CN109993050B - Synthetic aperture radar image identification method - Google Patents

Abstract

The invention discloses a synthetic aperture radar image recognition method, aiming to solve the problem of inaccurate recognition in the current SAR image recognition method. The technical solution is based on the convolutional neural network, and the weight of the convolution kernel is introduced into the convolutional layer. Firstly, the neural network model is constructed according to the SAR image, and the SAR image is propagated forward through the network to obtain the probability prediction value; the probability prediction value is matched and compared with the category label of the image to obtain the target loss function; The parameters in the network model are adjusted. Finally, the SAR image to be recognized is recognized through the trained network, and the recognition result is obtained. Adopting the present invention can avoid the dependence of the recognition process on expert experience, and avoid the subjectivity and arbitrariness of recognition; and the present invention introduces the weight of the convolution kernel in the convolution layer of the convolutional neural network, and the convolution The weight of the kernel is adaptively adjusted, which further improves the accuracy of target classification and recognition.

Description

A Synthetic Aperture Radar Image Recognition Method

technical field

The invention belongs to the field of image processing, and relates to a Synthetic Aperture Radar (SAR) image recognition method, especially a SAR image recognition method based on a deep learning framework. The method can also be extended and applied to automatic classification and recognition of other types of images.

Background technique

Synthetic Aperture Radar (SAR) has the characteristics of high resolution, long distance, all-weather, all-weather, etc. Compared with traditional radar, this new system expands the dimensionality of radar imaging and can provide two-dimensional scattering information of targets. It has a wide range of applications in many fields such as battlefield surveillance, weapon guidance, and terrain mapping. Traditional SAR image recognition is mainly realized by feature extraction and pattern classification methods based on artificial experience, such as literature 1: Qun Zhao, Jose C.Principe, "Support vector machines for SAR automatic target recognition", IEEETransactions on Aerospace and Electronic Systems , 2001, 37(2): 643-655 ("Support Vector Machines for SAR Automatic Target Recognition" published by Qun Zhao et al. in IEEE Aerospace and Electronic Systems Bulletin No. 37 in 2001) A support vector machine (Support Vector Machine, SVM) is proposed for object recognition and classification. This method first estimates the pose of the object, then normalizes all images, and finally inputs the normalized images into the classification train and test in the machine.

Document 2: Jayaraman J.Thiagarajan, Karthikeyan N.Ramamurthy, et al "Sparse representation for automatic target classification in SAR images", 4thInternational Symposium on Communications, Control and Signal Processing (ISCCSP), 2010: 1-4 (Jayaraman J.Thiagarajan et al. In the "Sparse Representation for Automatic Target Recognition of SAR Image" published at the 4th International Symposium on Communication, Control and Signal Processing in 2010, it was proposed to use the normalized training vector set to construct a sparse representation dictionary , and use this dictionary to find a local linear approximation to the underlying class manifold to compute a sparse representation of the test set.

Document 3: Ganggang Dong, Wang Na, et al "Sparse representation of monogenic signal: with application to target recognition in SAR images", IEEE Signal Processing Letters, 2014, 21(8): 952-956 (Ganggang Dong et al. in 2014 at In the "Sparse Representation of Single-cast Signals for SAR Image Target Recognition" published on the 21st Issue of Signal Processing Letters of the Institute of Electrical and Electronics Engineers, it is proposed to extract the single-cast signals of SAR images, and uniformly Downsampling, normalization, and cascading processing generate enhanced single-shot feature vectors, and finally the single-shot feature vectors are input to the Sparse Representation Classifier (Sparse Representation Classifier, SRC) for training and testing.

Document 4: Ganggang Dong, Gangyao Kuang "Target recognition in SAR image viaclassification on Riemannian manifolds", IEEE Geoscience and Remote Sensing Letters, 2015, 12(1): 199-204 (Ganggang Dong et al. in 2015 at IEEE Earth In the "Target Recognition of SAR Images Through the Classification of Riemannian Manifolds" published on the 12th issue of Science and Remote Sensing Letters, a method for recognizing SAR images through Riemannian geometry was proposed. In this method, the target image is first characterized by monogenetic signals, and the covariance matrix is constructed by calculating the correlation between monogenetic components. Due to the symmetry and positive definiteness of the covariance matrix, a connected Riemannian manifold can be constructed and transformed into a tangent vector space. Then use the obtained tangent vector as the feature vector, and use Sparse Representation Classifier (Sparse Representation Classifier, SRC) to classify.

The above methods usually require manual extraction of target features and selection of classifiers. The recognition effect is highly dependent on manual experience, and feature extraction and classifier design are two relatively independent links. As a data-driven method, the convolutional neural network can automatically learn effective feature information from the data through machine training, and at the same time complete the classification and recognition of the target. Compared with the traditional shallow neural network, the deep hidden features obtained It has a stronger target discrimination ability and provides a new feasible way for SAR image recognition.

Document 5: Sizhe Chen, Haipeng Wang, et al. "Target classification using the deep convolutional networks for SAR images." IEEE Transactions on Geoscience and Remote Sensing, 2016, 54(8): 4806-4817. (Sizhe Chen et al. in 2016 In the "Deep Convolutional Network for SAR Image Target Classification" published in the 54th issue of the Institute of Electrical and Electronics Engineers Earth Science and Remote Sensing, it is proposed to use a fully convolutional neural network to reduce training parameters and avoid too small training samples. The phenomenon of overfitting in the case of .

Document 6: Jun Ding, Bo Chen et al. "Convolutional neural network with data augmentation for SAR target recognition", IEEE Geoscience and Remote Sensing Letters, 2016, 13(3), 364-368. (Jun Ding et al. In "Convolutional Neural Networks with Dataset Expansion for SAR Target Recognition" published on the 13th issue of the Earth Science and Remote Sensing Letters of the Institute of Electronics Engineers, it is proposed to expand the data set by preprocessing the SAR image, thereby enhancing the The network's position transformation and anti-noise ability for the target.

Although the above method applies the convolutional neural network to the field of SAR image recognition, it does not consider the influence of the relationship between different convolution kernels on the generated feature map, which affects the further improvement of the recognition effect. The synthetic aperture radar image recognition method proposed by the present invention is based on a convolutional neural network. By introducing convolution kernel weights in the convolution layer, the relationship between convolution kernels is constructed, effective features are enhanced, and ineffective features are suppressed, thereby improving Classification performance of convolutional neural networks. At present, there is no public literature related to the introduction of convolution kernel weights in the convolutional layer of the convolutional neural network and its application in SAR image recognition.

