CN109584323A - The information constrained coeliac disease electrical impedance images method for reconstructing of ultrasonic reflection - Google Patents
The information constrained coeliac disease electrical impedance images method for reconstructing of ultrasonic reflection Download PDFInfo
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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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 electrical impedance tomography technical field, it is related to realizing a kind of content provided using ultrasonic reflection
Boundary information is as the total variation regularization electrical impedance tomography method constrained and for realizing human abdomen's organ inner disease foci
Exact Reconstruction.
Background technique
Electrical impedance tomography technology (EIT) is a kind of functional imaging technology, by tested field domain surface layout electricity
Pole array simultaneously applies certain current excitation and obtains boundary voltage data, is divided with this to rebuild the conductivity inside tested field domain
Cloth situation.Structure compared imaging technique such as Computed tomography (CT) and Magnetic resonance imaging (MRI), EIT skill
Art reconstructed image resolution is lower but image taking speed is greatly speeded up, and can achieve the requirement of real time imagery.As a kind of novel
Medical Imaging Technology, electrical impedance tomography have without intrusion, advantages radiationless, small in size and at low cost etc., are a kind of ideals
Real-time state of illness monitoring means.At the same time, EIT is as a kind of real-time monitoring tool, in medical image, mobile monitoring, geology
Also there is vast potential for future development in the fields such as exploration and building structure inspection.
The main reason for EIT imaging resolution is lower is that its inverse problem (rebuilds field internal conductance rate point by boundary survey value
Cloth) process have serious pathosis, it means that the small sample perturbations of boundary survey value will lead to being widely varied for solution.Together
When, the nonlinear problem that itself is imaged in electricity causes reconstruction image to have more artifact and noise.In order to overcome EIT inverse problem
Pathosis and non-linear, experts and scholars propose many image reconstruction algorithms, and regularization method therein is that one kind overcomes
The effective means of pathosis.Certain prior information is dissolved into inverse problem by way of constructing regularization penalty term by this method
Solution procedure in, the search space of constrained solution, guide majorization of solutions direction, with achieve the purpose that improve pathosis.Typically
Regularization method have M.Vauhkonen et al. 1998 in " IEEE medical imaging periodical " (IEEE Transactions
OnMedical Imaging) volume 17,285-93 pages, deliver it is entitled " Tikhonov regularization in electrical impedance imaging and
Prior information " (Tikhonov regularization andprior information in electrical
Impedancetomography the L2 regularization method mentioned in article), J.Zhao et al. are in " the world IEEE imaging system
With technical conference " (IEEE International Conference on Imaging Systems and Techniques)
The 25-30 pages entitled " sparse regularization method of small image objects in electrical resistance tomography " delivered
(Sparseregularization for small objects imagingwith
Electricalresistancetomography the L1 regularization method mentioned in article), A.Borsic et al. 2007
" inverse problem " (InverseProblems) volume 99, A12-A12 pages deliver entitled " total variance in electrical impedance imaging is just
Then change method " article of (Totalvariationregularizationin electricalimpedancetomography)
Total variation regularization (TV) method of middle proposition etc..Different regularization terms can introduce different types of prior information, such as
Be uniformly distributed information, the slickness information of Laplace prior and M.Cheney et al. of Tikhonov priori exist in nineteen ninety
" international imaging system and technical journal " (InternationalJournal ofImaging Systems&Technology)
Volume 2, the 66-75 pages deliver " a kind of NOSER: algorithm solving inverse electrical conductivity problems " (NOSER:
Analgorithmforsolvingthe inverse conductivityproblem) in propose NOSER priori it is corresponding
Non-uniform Distribution information.
