbest, updating pbest to the new position of the particle, and when the particle fitness is smaller than gbest, updating gbest to the new position of the particle;
8) if the generated random number r < P m If yes, executing mutation operation, otherwise, entering step 9);
9) and when the maximum iteration times are reached or the fitness value reaches a set error value, ending iteration and outputting the population extreme value gbest, otherwise, returning to the step 5) to output the population extreme value gbest in the next iteration cycle process as the optimized electrical impedance distribution of the measured area, and reconstructing an EIT image according to the electrical impedance distribution.
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