Contents of the invention

The technical problem to be solved by the present invention is to propose a synthetic aperture radar image recognition method to solve the problem of inaccurate recognition caused by the current SAR image recognition method based on convolutional neural network without considering the relationship between different convolution kernels.

The invention is based on the convolution neural network, and introduces the weight of the convolution kernel into the convolution layer. Firstly, the neural network model is constructed according to the SAR image, and the SAR image is propagated forward through the network to obtain the probability prediction value; the probability prediction value is matched and compared with the category label of the image to obtain the target loss function; The parameters in the network model are adjusted. Finally, the SAR image to be recognized is recognized through the trained network, and the recognition result is obtained.

The present invention mainly comprises the following steps:

The first step is to construct a SAR image database for training. The SAR image database consists of N SAR images and the category labels of N SAR images; N is the number of SAR images in the SAR image database, and each SAR image contains only one Target; SAR image is expressed as G ₁ ,…G _n ,…G _N , the size of G _n is W _n ×H _n , W _n is the width of G _n , H _n is the height of G _n ; the category label is expressed as L ₁ ,...L _n ,...L _N , L _n is a one-dimensional matrix, containing C elements, and the C elements correspond to C target categories, the elements in L _n that represent the real category are assigned 1, and the remaining elements are assigned 0; C is the number of image categories, C is a positive integer, C≤N;

The second step is to preprocess G ₁ ,...G _n ,...G _N by:

2.1 Initialize variable n=1;

2.2 If all pixels in G _n are complex data, go to 2.3; if all pixels in G _n are real data, go to 2.4;

2.3 Take the modulus of W _n × H _n pixels of G _n and convert them into real numbers, the method is:

2.3.1 command line variable p=1;

2.3.2 Order variable q=1;

2.3.3 order G _n (p, q) is the value of point (p, q) on G _n , a is the real part of G _n (p, q) complex data, b is the imaginary part of G _n (p, q) complex data.

2.3.4q=q+1;

2.3.5 Determine whether q is less than or equal to W _n , if satisfied, go to 2.3.3; if not, go to 2.3.6.

2.3.6 p = p + 1;

2.3.7 Determine whether p is less than or equal to H _n , if it is satisfied, go to 2.3.2; if not, it means that G _n has been transformed into a real number image, go to 2.4.

2.4 Manually determine the position and size of the target in G ₁ ,…,G _n ,…,G _N ( is the width of the target in G _n , is the height of the target in _Gn ).

2.5 Crop G ₁ ,...G _n ,...G _N so that all SAR images have a uniform size, and let the uniform size be W ^G ×H ^G . Both W ^G and H ^G are positive integers, the method is: take 1.1 to 2 times the maximum value in W ^G , take 1.1 to 2 times of the maximum value in is used as H ^G , and the image is cropped by W ^G ×H ^G with the target as the center.

2.6 Use a random sequence generation function (such as the randperm function in MATLAB) to generate a random sequence rn ₁ ...,rn _n ,...,rn _N from 1 to N, with the random sequence as the index, for G ₁ ,...G _n ,...G _N ，L ₁ ,…L _n ,…L _N are read, so that the read random image Random class labels read by order Get random image sequences G′ ₁ ,…G′ _n ,…,G′ _N and random category labels L′ ₁ ,…,L′ _n ,…,L′ _N .

2.7 Group G′ ₁ ,…G′ _n ,…,G′ _N , L′ ₁ ,…,L′ _n ,…,L′ _N , and let the number of images and labels in each group be in, 1 ≤in≤N, generally in∈[1,64], G′ ₁ ,…G′ _n ,…,G′ _N are divided into BN groups, L′ ₁ ,…,L′ _n ,…,L′ _N are also Divided into BN group. in Indicates rounding up.

The third step is to construct a neural network model according to W ^G × H ^G. The neural network model includes at least a convolutional layer. In order to reduce the dimension of the feature map in the propagation, a pooling layer can be constructed; in order to improve the robustness of the network model, it can be constructed Dropout layer; in order to get a better mapping of the final features, a fully connected layer can be built.

3.1 Initialize the layer number variable, set the layer number variable cn=1 of the convolutional layer, the layer number variable pn=1 of the pooling layer, the layer number variable dn=1 of the discarding layer, and the layer number variable fn=1 of the fully connected layer.

3.2 Calculate the size of the output feature map of the convolutional layer by:

3.2.1 If cn=1, set CW ^cn ＝W ^G , CH ^cn ＝H ^G , CD ^cn ＝1, otherwise go to 3.2.2, where CW ^cn is the input feature map CG ^cn of the cnth convolutional layer Width, CH ^cn is the height of CG ^cn , CD ^cn is the depth of CG ^cn , CW ^cn ×CH ^cn ×CD ^cn indicates the dimension of CG ^cn .

3.2.2 Construct a convolutional layer for CG ^cn , so that the size of the convolution kernel of the cnth convolutional layer is The number of convolution kernels of the cnth convolutional layer is KN ^cn , and the step size of the convolution kernel when sliding is The zero-element padding dimension is χ ^cn . make Represents the kn ^cn (1≤kn ^cn ≤KN ^cn ) convolution kernel of the cnth convolutional layer, Indicates the kn ^cnth offset of the cnth convolutional layer, Represents the weight of the kn ^cn convolution kernel of the cn convolution layer. make Output feature maps for convolutional layers size, then:

In the convolution layer, the size of the convolution kernel The range of values is usually and and When cn=1, the value range of KN ^cn is usually KN ^cn ∈[10,20], when cn≠1, the value range of KN ^cn is usually KN ^cn ∈[KN ^cn-1 ,2×KN ^{cn -1} ]. The step size of the convolution kernel when sliding Usually set to 1 or 2, zero element padding size

3.3 Construct the pooling layer and calculate the size of the output feature map of the pooling layer, the method is:

3.3.1 Let the input feature map of the pnth pooling layer make Where PW ^cn is the width of PG ^pn , PH ^cn is the height of PG ^pn , and PD ^cn is the depth of PG ^pn , then PW ^pn ×PH ^pn ×PD ^pn represents the dimension of PG ^pn .