Except pathosis and it is non-linear in addition to, EIT there is also field domain center susceptibility it is low and rebuild two side of content obscurity boundary
The defect in face.Due to the limitation of exciting current in the distribution character and electricity tomography of electric field, the sensitivity profile of EIT technology
It is relatively low at field domain center, effectively the content far from border electrode effectively cannot be rebuild.The shape of object is past
Toward being important information in image, boundary is the important feature of piece image, due to the soft field of electricity tomography,
Content boundary gradient is low in EIT reconstruction result, and conductivity value smooth transition can not effectively tell the profile of object.Such as
D.Liu et al. 2017 in " IEEE medical imaging transactions " (IEEE Transactions on Medical Imaging) the 9th
Volume, the article delivered " the parametrization Level Set Method for electrical impedance imaging " (the Aparametric level set of page 1
Method for electrical impedance tomography), it can establish the electrical impedance imaging algorithm based on boundary
To rebuild content boundary.However rebuild pixel value EIT image in, due to EIT low resolution object boundary often
It is relatively vague.Using the shape priors of content, structure form constrains regularization term, and being expected to can be in EIT reconstruction image
Retain obvious content boundary.
Human tissue structure is complicated, and the distribution of conductivity difference between different tissues and organ is totally different, carries out to lesion
During postoperative care or long-term detection, needs the change to focal size and shape to have and more clearly judge and understand.
In medical imaging field, the offer of shape priors is merged mostly by multi-modality imaging method to realize, such as Ali.F.M
Et al. 2010 " contemporary optics magazine " (Journal ofModern Optics) volume 57, the 273-286 pages is delivered
A kind of " Curve transform method for MR and CT image co-registration " (A curvelet transform approach for the
Fusion ofMR and CT image) in propose the CT-MRI blending algorithm based on curve wave conversion；Guo et al. 2008
" nerve calculate " (Neurocomputing) volume 72, the 203-211 page deliver " be based on multi-scale geometric analysis and profile
The multi-modality medical image of wave conversion merges " (Multimodality medical image fusion based on
Multi-scale geometric analysis of contourlettransform) in propose based on non-sampled profile
The MRI-SPECT image interfusion method of wave conversion.Equally as a kind of without intrusion, imaging radiationless, small in size and at low cost
Method, ultrasonic imaging technique are widely used in medical imaging diagnosis and postoperative care, and use environment is the same as electricity tomography
Similar, feature is close；Meanwhile ultrasound tomography technology has hard field characteristic, it is relatively sensitive to the variation of institutional framework,
Its reflect mode can shape to lesion and geometric dimension have relatively clear judgement, pass through ultrasonic reflection mode and obtain lesion
Boundary information and the reconstruction process for constraining electrical impedance imaging, the function that the structure imaging advantage and electricity of ultrasonic imaging can be imaged
Advantage can be imaged to combine, the size and conductivity variations to tested lesion are able to carry out complete and clearly characterize.Mesh
Before, ultrasound/electricity bimodal method mostly uses greatly respective mode to be imaged respectively and carries out the strategy of image co-registration, fusion results phase
To poor, the structural prior information of ultrasound cannot be made full use of.Therefore, it is necessary to a kind of lesion boundaries based on ultrasonic reflection about
Beam information more accurately instructs the reconstruction process of EIT.
Summary of the invention
For the present invention in human abdomen's lesion electrical impedance tomography image reconstruction, the anti-imaging method of traditional resistor cannot
The problem of effectively rebuilding focal size and boundary profile proposes a kind of electrical impedance chromatography based on ultrasonic reflection boundary constraint information
Image algorithm for reconstructing.
A kind of electrical impedance tomography image rebuilding method based on ultrasonic reflection boundary constraint information, including walk as follows
It is rapid:
Step 1: according to tested field domain, boundary voltage needed for obtaining image reconstruction measures difference DELTA V, specific calculating side
Formula is
Δ V=Vmea-Vref
V in formularefIndicate the reference field boundary voltage measured value obtained by simulation calculation, VmeaPresence to measure includes
Actual field boundary voltage measured value under object.
Step 2: building Jacobian matrix according to the reciprocity texture of electromagnetic field, is based on neighborhood total variation regularization method
Provide reverse temperature intensity objective function
[1] acquisition of Jacobian matrix refers to the reference field boundary voltage measured value obtained according to simulation calculation, in conjunction with
Reciprocal theorem is theoretical, meter sensitivity matrix, its calculation formula is:
In formula, SijI-th of electrode is indicated to the sensitivity coefficient of opposite j-th of electrode pair, is the of Jacobian matrix S
I row, jth column element, φi, φjRespectively indicate i-th of electrode to and j-th of electrode to being respectively I in exciting currentiAnd IjWhen
Field domain Potential Distributing,Indicate gradient operator, ∫x∫yDxdy expression integrates the length and width of pixel unit each in field domain.
