Summary of the invention
The purpose of the present invention is being directed to the image reconstruction problem of electricity tomography, a kind of V- based on deep learning is proposedNet Depth Imaging method, in network model training process not only can efficient self study with from extracting useful feature, but alsoThe calculating for avoiding sensitivity matrix time-consuming in traditional Class of Iterative algorithm based on sensitivity, it is quick to can solve industrial processVisual demand.Technical scheme is as follows:
A kind of V-Net Depth Imaging method is named as V-Net depth network structure using one kind, is a kind of 33 layers of netNetwork structure, the functional module being linked in sequence by three form, i.e., initial image-forming module, depth characteristic analysis and extraction module and depthImage-forming module is spent, the connection between network layer uses full connection, part connection, residual error connection and jump four kinds of connection sides of connectionFormula, the intersection entropy loss item and L that loss function is exported in network2Layer 5 output is added on the basis of regularization constraint itemIntersect entropy loss item, realizes the convergence process for accelerating network while initial imaging；V-Net depth network structure is in information processingThe spatial positional information of dielectric distribution is remained by the addition of pixel and shearing in the process, steps are as follows:
First step establishes the M group data for trained and test depth network, includes two sequences in every group of dataWherein, V is the electricity tomography boundary survey sequence for characterizing dielectric distribution projection,For quiltSurvey the true distribution series of medium inside region；
Second step designs the structure of V-Net depth network, and specific design scheme is as follows:
(1) input layer: input layer is electricity tomography boundary survey sequence V in V-Net Depth Imaging network structure, defeatedEntering layer matrix is 3 dimension matrixes, wherein the length of input layer matrix and the wide length and width for being equal to measurement sequence V, the 3rd dimension of input matrixIndicate that the characteristic pattern number of electricity tomography boundary survey sequence V, the characteristic pattern number being originally inputted are 1；
(2) connection by the way of connecting entirely between 5 layer network layers before, and neuron number is followed successively by fully connected network network layers812,406,250,406 and 812, the characteristic pattern number of fully connected network network layers output is 1；
First 5 layers of full articulamentum will characterize pipeline in electricity chromatographic imaging system in V-Net depth network training processThe boundary survey data Nonlinear Mapping of cross section information is the two-dimensional image vegetarian refreshments of cross-sectional image, realizes initial imaging, considers simultaneouslyThe pixel of image is increased to 1024 by addition pixel by the spatial positional information of dielectric distribution, is convenient for Depth Imaging network designThe extension of network structure in the process；
(3) the 6-19 layer depth structure of V-Net depth network structure gradually extends, and is mainly made of 5 convolution blocks, pointNot Wei 6-7 layers, 9-10 layers, 12-13 layers, 15-16 layers, 18-19 layers, containing there are two identical rulers in each convolution blockSpend the convolutional layer of 3 × 3 convolution kernels；It is connected between different convolution blocks by maximum pond layer, completes down-sampling, pond step-length is 2× 2, the local maxima information in maximum pondization operation keeping characteristics space ignores other features, uses maximum 4 layers of layer of pond altogether,Respectively the 8th layer, 11th layer, the 14th layer, the 17th layer；Based on convolution technique by the feature of 1 initial width low level during thisFigure, has gradually extracted the characteristic pattern of 1024 panel height levels, while analyzing the size of dielectric distribution in boundary survey and field domainWith position feature information, i.e. the analysis and extraction of features process of reconstruction image；
(4) Stepwize Shrink of the 20-33 layer depth network structure of V-Net depth network structure, mainly by 4 convolution blocksIt constitutes, respectively 21-22 layers, 24-25 layers, 27-28 layers, 30-31 layers, containing there are two identical rulers in each convolution blockSpend the convolutional layer of 3 × 3 convolution kernels；It is realized from de-convolution operation to up-sampling between different convolution blocks, uses warp lamination 4 altogetherLayer, respectively the 20th layer, the 23rd layer, the 26th layer, the 29th layer；The convolution kernel of 32nd layer of use 1 × 1 realizes the drop of Depth ImagingDimension；It is based on convolution technique during this, the number of network characterization figure gradually decreases, the recovery of simultaneous image pixelJourney, i.e. Depth Imaging process；