3.3.2 For PG ^pn to construct a pooling layer, let the size of the sliding window in the pnth pooling layer be The step size of the sliding window when sliding is make Output feature maps for pooling layers size, then:

in, Usually set to 2 or 3, the step size

3.4 Construct the discard layer and calculate the size of the feature map of the discard layer, the method is:

3.4.1 Let the input feature map of the dnth dropout layer make Where DW ^dn represents the width of DG ^dn , DH ^dn represents the height of DG ^dn , and DD ^dn represents the depth of DG ^dn , then DW ^dn ×DH ^dn ×DD ^dn represents the dimension of DG ^dn .

3.4.2 Construct the discarding layer for DG ^dn , let Indicates the drop probability of the dnth drop layer, usually let make Output feature maps for the dropout layer size, then:

3.5 Judgment thf is the output feature map for the dropout layer The first threshold of is a positive integer, usually set to 3000, if it is satisfied, let cn=cn+1, pn=pn+1, dn=dn+1, and then let and order Go to step 3.2; if it is not satisfied, it means that the dimension of the output feature map is already small, so go to step 3.6.

3.6 Calculate the size of the output feature vector of the fully connected layer.

3.6.1 If fn=1, let the dimension size of the input feature vector FG ^fn of the fnth fully connected layer

3.6.2 Construct a fully connected layer for FG ^fn whose dimension size is FW ^fn , so that the dimension size of the weight matrix A ^fn of the fully connected layer is The dimension size of the bias fb ^fn is in Output feature vectors for fully connected layers size, usually set

3.7 Calculate the feature vector size of the dropout layer.

3.7.1 Let dn=dn+1.

3.7.2 Let DW ^dn = 1, DH ^dn = 1, where DW ^dn ×DH ^dn ×DD ^dn = DD ^dn represents the dimension size of the input feature vector DG ^dn of the dnth discarding layer, where

3.7.3 For the DG ^dn whose dimension size is DW ^dn ×DH ^dn ×DD ^dn to construct the dropout layer, let Indicates the drop probability of the dnth drop layer, usually let make Output feature maps for the dropout layer size, then:

3.7.4 Judgment thd is the output feature map for the discard layer The second threshold of is a positive integer, usually set to 1000, if satisfied, set fn=fn+1, dn=dn+1, and order Go to step 3.6.1; if not satisfied, go to step 3.8.

3.8 For a dimension size of of Construct a fully connected layer, so that the dimension size of the weight matrix A ^fn of the fully connected layer is The dimension size of the bias fb ^fn is C.

3.9 Let CN=cn, PN=pn, DN=dn, FN=fn, that is, the neural network model has CN convolutional layers, PN pooling layers, DN discarding layers and FN+1 fully connected layers.

The fourth step is to use the Xavier method proposed in section 2.3 on page 2 of "Understanding the Difficulties of Training Deep Forward Neural Networks" published by Glorot Xavier et al. at the 13th International Conference on Artificial Intelligence and Statistics in 2010 to initialize the model of the neural network parameter. The specific operation method is as follows:

4.1 For the convolution kernel in the convolution layer to initialize.

4.1.1 Initialize the layer number variable cn=1 of the convolutional layer.

4.1.2 Initialize the variable kn ^cn =1 for the number of convolution kernels of the cnth convolutional layer.

4.1.3 Use random functions (such as the rand function in MATLAB) to generate random matrices The value range of each element in (0,1), has a dimension size of

4.1.4 pair To initialize, let:

Among them, formula (5) expresses Each element in is initialized to Subtract 0.5 from the element in the corresponding position and multiply by This is the meaning of matrix operations in the following.

4.1.5 Let kn ^cn =kn ^cn +1, determine kn ^cn ≤ KN ^cn , if satisfied, go to 4.1.3, if not, go to 4.1.6.

4.1.6 Let cn=cn+1, determine cn≤CN, if satisfied, go to 4.1.2; if not satisfied, explain the convolution kernel After the initialization is complete, go to 4.2.

4.2 The weight of the convolution kernel in the convolution layer to initialize.

4.2.1 Initialize the layer number variable cn=1 of the convolutional layer.

4.2.2 Initialize kn ^cn =1.

4.2.3 Use random functions (such as the rand function in MATLAB) to generate random number matrices The value range of each element in is in (0,1).

4.2.4 Pairs To initialize, let:

4.2.5 Let kn ^cn =kn ^cn +1, determine kn ^cn ≤ KN ^cn , if satisfied, go to 4.2.3; if not, go to 4.2.6.

4.2.6 Set cn=cn+1, determine cn≤CN, if satisfied, go to 4.2.2; if not satisfied, it means that the weight initialization of the convolution kernel is completed, and go to 4.3.

4.3 Initialize the weight matrix A ¹ ,...,A ^fn ,...,A ^FN+1 in the fully connected layer.

4.3.1 Initialize fn=1.

4.3.2 Use a random function (such as the rand function in MATLAB) to generate a random number matrix RA ^fn , and the value range of each element in RA ^fn is within (0,1).

4.3.3 Initialize A ^fn , make:

4.3.4 Let fn=fn+1, determine that fn≤FN+1, if it is satisfied, go to 4.3.2, if it is not satisfied, it means that the initialization of the weight matrix in the fully connected layer is completed, go to 4.4.

4.4 Bias in the convolution kernel Initialize with the bias fb ¹ ,...,fb ^fn ,...,fb ^FN+1 in the fully connected layer, and assign all biases to 0.

In the fifth step, in the training phase, the parameters in the neural network model need to be updated through continuous iterative forward propagation and backward propagation. The number of initialization iterations en=1.

The sixth step is to initialize the number of groups bn=1.

The seventh step is to initialize the variable n=(bn-1)×in+1.

The eighth step is to use the forward propagation method for G′ _n to carry out forward propagation, that is, carry out forward propagation on the nth SAR image in the constructed neural network model, and obtain the probability prediction value of the SAR image category. The output of each layer in the propagation process is the feature extracted by the neural network.

8.1 Initialize the layer number variable, set the layer number variable cn=1 of the convolutional layer, the layer number variable pn=1 of the pooling layer, the layer number variable dn=1 of the discarding layer, and the layer number variable fn=1 of the fully connected layer.