[2] electrical impedance tomography reverse temperature intensity objective function is provided based on neighborhood total variation regularization method, counted
Calculate formula are as follows:
Wherein, g indicates the conductivity value of each pixel unit in reconstruction image result,Expression meets expression formula and takes
The value of g when obtaining minimum value, S indicate Jacobian matrix,Indicate that square of two norms, λ are indicating total variation regularization just
Then change parameter, LpIndicate total variation regularization matrix, by the way that positional relationship different pixels is calculated, β indicates a thing
First selected normal number, is generally chosen for 0.01, and main function is to prevent when pixel value gradient is equal to 0 that regularization term can not
Micro- situation occurs, and p indicates that p-th of pixel in field domain, reconstruction image pixel unit total number are N.
[3] electrical impedance tomography reverse temperature intensity objective function is unfolded using least square method, obtains kth time
The objective function of iterative approximation, its calculation formula is:
Wherein, gk+1Indicate the objective function of kth time iteration, gkIndicate the pixel conductivity value that kth time iteration uses, Δ gk
Indicate the pixel conductivity value variable quantity optimized needed for kth time iteration.
Step 3: lesion boundary profile point position is obtained using ultrasonic reflection mode and constructs constraint equation:
[1] it is based on ultrasonic reflection mode, ultrasonic transducer emission pulse ultrasonic records transmitting transducer and closes on ultrasound
The sound pressure signal received on energy converter changes with time, transition time and meter between record transmitting sound wave and reception sound wave
Vertical range of the boundary profile point away from probe or center probe line is calculated, calculation can be written as:
D=ctf/2
Wherein d indicates vertical range of the lesion boundary profile point away from probe or center probe line, and c indicates human abdomen's group
The bulk sound velocity knitted, tfIt indicates transmitting sound wave and receives the transition time between sound wave.It away from probe or is visited according to boundary profile point
The vertical range of the head line of centres obtains the specific coordinate of boundary profile point.
[2] it is generally believed that abdomen homogeneous organ inner disease foci is convex closed curve under two-dimentional interface, in order to quantification its
Shape Indexes, the fit object using elliptical shape as boundary profile point obtain closed boundary profile, indicate are as follows:
Wherein, x indicates the abscissa put on profile, xcFor the abscissa of fitted ellipse profile central point, y is indicated on profile
The ordinate of point, ycFor the ordinate of fitted ellipse profile central point, a is the long axis of fitted ellipse, and b is the short of fitted ellipse
Axis.
[3] constraint equation of boundary point is constructed, it is desirable that the gradient drop-out value on oval boundary is taken as biggish numerical value, other areas
The gradient drop-out value in domain is taken as lesser numerical value.Constructing constraint equation with this indicates are as follows:
H (g)=[g (pi)-α·gb,...,g(pb)-gb,…,g(po)-α-1·gb..., g (p)-g]=0
Wherein, piIndicate the pixel unit that normal vector is directed toward in pixel on fitting profile, pbIt indicates on fitting profile
Pixel unit, po indicate the pixel unit that the outer normal vector of pixel is directed toward on fitting profile, gbIndicate pixel list on fitting profile
The conductivity value of member, other pixel units uniformly indicate that conductivity value is indicated using g using p, and α is that gradient declines value,
It is chosen for 105。
Step 4: based on method of Lagrange multipliers to the electrical impedance tomography objective function under the guidance of ultrasonic constraint equation
It optimizes.
[1] Lagrangian is constructed: in each iterative process of inverse problem algorithm for reconstructing, electrical impedance tomography target
Function F (Δ gk) can indicate are as follows:
Ultrasound contour gradient constraint equation G (Δ gk) can indicate are as follows:
G(Δgk)=H (gk)+JH(gk)·Δgk=0
Wherein JH(gk) indicate in kth time iterative process, equation H (gk) single order partial differential matrix.According to Lagrange
Multiplier method constructs new LagrangianL (Δ gk, μ), it indicates are as follows:
L(Δgk, μ) and=F (Δ gk)+μG(Δgk)
Wherein, μ is Lagrange coefficient.