(5) residual error connects: using residual error in network between the 5th layer and the 32nd layer and connects, so that depth network is in forward directionThe property of communication process operation becomes addition of matrices by matrix multiplication；In back-propagation process, no matter network travels to whichLayer, the high-rise biggish ingredient of gradient components, that is, gradient can be directly transmitted through；
(6) jump connection: the 7th layer and the 29th layer in network, the 10th layer and the 26th layer, the 13rd layer and the 23rd layer, the 16th layerWith the 20th layer between using jump connection, jump connection keeping characteristics extraction process is ignored due to being operated using maximum pondizationLocal message, the information bank of complete depth image reconstruction process, so that the image rebuild is more accurate；
The design of third step loss function is as follows:
It is constituted shown in V-Net Depth Imaging network losses function such as formula (1) by three, respectively the 5th layer of output electricity of networkThe intersection entropy loss L of conductance distributionout5(w), network output is the intersection entropy loss L of the 33rd layer of distribution of conductivityout33(w) andL2Regularization term, a, b, c are respectively Lout5(w)、Lout33(w)、L2Weight coefficient:
L (w)=a*Lout5(w)+b*Lout33(w)+c*L2(w) (1)
Wherein, intersect loss item Lout5(w) and Lout33(w) it is calculated using formula (2), σjiIt is defeated for jth layer network layerThe predicted value of dielectric distribution out；
When 4th step carries out electricity tomographic image reconstruction, the boundary survey sequence conduct of electricity chromatographic imaging systemThe input of trained V-Net network model, the output of V-Net network are the specific distribution of medium in tested object field.
Novel V-Net Depth Imaging method proposed by the present invention, the self study boundary survey information in a manner of supervised trainingNonlinear Mapping relationship between distribution with medium in field domain.Using full connection, part between V-Net Depth Imaging network layerConnection, residual error connection and jump four kinds of connection types of connection constitute sequential connection it is initial be imaged, feature extraction and depth atAs three functional blocks.In addition, considering the spatial positional information of dielectric distribution in V-Net Depth Imaging network structure.Advantage is such asUnder:
1) novelty of the V-Net Depth Imaging algorithm in structure be using full connection, part connection, residual error connection withFour kinds of connection types of jumping constitute the functional block of three sequential connections of initial imaging, feature extraction and Depth Imaging, realizeNonlinear Mapping between boundary survey and tested object field dielectric distribution, improves the reconstruction precision of image.
2) V-Net Depth Imaging algorithm can effectively derive from study in the training process and extract different characteristic space certainlyCharacteristics of image, the algorithm have certain anti-noise ability and model generalization ability.
3) V-Net Depth Imaging algorithm does not need to solve time-consuming sensitivity matrix, can be fast according to trained modelSpeed solves the dielectric distribution of tested region.
Specific embodiment
V-Net Depth Imaging method is by taking electrical resistance tomography (ERT) as an example, for solving the problems, such as the image reconstruction of ERT.It shouldMethod can not only be empty in different features compared with tradition is based on the regularization class image reconstruction algorithm method of sensitivity matrixBetween middle self study with from extracting useful feature, and do not need to solve time-consuming sensitivity matrix, as long as the boundary of ERT is surveyedSequence inputting is measured into trained V-Net network model, so that it may quick, accurate to rebuild medium in ERT field domainTrue distribution, the algorithm for reconstructing have good model generalization ability and noiseproof feature.
The functional module that 33 layers of V-Net Depth Imaging network structure of shape approximation V-type are linked in sequence by three forms, i.e.,Initial image-forming module, depth characteristic analysis and extraction module and Depth Imaging module.Connection in network structure between network layerUsing full connection, part connection, residual error connection and jump four kinds of connection types of connection.The loss function of V-Net network is in netThe intersection entropy loss item and L of network output2The intersection entropy loss item of layer 5 output is added on the basis of regularization constraint item, it is realNow accelerate the convergence process of network while initial imaging.In addition, V-Net depth network structure passes through in information processThe addition and shearing of pixel remain the spatial positional information of dielectric distribution.Above-mentioned network structure feature enables Depth Imaging algorithmEnough solve the problems, such as the image reconstruction from data to image.