8.2 Calculate the output feature map of the convolutional layer by:

8.2.1 If cn=1, then let in The input feature map of the nth input image in the cnth convolutional layer, otherwise, perform 8.2.2.

8.2.2 Pairs Carry out zero element padding, the specific operation is as follows:

8.2.2.1 The initialization size is (CW ^cn +2×χ ^cn )×(CH ^cn +2×χ ^cn )×CD ^cn The matrix is all zeros.

8.2.2.2 Initialize cd ^cn =1, where cd ^cn is the coordinate of the third dimension on the feature map.

8.2.2.3 Initialize ch ^cn =1, where ch ^cn is the coordinate of the second dimension on the feature map.

8.2.2.4 Initialize cw ^cn =1, where cw ^cn is the coordinate of the first dimension on the feature map.

8.2.2.5 Order in express The values on the coordinates (cw ^cn +χ ^cn , ch ^cn +χ ^cn , cd ^cn ) are the same below.

8.2.2.6 Let cw ^cn =cw ^cn +1, judge that cw ^cn ≤ CW ^cn , if satisfied, go to 8.2.2.5, if not, go to 8.2.2.7.

8.2.2.7 Let ch ^cn =ch ^cn +1, determine ch ^cn ≤ CH ^cn , if satisfied, go to 8.2.2.4, if not, go to 8.2.2.8.

8.2.2.8 Let cd ^cn =cd ^cn +1, judge that cd ^cn ≤ CD ^cn , if satisfied, go to 8.2.2.3, if not, it means the assignment is completed, go to 8.2.3.

8.2.3 Initialize kn ^cn =1.

8.2.4 Calculate the kn ^cn convolution kernel and The convolution result of It is calculated as follows:

in, express The value on the coordinates (cw ^cn , ch ^cn , kn ^cn ); (kw ^cn , kh ^cn ) is the position coordinate of the convolution kernel, (cw ^cn , ch ^cn , cd ^cn ) is the input feature map location coordinates.

8.2.5 Using the activation function σ( ) to The value in is nonlinearized to obtain the convolution result after nonlinearization Common activation functions include sigmoid function (sigmoid), hyperbolic tangent function (tanh) and corrections proposed by Alex Krizhevsky et al. in "ImageNet Classification with Deep Neural Networks" published at the International Conference on Neural Information Processing Systems in 2012. Linear unit (Rectified Linear Unit, ReLU), etc.

8.2.6 Using the sigmoid function to convert Mapped to between 0 and 1 to get the weight of the mapped convolution kernel

8.2.7 Exploitation right Weighted to get the output of the convolutional layer The specific operation is as follows:

8.2.7.1 Initialize kn ^cn =1.

8.2.7.2 Initialize ch ^cn =1.

8.2.7.3 Initialize cw ^cn =1.

8.2.7.4 Order

8.2.7.5 Let cw ^cn =cw ^cn +1, judge that cw ^cn ≤ CW ^cn +2×χ ^cn , if satisfied, go to 8.2.7.4, if not, go to 8.2.7.6.

8.2.7.6 Let ch ^cn =ch ^cn +1, judge ch ^cn ≤ CH ^cn +2×χ ^cn , if satisfied, go to 8.2.7.3, if not, go to 8.2.7.7.

8.2.7.7 Let kn ^cn = kn ^cn +1, determine kn ^cn ≤ KN ^cn , if satisfied, go to 8.2.7.2, if not, it means the assignment is completed, go to 8.3.

8.3 Calculate the output feature map of the pooling layer by:

8.3.1 Let the input feature map of the pnth pooling layer

8.3.2 According to the size of the sliding window and the step size of the sliding window when sliding Sliding window operation is performed on PG ^pn to get area.

8.3.3 Pairs The regions are pooled separately, where Represents the position coordinates of the output feature map of the pooling layer, and uses this coordinate to indicate that the position of the output feature map corresponds to the area of the input feature map. The specific operation is as follows:

in, is the coordinate relative to the sliding window area, Usually the function of taking the maximum value or take the average function If the maximum value function is taken, the coordinates of the sliding window area where the maximum value is located need to be recorded Go to 8.4; if you take the average function, go to 8.4 directly.

8.4 Calculate the output feature map of the dropout layer by:

8.4.1 Let the input feature map of the dnth dropout layer

8.4.2 Use a random sequence generation function (such as the randperm function in MATLAB) to generate a random sequence from 1 to DD ^dn Using the random sequence as the index, assign a value to the one-dimensional matrix Φ with dimension size DD ^dn . make is 0, let is 1. in Indicates rounding down.

8.4.3 Multiply Φ by DG ^dn . The specific operation is:

8.4.3.1 Initialize dd ^dn =1.

8.4.3.2 Initialize dh ^dn =1.

8.4.3.3 Initialize dw ^dn =1.

8.4.3.4 Order

8.4.3.5 Let dw ^dn =dw ^dn +1, judge that dw ^dn ≤ DW ^dn , if satisfied, go to 8.4.3.4, if not, go to 8.4.3.6.

8.4.3.6 Let dh ^dn =dh ^dn +1, judge that dh ^dn ≤ DH ^dn , if satisfied, go to 8.4.3.3, if not, go to 8.4.3.7.

8.4.3.7 Let dd ^dn =dd ^dn +1, judge that dd ^dn ≤ DD ^dn , if it is satisfied, go to 8.4.3.2, if it is not satisfied, it means that the assignment is completed, and go to 8.5.

8.5 Let cn=cn+1, pn=pn+1, dn=dn+1, determine cn≤CN, if satisfied, go to 8.2, if not, go to 8.6.

8.6 Calculate the output feature vector of the fully connected layer by:

8.6.1 If fn=1, discard the feature map output by the layer dn-1 Convert to a one-dimensional feature vector, as the input feature vector FG ^fn of the fully connected layer, the specific operation steps are as follows:

8.6.1.1 Initialization

8.6.1.2 Initialization

8.6.1.3 Initialization

8.6.1.4 Order:

8.6.1.5 Order determination If satisfied, go to 8.6.1.4; if not, go to 8.6.1.6.

8.6.1.6 Order determination If satisfied, go to 8.6.1.3; if not, go to 8.6.1.7.

8.6.1.7 order determination If it is satisfied, go to 8.6.1.2. If it is not satisfied, it means that the assignment is completed and go to 8.6.2.