[2] Lagrangian solves: Lagrangian existsObtain the condition necessary condition of extreme value (minimum value)
Are as follows:
Wherein,Indicate that partial differential solves.According to above-mentioned objective function and constraint equation, above formula can be unfolded and table
It is shown as:
Wherein,
[3] new electricity imageable target equation and Optimization Solution target are constructed according to Lagrange multiplier extreme value of a function condition
Function, target equation are expressed as:
Upper formula is used into SnewΔ x=bnewIt indicates, and the equation is solved using Gaussian weighting marks, solve
In every step iteration indicate are as follows:
Δxk+1=Δ xk-(Snew TSnew+ηI)-1·Snew T·(SnewΔxk-bnew)
Wherein, k indicates the number of iterations, and I indicates regularization matrix (being substituted herein with unit matrix), and η is Gaussian weighting marks
In regularization parameter.
[4] iteration for passing through above formula gauss-newton method, obtains Δ gkWeight coefficient and to update each pixel unit
Distribution of conductivity, calculation indicate are as follows:
gk+1=gk+ξ·Δgk
Wherein, ξ is the step-length for updating pixel unit conductivity value.
Step 5: repeating step 4 until residual error is met the requirements
Wherein, Regk=| | SgkΔ V | | indicate residual values, ε is the threshold residual value being manually set.
Method proposed in the present invention can retain more complete accurate content side in electrical impedance imaging result
Boundary effectively reduces imaging artefacts while providing and including object location accurate location, size, significantly improves abdomen lesion
The reconstruction quality of EIT image reverse temperature intensity.
Mentioned algorithm is based on neighborhood total variation regularization algorithm for reconstructing, lesion profile and border that ultrasonic reflection is obtained
Point is changed into pixel gradient constraint equation, the Optimization Solution process of guide image algorithm for reconstructing objective function.Mentioned method solves
Conventional electrical imaging algorithm in carrying out human abdomen's homogeneous organ lesion Visual retrieval obscurity boundary, artifact is serious asks
Topic, significantly improves electrical impedance tomography technology to the resolution capability of different sizes, different location lesion.Extend total variance
The application of regularization algorithm for reconstructing improves the solving precision and image reconstruction quality of electrical impedance tomography inverse problem.It is mentioned
Electrical impedance images algorithm for reconstructing out based on ultrasonic reflection boundary constraint information, core concept are " by ultrasonic reflection mode
It determines lesion boundary profile point position and is converted into gradient constraint equation, construct Lagrangian and solve and rebuild conductivity point
Cloth " is wherein: obtaining lesion boundary profile point position by ultrasonic reflection mode and is fitted, realizes to lesions position, size etc.
Effective acquisition of information；Lagrangian and solved using gauss-newton method by building, efficiently solve conventional electrical at
As the image reconstruction algorithm problem unclear to lesion reconstructed results obscurity boundary, dimensional resolution.The algorithm can be in reconstructed results
It is middle to retain relatively clear and accurate content shape and structure, electrical impedance chromatography is obviously improved on the basis of guaranteeing image taking speed
Imaging precision.
Detailed description of the invention
Fig. 1 is that the electrical impedance tomography image reconstruction algorithm of the invention based on ultrasonic reflection boundary constraint information is complete
Flow chart is broadly divided into ultrasonic reflection boundary constraint acquisition of information, rebuilds reverse temperature intensity with electrical impedance under ultrasonic constraint equation
Two parts.
Fig. 2 is in the present invention for electrical impedance tomography system construction drawing used in human abdomen's lesion；
Fig. 3 is five exemplary simulation models of the invention, and corresponding neighborhood total variation regularization (TV) is set forth
Imaging results and inventive algorithm are ultimately imaged result；
Fig. 4 is the relative error and image correlation coefficient comparison for five groups of simulation model difference imaging results of the present invention.
Specific embodiment
In conjunction with the accompanying drawings and embodiments to the electrical impedance tomography figure of the invention based on ultrasonic reflection boundary constraint information
As algorithm for reconstructing is illustrated.