Steps are as follows for the realization of V-Net Depth Imaging algorithm:
It include two sequences in every group of data 1. establishing the M group data for trained and test depth networkWherein, V is the boundary survey sequence for characterizing dielectric distribution projection,Inside tested regionThe true distribution series of medium.
2. designing the structure of V-Net Depth Imaging network, specific design scheme is as follows:
(1) input layer: input layer is electricity tomography boundary survey sequence V in V-Net Depth Imaging network structure, defeatedEntering layer matrix is 3 dimension matrixes, wherein the length of input layer matrix and the wide length and width for being equal to measurement sequence V, the 3rd dimension of input matrixIndicate that the characteristic pattern number of measurement sequence V, the characteristic pattern number being originally inputted are 1.
(2) connection by the way of connecting entirely between 5 layer network layers before, and neuron number is followed successively by fully connected network network layers812,406,250,406 and 812, the characteristic pattern number of fully connected network network layers output is 1.
First 5 layers of full articulamentum will characterize pipeline in electricity chromatographic imaging system in V-Net depth network training processThe boundary survey data Nonlinear Mapping of cross section information is the two-dimensional image vegetarian refreshments of cross-sectional image, realizes initial imaging, considers simultaneouslyThe pixel of image is increased to 1024 (32 × 32) by addition pixel by the spatial positional information of dielectric distribution, is convenient for Depth ImagingThe extension of network structure in network design process.
(3) the 6-19 layer depth structure of V-Net depth network structure gradually extends, and is mainly made of 5 convolution blocks, pointNot Wei 6-7 layers, 9-10 layers, 12-13 layers, 15-16 layers, 18-19 layers, containing there are two identical rulers in each convolution blockSpend the convolutional layer of 3 × 3 convolution kernels；It is connected between different convolution blocks by maximum pond layer, completes down-sampling, pond step-length is 2× 2, the local maxima information in maximum pondization operation keeping characteristics space has ignored other features, altogether using maximum pond layer 4Layer, respectively the 8th layer, 11th layer, the 14th layer, the 17th layer；Based on convolution technique by the spy of 1 initial width low level during thisSign figure, gradually extracted the characteristic pattern of 1024 panel height levels, at the same analyze boundary survey in field domain dielectric distribution it is bigSmall and position feature information, i.e. the analysis and extraction of features process of reconstruction image.
(4) Stepwize Shrink of the 20-33 layer depth network structure of V-Net depth network structure, mainly by 4 convolution blocksIt constitutes, respectively 21-22 layers, 24-25 layers, 27-28 layers, 30-31 layers, containing there are two identical rulers in each convolution blockSpend the convolutional layer of 3 × 3 convolution kernels；It is realized from de-convolution operation to up-sampling between different convolution blocks, uses warp lamination 4 altogetherLayer, respectively the 20th layer, the 23rd layer, the 26th layer, the 29th layer；The convolution kernel of 32nd layer of use 1 × 1 realizes the drop of Depth ImagingDimension；It is based on convolution technique during this, the number of network characterization figure gradually decreases, the recovery of simultaneous image pixelJourney, i.e. Depth Imaging process.
(5) residual error connects: using residual error in network between the 5th layer and the 32nd layer and connects, so that depth network is in forward directionThe property of communication process operation becomes addition of matrices by matrix multiplication, and calculating becomes simpler.In back-propagation process, netWhich layer no matter network travel to, and the high-rise biggish ingredient of gradient components, that is, gradient can be directly transmitted through.Such propagationMode, which makes the gradient of the depth network in back-propagation process decay, to be further inhibited, and the performance of network is more stable.
(6) jump connection: the 7th layer and the 29th layer in network, the 10th layer and the 26th layer, the 13rd layer and the 23rd layer, the 16th layerWith the 20th layer between using jump connection.Jump connection remains characteristic extraction procedure due to ignoring using maximum pondization operationLocal message, the complete information bank of depth image reconstruction process, so that the image rebuild is more accurate.