8.6.2 Calculate the product of the weight matrix A ^fn and FG ^fn , and add it to the bias fb ^fn to obtain the feature vector FG ^fn ′ in the middle of the convolutional layer. The calculation method is as follows:

FG ^fn ′＝A ^fn ×FG ^fn +fb ^fn (11)

8.6.3 Use the activation function σ( ) to nonlinearize the value in FG ^fn ′ to obtain the nonlinearized feature vector

8.7 Calculate the output feature vector of the dropout layer by:

8.7.1 Let the input feature map of the dnth dropout layer

8.7.2 Use a random sequence generation function (such as the randperm function in MATLAB) to generate a random sequence from 1 to DD ^dn Using the random sequence as the index, assign a value to the one-dimensional matrix Φ with dimension size DD ^dn . make is 0, let is 1. in Indicates rounding down.

8.7.3 Multiply Φ by DG ^dn . The specific operation is:

8.7.3.1 Initialize dd ^dn =1.

8.7.3.2 Order

8.7.3.3 Let dd ^dn =dd ^dn +1, judge that dd ^dn ≤DD ^dn , if satisfied, go to 8.7.3.2, if not, it means the assignment is completed, go to 8.8.

8.8 Let fn=fn+1, dn=dn+1, determine fn≤FN, if satisfied, go to 8.6, if not, go to 8.9.

8.9 Calculate the output feature vector of the fully connected layer by:

8.9.1 Calculate the product of the weight matrix A ^fn and FG ^fn , and add it to the bias fb ^fn to obtain the feature vector (FG ^fn )′ in the middle of the fully connected layer. The calculation method is as follows:

(FG ^fn )'=A ^fn ×FG ^fn +fb ^fn (12)

8.9.2 Use the softmax function to nonlinearize the value in (FG ^fn )′ to obtain the result of the fully connected layer by For example, the calculation is as follows:

Then it is the predicted value of the probability that the image is the c-th class.

The ninth step, according to and L′ _n , calculate the loss function J _n of the nth SAR image:

L' _n (cc) represents the cc-th element in L'_n; 9.1 sets n=n+1, judges bn=BN, if satisfied, executes 9.2; if not satisfied, executes 9.3.

9.2 Determine n≤N, if it is satisfied, go to the eighth step; if not, go to the tenth step.

9.3 Determine n≤bn×in, if satisfied, go to the eighth step, if not, go to the tenth step.

In the tenth step, the loss function obtained by the SAR images in the bnth group is averaged, and the loss function JJ _{(en-1)×in+bn} of the bnth group in the en iteration is calculated (that is, the SAR image in the group The average value of the loss function), determine bn=BN, if satisfied, go to 10.1, if not, go to 10.2.

10.1

10.2

In the eleventh step, determine the loss function JJ _{(en-1)×in+bn} ≤ JJM of the bn-th group in the en-th iteration, where JJM is the set loss function threshold (usually less than 0.01), if satisfied, then It means that the forward propagation is completed, go to the seventeenth step, if not satisfied, go to the twelfth step.

In the twelfth step, J _n is propagated backward in the network, so that the convolution kernel in the convolution layer, the weight and bias of the convolution kernel, and the weight matrix in the fully connected layer, bias these neurons Network model parameters are adjusted. Specific steps are as follows:

12.1 Initialize the layer number variable, let the layer number variable of the convolutional layer cn=CN, the layer number variable of the pooling layer pn=PN, the layer number variable of the discarding layer dn=DN, and the layer number variable of the fully connected layer fn=FN+ 1.

12.2 Calculate the partial derivatives of J _n to the weight matrix A ¹ ,…,A ^fn ,…,A ^FN+1 and biases fb ¹ ,…,fb ^fn ,…,fb ^FN+1 in the fully connected layer.

12.2.1 If fn=FN+1, then otherwise, Among them, softmax'( ) and S'( ) represent the derivatives of softmax function and sigmoid function.

12.2.2 Calculate the partial derivative of J _n to weight matrix A ^fn and J _n to bias fb ^fn .

12.2.3 Let fn=fn-1, determine fn≥1, if satisfied, go to 12.2; if not satisfied, go to 12.3.

12.3 If pn=PN, the partial derivative of J _n to FG ^fn+1 ′ converted to is a three-dimensional matrix, the specific operation steps are as follows, otherwise go to 12.4.

12.3.1 Initialization

12.3.2 Initialization

12.3.3 Initialization

12.3.4 Order:

12.3.5 determination If satisfied, go to 12.3.4; if not, go to 12.3.6.

12.3.6 determination If satisfied, go to 12.3.3; if not, go to 12.3.7.

12.3.7 determination If it is satisfied, go to 12.3.2; if it is not satisfied, it means the assignment is completed, go to 12.4.

12.4 Using J _n pairs partial derivative of Find the loss function J _n to PG ^pn Partial derivatives of elements in the equal region.

12.4.1 If in 8.3.2 If it is the maximum value function, go to 12.4.2, if it is the average value function, then go to 12.4.3.

12.4.2 Let the position of J _n to PG ^pn be The partial derivatives of the elements of are:

The partial derivatives of J _n with respect to the remaining elements in PG ^pn are 0.

12.4.3 Let the partial derivatives of J _n with respect to all elements in PG ^pn be

12.5 According to 8.3.1, so you can make

12.6 Calculating J _n pairs of convolutional kernels in convolutional layers The weight of the convolution kernel and the bias in the convolution kernel The partial derivative of , by:

12.6.1 Calculating J _n pairs of convolution kernels partial derivative of .

12.6.2 Calculating the weight of J _n to the convolution kernel partial derivative of .

12.6.3 Calculating the offset of J _n to the convolution kernel partial derivative of .

12.6.4 Let cn=cn-1, pn=pn-1, dn=dn-1, determine cn≥1, if not satisfied, it means that the propagation has been completed, go to step 13; if satisfied, go to 12.6.5.

12.6.5 Computing J _n pairs partial derivative of The calculation method is:

12.6.5.1 pair Carry out zero element padding, the specific operation is as follows:

12.6.5.1.1 The initialization size is The all-zero matrix JC ^cn+1 of .

12.6.5.1.2 Initialization for Coordinates in the third dimension on .

12.6.5.1.3 Initialization for Coordinates in the second dimension on .

12.6.5.1.4 Initialization for Coordinates in the first dimension on .

Order 12.6.5.1.5

12.6.5.1.6 determination If satisfied, go to 12.6.5.1.5; if not, go to 12.6.5.1.7.