Electrical impedance tomography image reconstruction algorithm based on ultrasonic reflection boundary constraint information of the invention, in embodiment
For this visualization application form of human body upper abdomen homogeneous organ inner disease foci visualizing monitor.It is cut using human body upper abdomen two dimension
The direct problem model of middle tumour electrical impedance tomography, passes through ultrasonic reflection mould in face structure priori building characterization liver, kidney
State determines the boundary profile location information of lesion and is converted into constraint equation.The iterative solution process of image reconstruction inverse problem can be with
It is decomposed into the Lagrangian building based on neighborhood total variation regularization method and solves pixel unit using gauss-newton method
Ultrasonic constraint equation and electricity optimization object function are unified in by the building of conductivity iterative value two parts, Lagrangian
Under one solution frame, the iterative solution of gauss-newton method can quickly provide conductivity under conditions of meeting constraint equation
The numerical solution of iterative value, and the distribution of conductivity to update pixel unit and Lagrangian.
As shown in Figure 1, being the electrical impedance tomography image reconstruction of the invention based on ultrasonic reflection boundary constraint information
Algorithm.Algorithm is broadly divided into the acquisition of boundary survey value, the building of reciprocal theorem meter sensitivity, ultrasonic reflection constraint equation, glug
Bright day function building, gauss-newton method iterative calculation conductivity iterative value simultaneously update five parts of Lagrangian.Fig. 2 is it
For the basic signal of the electrical impedance tomography test mode of human abdomen's inner disease foci.
The imaging results of the anti-image algorithm for reconstructing of traditional resistor and the imaging of this algorithm are set forth in Fig. 3, Fig. 4
As a result with reconstruction index comparison, rebuilding index includes two kinds of relative error (RE) and image correlation coefficient (CC), calculation method
It can indicate are as follows:
Wherein, σ indicates the pixel unit distribution of conductivity rebuild, σ*Indicate the distribution of conductivity under truth, σjWith
σj *Indicate distribution of conductivity that j-th of pixel unit is rebuild and true,WithConductivity point that expression is rebuild and true
The average value of cloth.
This algorithm embodiment comprises the following specific steps that:
(1) for the content distribution situation of model 1- model 4 in Fig. 4, the boundary electricity needed for respectively rebuilding is obtained respectively
Measurement data is pressed, according to tested field domain, boundary voltage needed for obtaining image reconstruction measures difference DELTA V, and specific calculation is
Δ V=Vmea-Vref
V in formularefIndicate the reference field boundary voltage measured value obtained by simulation calculation, VmeaPresence to measure includes
Actual field boundary voltage measured value under object, as shown in Fig. 2, totally 32 electrodes participate in measurement and rebuild, according to " adjacent current swashs
Encourage, neighboring voltage measurement " excitation acquisition strategies, Vmea、VrefIt include 928 groups of voltage measurement datas.
(2) Jacobian matrix is built according to the reciprocity texture of electromagnetic field, is provided based on neighborhood total variation regularization method
Reverse temperature intensity objective function
The acquisition of a.Jacobian matrix refers to the reference field boundary voltage measured value obtained according to simulation calculation, in conjunction with
Reciprocal theorem is theoretical, meter sensitivity matrix, its calculation formula is:
In formula, SijI-th of electrode is indicated to the sensitivity coefficient of opposite j-th of electrode pair, is the of Jacobian matrix S
I row, jth column element, φi, φjRespectively indicate i-th of electrode to and j-th of electrode to being respectively I in exciting currentiAnd IjWhen
Field domain Potential Distributing,Indicate gradient operator, ∫x∫yDxdy expression integrates the length and width of pixel unit each in field domain.
B. electrical impedance tomography reverse temperature intensity objective function is provided based on neighborhood total variation regularization method, calculated
Formula are as follows:
Wherein, g indicates the conductivity value of each pixel unit in reconstruction image result,Expression meets expression formula and takes
The value of g when obtaining minimum value, S indicate Jacobian matrix,Indicate that square of two norms, λ are indicating total variation regularization just
Then change parameter, choosing empirical value is 3 × 10-4, LpTotal variation regularization matrix is indicated, by between positional relationship meter different pixels
It obtains, β indicates a normal number selected in advance, is chosen for 0.01 here, main function is to prevent from working as pixel value gradient
The case where regularization term non-differentiability, occurs when equal to 0, and p indicates that p-th of pixel in field domain, reconstruction image pixel unit total number are
N。
C. electrical impedance tomography reverse temperature intensity objective function is unfolded using least square method, obtains kth time
The objective function of iterative approximation, its calculation formula is:
Wherein, gk+1Indicate the objective function of kth time iteration, gkIndicate the pixel conductivity value that kth time iteration uses, Δ gk
Indicate the pixel conductivity value variable quantity optimized needed for kth time iteration.