The design of the loss function of 3.V-Net Depth Imaging network is as follows:
It is constituted shown in V-Net Depth Imaging network losses function such as formula (1) by three, respectively the 5th layer of output electricity of networkThe intersection entropy loss L of conductance distributionout5(w), network output is the intersection entropy loss L of the 33rd layer of distribution of conductivityout33(w) andL2Regularization term.A, b, c are respectively Lout5(w)、Lout33(w)、L2Weight coefficient.
L (w)=a*Lout5(w)+b*Lout33(w)+c*L2(w) (1)
Wherein, intersect loss item Lout5(w) and Lout33(w) it is calculated using formula (2).True point of mediumCloth, σjiFor the predicted value of the dielectric distribution of jth layer network layer output.
4. be used for electricity tomographic image reconstruction using V-Net Depth Imaging algorithm, electricity chromatographic imaging systemInput of the boundary survey sequence as trained V-Net network model, the output of V-Net network are to be situated between in tested object fieldThe specific distribution of matter.
It is described in detail below to manufacture and operate step of the invention, it is intended to be described as the embodiment of the present invention, be notThe unique forms that can be manufactured or be utilized can realize that the embodiment of identical function should also be included in the scope of the present invention to otherIt is interior.
Below with reference to specification annex, the preferred embodiments of the present invention are described in detail.
(1) 40000 group data sets are constructed using 16 electrode ERT simulation model of adjacent current excitation-voltage measurement, be used forTraining and measurement V-Net Depth Imaging model, wherein including a boundary survey voltage value sequence of ERT system in each group of dataTrue distribution of conductivity sequence in column and a field domain.Include different size, different numbers, the bubble of different location in data setDistribution.
(2) 40000 training set datas are divided into 5 equal portions, will wherein 4 equal portions totally 36000 pairs of data as training setTraining V-Net network, remaining 1 part generalization ability of totally 4000 pairs of data as test set test model, successively alternately.I.e.5 models have been respectively trained in 5 different data sets using 5 times of cross validation methods shown in Fig. 2, have been carried out simultaneouslyThe test of model.Select one of data set as the input of network, training process is as follows:
(a) V-Net depth network structure proposed by the present invention is constructed for the simulation data base of ERT.The network structure is totalThere are 33 layers, as shown in figure 1 each layer of each rectangle expression network, wherein input of the ERT boundary survey contact potential series as network,It is the number that ERT measure contact potential series that the number of input layer, which is 208, the digital representation layer right above each rectangleNetwork exports the number of characteristic pattern, and the ERT contact potential series characteristic pattern number of network inputs is 1；First 5 layers are full articulamentum, eachThe number of neuron in the digital representation of the rectangle lower left layer network is respectively 812 from the 1st layer to the 5th layer, 406,250,406 and 812, the number of characteristic pattern is all 1 in fully connected network network layers；Totally 27 layers of the locally-attached network layer of V-Net network, whereinComprising 9 convolution blocks, each convolution block includes the convolutional layer that two layers of convolution kernel is 3 × 3, amounts to 18 layers of convolutional layer；Feature extraction5 convolution blocks are used in the process, and the characteristic pattern number that a convolutional layer is connected in each convolution block is equal, according to the sequence of network layerThe characteristic pattern number of convolutional layer is followed successively by 64,128,256,512,1024 in different convolution blocks, uses pond between each convolution blockChange the maximum pond layer that region is 2 × 2 to connect, use 4 layers of maximum pond layer altogether, characteristic pattern number is followed successively by 64,128,256,512；Depth Imaging process uses 4 convolution blocks, according to the feature of convolutional layer in the sequence difference convolution block of network layerFigure number is followed successively by 512,256,128,64, uses warp lamination between each convolution block, uses 4 layers of warp lamination altogether,The number of characteristic pattern is followed successively by 512,256,128,64；32nd layer uses convolution kernel for 1 × 1 convolutional layer, by depth reconstructionImage number is reduced to 1 by 64, and the last layer is the output layer of whole network.The activation primitive of every layer network is repaired using unsaturationLinear positive function Relu.