12.6.5.1.7 determination If satisfied, go to 12.6.5.1.4; if not, go to 12.6.5.1.8.

12.6.5.1.8 determination If it is satisfied, go to 12.6.5.1.3, if not, it means the assignment is completed, go to 12.6.5.2.

12.6.5.2 will Rotate 180° clockwise to get rotated matrix

12.6.5.3 Calculation:

12.6.5.4 to 12.4.

The thirteenth step, make n=n+1, determine bn=BN, if satisfied, go to 13.1; if not satisfied, go to 13.2.

13.1 Determine n≤N, if satisfied, go to 12.1.2; if not, go to 13.3.

13.2 Determine that n≤bn×in, if satisfied, go to 12.1.2; if not, go to 13.3.

13.3 The loss function obtained for the SAR image in the bn group is for the convolution kernel in the convolution layer The weight of the convolution kernel in the convolution layer Bias in convolution kernel Average the partial derivatives of the weight matrix A ¹ ,…,A ^fn ,…,A ^FN+1 in the fully connected layer and the bias fb ¹ ,…,fb ^fn ,…,fb ^FN+1 in the fully connected layer value, by:

13.3.1 Determine bn=BN, if satisfied, go to 13.3.2; if not, go to 13.3.3.

13.3.2

Go to step fourteen;

13.3.3

The fourteenth step, using the output of the thirteenth step, uses the Adam algorithm proposed by Diederik P. Kingma et al. in "Adam: A Stochastic Optimization Method" published at the 2015 International Conference on Learning Representation to update the convolution kernel The weight of the convolution kernel Bias in convolution kernel The weight matrix A ¹ ,…,A ^fn ,…,A ^FN+1 in the fully connected layer and the bias fb ¹ ,…,fb ^fn ,…,fb ^FN+1 in the fully connected layer are as follows:

14.1 order

Where β ₁ is a given first hyperparameter, usually set as β ₁ =0.9.

14.2 order

Where β ₂ is a given second hyperparameter, usually set to β ₂ =0.999.

14.3 order

14.4 update A ^fn and fb ^fn , let:

Where η is the initial learning rate, usually set to η≤0.01.

The fifteenth step sets bn=bn+1, and judges that bn≤BN, if satisfied, go to the seventh step; if not satisfied, go to the sixteenth step.

The sixteenth step, let en=en+1, determine en≤EN, if satisfied, turn to the sixth step; if not satisfied, it indicates that the training is completed, and execute the seventeenth step.

In the seventeenth step, use the trained network model to identify the SAR image TG to be identified.

17.1 Forward propagating the image through the network.

17.1.1 Initialize the layer number variable dn=1 of the discarded layer

17.1.2 Order Both are 0,.

17.2 Use the forward propagation method described in the eighth step to propagate TG forward in the network, and get

17.3 Finding The position of the maximum value in cm, that is:

17.4 Output the cm-th category among the C categories in the label as the recognition result.

Note: In actual use, except for the convolutional layer, other layers can be constructed as needed. For the pooling layer, if the dimension of the feature map during propagation is too large, the pooling layer can be used to reduce the dimension of the feature map. For the dropout layer, if the training sample is too small or overfitting occurs during training, the dropout layer can be used. For the fully connected layer, in order to better map the features, a fully connected layer can be constructed. The present invention provides methods for constructing and using convolutional layers, pooling layers, discarding layers, and fully connected layers, but users can also construct corresponding layers according to actual needs, and only the convolutional layer must be constructed.

Beneficial effects of the present invention:

(1) The training of the convolutional neural network model (that is, the eighth step to the sixteenth step) is completely automatically completed through machine learning, which avoids the dependence of the recognition process on expert experience, and also avoids the subjectivity and arbitrariness of the recognition , which improves the accuracy of image recognition.

(2) The neural network model construction method for SAR images proposed in the third step can construct more effective network models for SAR images of different sizes. Compared with constructing the neural network model subjectively in the past, the present invention provides a guideline for the construction of the neural network model.

(3) In the eighth step, the weight of the convolution kernel is introduced into the convolution layer of the convolutional neural network, and the purpose of weighting the features extracted by the convolution kernel is achieved by weighting the convolution kernel. The weight can be used to adjust the proportion of the features extracted by the convolution kernel in the output feature map, enhance the representation ability of the features, and finally affect the recognition results, further improving the accuracy of target classification and recognition.

(4) In the twelfth step, a method of backpropagating the convolutional layer including the weight of the convolution kernel is proposed, which can adaptively adjust the weight of the convolution kernel. Adaptive adjustment avoids the subjectivity of manual setting, and can obtain more appropriate weights according to training.

(5) In the fourteenth step, by introducing the Adam algorithm, the network parameters can be adjusted adaptively according to the gradient obtained from training, avoiding the disadvantage of the fixed learning rate in the original algorithm, and making the network model complete faster and more stably train.

Description of drawings

Fig. 1 is the overall flow chart of the present invention;

Fig. 2 is that the third step of the present invention builds the neural network model flowchart;

Fig. 3 is the eighth step forward propagation method flowchart of the present invention;

Fig. 4 is a flow chart of the twelfth step backward propagation method of the present invention.

Detailed ways

Fig. 1 is the general flowchart of the present invention. The present invention is further described in conjunction with experiment:

The first step is to construct a SAR image database for training. In the experiment, the SAR image data used for training in the MSTAR data set is used, N=2747, W _n ×H _n =128×128.

In the second step, the SAR images are preprocessed to obtain 2747 SAR images with a size of W ^G ×H ^G =96×96. Here set in=30, BN=92, that is, the number of images and labels in each group is 30, and the images are divided into 92 groups.

The third step is to build a neural network model based on the preprocessed SAR images. The construction process is shown in Figure 3.

3.1 Initialize the layer number variable, set the layer number variable cn=1 of the convolutional layer, the layer number variable pn=1 of the pooling layer, the layer number variable dn=1 of the discarding layer, and the layer number variable fn=1 of the fully connected layer.