(3) lesion boundary profile point position is obtained using ultrasonic reflection mode and construct constraint equation:
A. it is based on ultrasonic reflection mode, ultrasonic transducer emission pulse ultrasonic records transmitting transducer and closes on ultrasound
The sound pressure signal received on energy converter changes with time, transition time and meter between record transmitting sound wave and reception sound wave
Vertical range of the boundary profile point away from probe or center probe line is calculated, calculation indicates are as follows:
D=ctf/2
Wherein d indicates vertical range of the lesion boundary profile point away from probe or center probe line, and c indicates human abdomen's group
The bulk sound velocity knitted, tfIt indicates transmitting sound wave and receives the transition time between sound wave.It away from probe or is visited according to boundary profile point
The vertical range of the head line of centres obtains the specific coordinate of boundary profile point.
B. it is generally believed that abdomen organ inner disease foci is convex closed curve under two-dimentional interface in heterogeneity, for quantification
Its Shape Indexes, the fit object using elliptical shape as boundary profile point obtain closed boundary profile, indicate are as follows:
Wherein, x indicates the abscissa put on profile, xcFor the abscissa of fitted ellipse profile central point, y is indicated on profile
The ordinate of point, ycFor the ordinate of fitted ellipse profile central point, a is the long axis of fitted ellipse, and b is the short of fitted ellipse
Axis.
C. the constraint equation of boundary point is constructed, it is desirable that the gradient drop-out value on oval boundary is taken as biggish numerical value, other areas
The gradient drop-out value in domain is taken as lesser numerical value.Constructing constraint equation with this indicates are as follows:
H (g)=[g (pi)-α·gb,...,g(pb)-gb,…,g(po)-α-1·gb..., g (p)-g]=0
Wherein, piIndicate the pixel unit that normal vector is directed toward in pixel on fitting profile, pbIt indicates on fitting profile
Pixel unit, po indicate the pixel unit that the outer normal vector of pixel is directed toward on fitting profile, gbIndicate pixel list on fitting profile
The conductivity value of member, other pixel units uniformly indicate that conductivity value is indicated using g using p, and α is that gradient declines value,
It is chosen for 105。
(4) based on method of Lagrange multipliers to ultrasonic constraint equation guidance under electrical impedance tomography objective function into
Row Optimization Solution.
A. Lagrangian is constructed: in each iterative process of inverse problem algorithm for reconstructing, electrical impedance tomography target
Function F (Δ gk) can indicate are as follows:
Ultrasound contour gradient constraint equation G (Δ gk) can indicate are as follows:
G(Δgk)=H (gk)+JH(gk)·Δgk=0
Wherein JH(gk) indicate in kth time iterative process, equation H (gk) single order partial differential matrix.According to Lagrange
Multiplier method constructs new LagrangianL (Δ gk, μ), it indicates are as follows:
L(Δgk, μ) and=F (Δ gk)+μG(Δgk)
Wherein, μ is Lagrange coefficient, and experience value is 5 × 10-4。
B. Lagrangian solves: Lagrangian existsObtain the condition necessary condition of extreme value (minimum value)
Are as follows:
Wherein,Indicate that partial differential solves.According to above-mentioned objective function and constraint equation, above formula can be unfolded and table
It is shown as:
Wherein,
C. new electricity imageable target equation and Optimization Solution target are constructed according to Lagrange multiplier extreme value of a function condition
Function, target equation are expressed as:
Upper formula is used into SnewΔ x=bnewIt indicates, and the equation is solved using Gaussian weighting marks, solve
In every step iteration indicate are as follows:
Δxk+1=Δ xk-(Snew TSnew+ηI)-1·Snew T·(SnewΔxk-bnew)
Wherein, k indicates the number of iterations, and I indicates regularization matrix (being substituted herein with unit matrix), and η is Gaussian weighting marks
In regularization parameter, experience value be 3 × 10-4。
D. the iteration for passing through above formula gauss-newton method, obtains Δ gkWeight coefficient and the electricity to update each pixel unit
Conductance distribution, calculation can be written as:
gk+1=gk+ξ·Δgk
Wherein, ξ is the step-length for updating pixel unit conductivity value, and experience value is 2.5 × 10-2。