(b) parameters in network are initialized:
The weight w of each layer of networkm0: random number (mean value 0, variance 0.01)；Deviation bm0: 0.1；
Initial learning rate: η0=0.01；Learning rate attenuation rate: ρ=0.99；Lot number: batch=100；
Every coefficient in loss function: a=1, b=1, c=0.0001；Momentum: γ=0.99；
Total the number of iterations: steps=60000；
(b) input of the ERT boundary survey contact potential series as network, input matrix are 100 × 208 × 1, input streamInitial conductivity, which is rebuild, through 5 layers of realization before V-Net feedforward network is distributed σ5i, initial conductivity be distributed σ5iInformation passes through V-Net netThe self study that 6-19 layer of network with from after excavating imaging depth feature, finally 20-33 layers of completion depth of V-Net network atAs process reconstructs more accurate ERT field domain internal conductance rate distribution σ in the output end of network33i.Calculate separately network the 5th, 33The intersection entropy loss L of layer output conductance rate distributionout5(w) and Lout33(w)。
(c) loss function of V-Net network is calculated
L (w)=a*Lout 5(w)+b*Lout 33(w)+c*L2(w) (2)
(d) loss function is calculated to the gradient of each parameter using chain type Rule for derivation in network backpropagation, in conjunction withLearning rate updates the weight w of each layer network using small lot momentum stochastic gradient descent methodmWith deviation bm, renewal equation is such asFormula (3).
Wherein learning rate η updates in the way of exponential damping in formula (4):
η=η0*ρsteps/batch (4)
(e) step (a)~(c) is repeated, the number of iterations of network training is equal to steps, and model training stops, and saves mouldType.
(3) trained 5 models are tested in respective measurement concentration respectively, and is calculated according to formula (5)-(6)Corresponding image error and related coefficient out select image error minimum, and the maximum model of related coefficient is as V-Net networkFinal mask.
WhereinFor true conductivityAverage value,For neural network forecast conductivityσiAverage value.
(4) using the experiment boundary survey contact potential series of different distributions as the network inputs of (3) step preference pattern, networkOutput be field domain internal conductance rate true distribution.
Emulation experiment is carried out to verify validity and the noise immunity of inventive algorithm.During emulation experiment in test setThe random noise of 20-60dB is added respectively, and the simulation imaging result of different medium distribution is as shown in figure 3, first is classified as true pointCloth, second is classified as the imaging results for not adding noise, and third arranges the imaging results being sequentially increased to the 4th column noise.It can by Fig. 3Know, V-Net Depth Imaging algorithm can be used to solve the problems, such as the image reconstruction of ERT, while the algorithm has certain noise immunity.
Shown in Fig. 4, is tested for different medium distributed model and V-Net Depth Imaging algorithm is verified.Due toThe conductivity of PVC material and the conductivity of water choose various sizes of PVC stick simulating in experiment and are tested area there are biggish differenceThe measured medium of different distributions in domain, tap water is as the background media in tested region.The PVC of two scales is chosen in experimentStick, diameter are respectively 21.4mm and 30.0mm, and the pipe diameter of tested region is 125mm.There are biggish in experimentationSystem noise and random noise, this experiment not only demonstrate feasibility of the V-Net Depth Imaging algorithm in tomographic processWith applicability, while the noiseproof feature of the algorithm and the generalization ability of model are demonstrated.
(a) is the experiment scene for single isolated bubbles in pipeline in Fig. 4, quick and precisely using V-Net Depth Imaging algorithmThe distribution of conductivity figure reconstructed.The image error and related coefficient of the imaging results are respectively 4%, 99%.
(b) is the experiment scene for two bubbles of different sizes in pipeline in Fig. 4, using V-Net Depth Imaging algorithmThe distribution of conductivity figure quick and precisely reconstructed.
(c) is the experiment scene for three bubbles of different sizes in pipeline in Fig. 4, using V-Net Depth Imaging algorithmThe distribution of conductivity figure quick and precisely reconstructed.