3.2 Calculate the size of the output feature map of the convolutional layer.

3.3 Build a pooling layer and calculate the size of the output feature map of the pooling layer.

3.4 Construct the dropout layer and calculate the feature map size of the dropout layer.

3.5 Judgment thf is the output feature map for the dropout layer The first threshold of , if satisfied, let cn=cn+1, pn=pn+1, dn=dn+1, then let and order Go to step 3.2; if not satisfied, go to step 3.6.

3.6 Calculate the size of the output feature vector of the fully connected layer.

3.7 Calculate the feature vector size of the dropout layer.

3.7.1 Let dn=dn+1.

3.7.2 Let DW ^dn = 1, DH ^dn = 1, where DW ^dn ×DH ^dn ×DD ^dn = DD ^dn represents the dimension size of the input feature vector DG ^dn of the dnth discarding layer, where

3.7.3 For the DG ^dn whose dimension size is DW ^dn ×DH ^dn ×DD ^dn to construct the dropout layer, let Indicates the drop probability of the dnth drop layer, usually let make Output feature maps for the dropout layer size, then:

3.7.4 Judgment thd is the output feature map for the discard layer The second threshold of , if satisfied, set fn=fn+1, dn=dn+1, and order Go to step 3.6; if not satisfied, go to step 3.8.

3.8 For a dimension size of of Construct a fully connected layer, so that the dimension size of the weight matrix A ^fn of the fully connected layer is The dimension size of the bias fb ^fn is C.

3.9 Let CN=cn, PN=pn, DN=dn, FN=fn, that is, the neural network model has CN convolutional layers, PN pooling layers, DN discarding layers and FN+1 fully connected layers.

In the experiment, first set thf=3000, and then according to 3.2, set the parameters of the first convolutional layer as: KN ¹ =16, χ ¹ = 3, the output feature map size is 96×96×16; according to 3.3, set the parameters of the first pooling layer as: The output feature map size is 48×48×16; according to 3.4, set the parameters of the first discard layer as: The size of the output feature map is 48×48×16; according to 3.5, it is judged that 48×48×16>thf, so return to 3.2 and continue to build the convolutional layer, pooling layer and discarding layer according to the above steps as follows:

Set the parameters of the second convolutional layer as: KN ² =32, χ ² =3, the output feature map size is 48×48×32; the parameters of the second pooling layer are: The output feature map size is 24×24×32; the parameters of the second dropout layer are: The output feature map size is 24×24×32, because 24×24×32>thf, so it returns 3.2.

Set the parameters of the third convolutional layer as: KN ³ =64, χ ³ =2, the output feature map size is 24×24×64; the parameters of the third pooling layer are: The output feature map size is 12×12×64; the parameters of the third dropout layer are: The output feature map size is 12×12×64, because 12×12×64>thf, so it returns 3.2.

Set the parameters of the fourth convolutional layer as: KN ⁴ =128, χ ⁴ =2, the output feature map size is 12×12×128; the parameters of the fourth pooling layer are: The output feature map size is 6×6×128; the parameters of the fourth dropout layer are: The output feature map size is 6×6×128, because 6×6×128>thf, so it returns 3.2.

Set the parameters of the fifth convolutional layer as: KN ⁵ =128, χ ⁵ =1, the output feature map size is 6×6×128; the parameters of the fifth pooling layer are: The output feature map size is 3×3×128; the parameters of the fifth dropout layer are: The output feature map size is 3×3×128, because 3×3×128<thf, proceed to the next step.

Set thd=1000, then according to 3.6, set the parameters of the first fully connected layer as: The output feature vector size is 512; according to 3.7, set the parameters of the sixth discard layer as: The size of the output feature vector is 512. According to 3.7.4, it is determined that 512<thd, and the fully connected layer is constructed according to 3.8. The image data in the experiment has 10 types of objects, and the setting parameters are: C=10. In the finally constructed network, CN=5, PN=5, DN=6, FN=1.

The fourth step is to use the Xavier method to initialize the model parameters of the neural network. .

The fifth step is to set EN=300 and initialize the number of iterations en=1;

The sixth step is to initialize the number of groups bn=1;

The seventh step, initialize variable n=(bn-1)×in+1;

The eighth step, as shown in Fig. 3, uses the forward propagation method to carry out forward propagation on _G′n , and obtains the probability prediction value of the SAR image category.

8.1 Initialize the layer number variable, set the layer number variable cn=1 of the convolutional layer, the layer number variable pn=1 of the pooling layer, the layer number variable dn=1 of the discarding layer, and the layer number variable fn=1 of the fully connected layer.

8.2 Calculate the output feature map of the convolutional layer.

8.3 Calculate the output feature map of the pooling layer.

8.4 Compute the output feature map of the dropout layer.

8.5 Let cn=cn+1, pn=pn+1, dn=dn+1, determine cn≤CN, if satisfied, go to 8.2, if not, go to 8.6.

8.6 Calculate the output feature vector of the fully connected layer.

8.7 Compute the output feature vector of the dropout layer.

8.8 Let fn=fn+1, dn=dn+1, determine fn≤FN, if satisfied, go to 8.6, if not, go to 8.9.

8.9 Calculate the output feature vector of the fully connected layer.

In the experiment, calculate the output feature maps of each convolutional layer, pooling layer and dropout layer according to the calculation methods of 8.2, 8.3, 8.4 and the determination method of 8.5; calculate the first one according to the calculation methods of 8.6, 8.7 and the determination method of 8.8 The output feature vector of the fully connected layer and the sixth pooling layer. Then according to the calculation method in 8.9, we get

The ninth step, according to and L′ _n , calculate the loss function J _n of the nth SAR image according to formula (14):

9.1 Set n=n+1, determine bn=BN, if satisfied, execute 9.2; if not, execute 9.3.

9.2 Determine n≤N, if it is satisfied, go to the eighth step; if not, go to the tenth step.

9.3 Determine n≤bn×in, if satisfied, go to the eighth step, if not, go to the tenth step.

In the tenth step, the loss function obtained by the SAR images in the bn group is averaged, and the loss function JJ _{(en-1)×in+bn} of the bn group in the en iteration is calculated;

The eleventh step is to determine the loss function JJ _{(en-1)×in+bn} ≤ JJM of the bn-th group in the en-th iteration, where JJM is the set loss function threshold, which is set to 0.01 here. If it is satisfied, It means that the forward propagation is completed, go to the seventeenth step, if not satisfied, go to the twelfth step;

In the twelfth step, as shown in Figure 4, J _n is propagated backward in the network, and the convolution kernel in the convolution layer, the weight and bias of the convolution kernel, and the weight matrix in the fully connected layer , Bias these neural network model parameters to adjust.