(5) is updated Lagrangian and is solved using Gaussian weighting marks method, is repeated the above steps until residual error meets
It is required that:
Wherein, Regk=| | SgkΔ V | | indicate residual values, ε be artificial settings threshold residual value, experience value 1 ×
10-4。
Method proposed in the present invention can retain more complete accurate content side in electrical impedance imaging result
Boundary effectively reduces imaging artefacts while providing and including object location accurate location, lesion, significantly improves abdomen lesion
The reconstruction quality of EIT image reverse temperature intensity.Lesion boundary profile point position is obtained by ultrasonic reflection mode and is fitted, and is realized
Effective acquisition to information such as lesions position, sizes；It is solved by building Lagrangian and using gauss-newton method, is had
Effect solves the problems, such as that conventional electrical image algorithm for reconstructing is unclear to lesion reconstructed results obscurity boundary, dimensional resolution.It should
Algorithm can retain relatively clear and accurate content shape and structure in reconstructed results, on the basis of guaranteeing image taking speed
It is obviously improved electrical impedance tomography precision.
Embodiment described above is several example models of the invention, and it is public that the present invention is not limited to embodiment and attached drawing institute
The content opened.It is all not depart from the lower equivalent or modification completed of spirit disclosed in this invention, all in the scope of protection of the invention.
Claims (2)
1. a kind of coeliac disease electrical impedance images method for reconstructing that ultrasonic reflection is information constrained is suitable for electrical impedance tomography figure
As rebuilding, lesion boundary profile point position is determined by ultrasonic reflection mode and is converted into gradient constraint equation, construction glug is bright
Day function simultaneously solves reconstruction distribution of conductivity, and steps are as follows
Step 1: according to tested field domain, boundary voltage needed for obtaining image reconstruction measures difference DELTA V:
Δ V=Vmea-Vref
V in formularefIndicate the reference field boundary voltage measured value obtained by simulation calculation, VmeaFor measure there are under content
Actual field boundary voltage measured value.
Step 2: Jacobian matrix is built according to the reciprocity texture of electromagnetic field, is provided based on neighborhood total variation regularization method
Reverse temperature intensity objective function, method are as follows
[1] acquisition of Jacobian matrix refers to the reference field boundary voltage measured value obtained according to simulation calculation, in conjunction with reciprocity
Theorem is theoretical, meter sensitivity matrix；
[2] electrical impedance tomography reverse temperature intensity objective function is provided based on neighborhood total variation regularization method, calculated public
Formula are as follows:
Wherein, g indicates the conductivity value of each pixel unit in reconstruction image result,Expression meets expression formula and obtains most
The value of g when small value, S indicate Jacobian matrix,Indicate that square of two norms, λ indicate the regularization of total variation regularization
Parameter, LpIndicate total variation regularization matrix, by the way that positional relationship different pixels is calculated, β indicates a choosing in advance
Fixed normal number is generally chosen for 0.01, and main function prevents the regularization term non-differentiability when pixel value gradient is equal to 0
Situation occurs, and p indicates that p-th of pixel in field domain, reconstruction image pixel unit total number are N；
[3] electrical impedance tomography reverse temperature intensity objective function is unfolded using least square method, obtains kth time iteration
The objective function of reconstruction, its calculation formula is:
Wherein, gk+1Indicate the objective function of kth time iteration, gkIndicate the pixel conductivity value that kth time iteration uses, Δ gkIt indicates
The pixel conductivity value variable quantity optimized needed for kth time iteration；
Step 3: lesion boundary profile point position is obtained using ultrasonic reflection mode and constructs constraint equation:
[1] it is based on ultrasonic reflection mode, ultrasonic transducer emission pulse ultrasonic records transmitting transducer and closes on ultrasonic transduction
The sound pressure signal received on device changes with time, and the transition time between record transmitting sound wave and reception sound wave simultaneously calculates side
Vertical range of boundary's profile point away from probe or center probe line:
D=ctf/2
Wherein d indicates vertical range of the lesion boundary profile point away from probe or center probe line, and c indicates human abdomen's soft tissue
Bulk sound velocity, tfIt indicates transmitting sound wave and receives the transition time between sound wave, according to boundary profile point away from probe or probe
The vertical range of the line of centres obtains the specific coordinate of boundary profile point；
[2] abdomen mean value organ inner disease foci is considered as under two-dimentional interface convex closed curve, is its Shape Indexes of quantification, uses
Fit object of the elliptical shape as boundary profile point, obtains closed boundary profile；
[3] constraint equation of boundary point is constructed, it is desirable that the gradient drop-out value on oval boundary is taken as biggish numerical value, other regions
Gradient drop-out value is taken as lesser numerical value；Constructing constraint equation with this indicates are as follows:
H (g)=[g (pi)-α·gb,...,g(pb)-gb,…,g(po)-α-1·gb..., g (p)-g]=0
Wherein, piIndicate the pixel unit that normal vector is directed toward in pixel on fitting profile, pbIndicate the pixel on fitting profile
Unit, poIndicate the pixel unit that the outer normal vector of pixel is directed toward on fitting profile, gbIndicate the electricity of pixel unit on fitting profile
Conductivity value, other pixel units uniformly indicate that conductivity value is indicated using g using p, and α is that gradient declines value, are chosen for
105；
Step 4: the electrical impedance tomography objective function under the guidance of ultrasonic constraint equation is carried out based on method of Lagrange multipliers
Optimization Solution；
[1] Lagrangian is constructed: in each iterative process of inverse problem algorithm for reconstructing, electrical impedance tomography objective function
F(Δgk) indicate are as follows:
Ultrasound contour gradient constraint equation G (Δ gk) indicate are as follows:
G(Δgk)=H (gk)+JH(gk)·Δgk=0
Wherein JH(gk) indicate in kth time iterative process, equation H (gk) single order partial differential matrix；According to Lagrange multiplier
Method constructs new LagrangianL (Δ gk, μ):
L(Δgk, μ) and=F (Δ gk)+μG(Δgk)
Wherein, μ is Lagrange coefficient；
[2] Lagrangian solves: new electricity imageable target equation is constructed according to Lagrange multiplier extreme value of a function condition
And Optimization Solution objective function, target equation are expressed as:
Wherein,
It indicates that partial differential solves, S will be usednewΔ x=bnewIt indicates target equation, and the equation is carried out using Gaussian weighting marks
It solves, every step iteration indicates in solution are as follows:
Δxk+1=Δ xk-(Snew TSnew+ηI)-1·Snew T·(SnewΔxk-bnew)
Wherein,Indicate the coefficient matrix of target equation,Indicate mesh
Non trivial solution is marked,Indicate the dependent variable of target equation；K indicates the number of iterations, I table
Show regularization matrix (being substituted herein with unit matrix), η is the regularization parameter in Gaussian weighting marks；
[4] iteration for passing through above formula gauss-newton method, obtains Δ gkWeight coefficient and the conductivity to update each pixel unit
Distribution, calculation are as follows:
gk+1=gk+ξ·Δgk
Wherein, ξ is the step-length for updating pixel unit conductivity value；
Step 5: repeating step 4 until residual error is met the requirements
Wherein, Regk=| | SgkΔ V | | indicate residual values, ε is the threshold residual value being manually set.
2. ultrasonic procedure tomographic reconstruction method according to claim 1, it is characterised in that: boundary in the step 1
The acquisition of measured value refers to and places a certain number of square-shaped electrodes on human abdomen's two-dimensional section surface, is swashed based on adjacent current
It encourages, the measurement pattern of neighboring voltage measurement, the measurement strategies received entirely using cycle motivation, a hair, boundary needed for image reconstruction
Voltage measurement difference DELTA V be the reference field boundary voltage measured value obtained by simulation calculation and measure there are under content
Difference between actual field boundary voltage measured value.
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