12.1 Initialize the layer number variable, let the layer number variable of the convolutional layer cn=CN, the layer number variable of the pooling layer pn=PN, the layer number variable of the discarding layer dn=DN, and the layer number variable of the fully connected layer fn=FN+ 1.

12.2 Calculate the partial derivatives of J _n to the weight matrix A ¹ ,…,A ^fn ,…,A ^FN+1 and biases fb ¹ ,…,fb ^fn ,…,fb ^FN+1 in the fully connected layer.

12.2.1 If fn=FN+1, then otherwise, Among them, softmax'( ) and S'( ) represent the derivatives of softmax function and sigmoid function.

12.2.2 Calculate the partial derivatives of J _n to weight matrix A ^fn and J _n to bias fb ^fn according to formula (17).

12.2.3 Let fn=fn-1, determine fn≥1, if satisfied, go to 12.2; if not satisfied, go to 12.3.

12.3 If pn=PN, the partial derivative of J _n to FG ^fn+1 ′ converted to Go to 12.4 after it is a three-dimensional matrix, otherwise go to 12.4 directly.

12.4 Using J _n pairs partial derivative of Find the loss function J _n to PG ^pn Partial derivatives of elements in the equal region.

12.5 orders

12.6 Calculating J _n pairs of convolutional kernels in convolutional layers The weight of the convolution kernel and the bias in the convolution kernel The partial derivative of , by:

12.6.1 Calculate J _n pairs of convolution kernels according to formula (20) partial derivative of .

12.6.2 Calculate the weight of J _n to the convolution kernel according to formula (21) partial derivative of .

12.6.3 Calculate the bias of J _n to the convolution kernel according to formula (22) partial derivative of .

12.6.4 Let cn=cn-1, pn=pn-1, dn=dn-1, determine cn≥1, if not satisfied, it means that the propagation has been completed, go to step 13; if satisfied, go to 12.6.5.

12.6.5 Computing J _n pairs partial derivative of Go to 12.4.

In the experiment, calculate the partial derivative of the loss function to the weight matrix and bias in the fully connected layer according to 12.2; judge fn≥1 according to 12.2.3, if it is satisfied, go to 12.2, if not, go to 12.3. According to 12.3, judge that pn=PN, if it is satisfied, convert the partial derivative of the loss function to the feature map into three-dimensional, if not, go directly to 12.4. According to 12.4, calculate the partial derivative of the loss function to the elements in each pooling area in the feature map. According to 12.6, calculate the partial derivative of the loss function with respect to the convolution kernel in the convolution layer, the weight of the convolution kernel and the bias in the convolution kernel.

The thirteenth step, make n=n+1, determine bn=BN, if satisfied, go to 13.1; if not satisfied, go to 13.2;

13.1 Determine n≤N, if satisfied, go to 12.1.2; if not, go to 13.3.

13.2 Determine that n≤bn×in, if satisfied, go to 12.1.2; if not, go to 13.3.

13.3 The loss function obtained for the SAR image in the bn group is for the convolution kernel in the convolution layer The weight of the convolution kernel in the convolution layer Bias in convolution kernel Average the partial derivatives of the weight matrix A ¹ ,…,A ^fn ,…,A ^FN+1 in the fully connected layer and the bias fb ¹ ,…,fb ^fn ,…,fb ^FN+1 in the fully connected layer value.

The fourteenth step, using the Adam algorithm to update the convolution kernel The weight of the convolution kernel Bias in convolution kernel The weight matrix A ¹ ,…,A ^fn ,…,A ^FN+1 in the fully connected layer, and the bias fb ¹ ,…,fb ^fn ,…,fb ^FN+1 in the fully connected layer.

The fifteenth step, let bn=bn+1, determine that bn≤BN, if satisfied, go to the seventh step; if not satisfied, go to the sixteenth step;

The sixteenth step, let en=en+1, determine en≤EN, if satisfied, go to the sixth step; if not satisfied, it means that the training is completed, and execute the seventeenth step;

The eighth step to the twelfth step is to forward and backward propagate the image in the model; the thirteenth and fourteenth steps are to update the parameters of the model. The eighth to fourteenth steps are iterative process, according to the fifteenth and sixteenth steps to judge whether the iteration is over. Finally, when en=301, since the requirement of en≤300 is not satisfied, the training is completed and the final model for recognition is obtained.

In the seventeenth step, use the trained neural network model to identify the SAR image to be identified. In the experiment, 3203 SAR images used for testing in the MSTAR dataset are used to test the neural network model. If the output category is the same as the actual category, the recognition is considered correct. The finally obtained correct recognition rate is 98.39%, which illustrates the effectiveness of the present invention.

Claims (13)

1. A synthetic aperture radar image identification method is characterized by comprising the following steps:

first, build for trainingThe SAR image database consists of N SAR images and category labels of the N SAR images; n is the number of SAR images in an SAR image database, and each SAR image only comprises one target; SAR image is denoted as G₁,…G_n,…G_N，G_nIs of size W_n×H_n，W_nIs G_nWidth of (H)_nIs G_nHigh of (d); class label denoted L₁,…L_n,…L_N，L_nIs a one-dimensional matrix containing C elements corresponding to C object classes, L_nThe middle element representing the real category is assigned with 1, and the rest elements are assigned with 0; c is the number of the image categories, C is a positive integer, and C is less than or equal to N;

second step, for G₁,…G_n,…G_NThe pretreatment is carried out, and the method comprises the following steps:

2.1 initializing variable n ═ 1;

2.2 if G_nAll the pixels in the pixel array are complex data, and 2.3 is converted; if G is_nAll the pixels in the image are real number data, and 2.4 turns;

2.3 mixing G_nW of (2)_n×H_nEach pixel is converted into a real number, and the real number is converted into 2.4;

2.4 determination of G₁,…,G_n,…,G_NPosition of the target and size of the target Is G_nThe width of the medium target is greater than the target width,is G_nHigh for medium targets;

2.5 pairs of G₁,…G_n,…G_NCutting to make all SAR images have uniform size, and making uniform size be W^G×H^G，W^GAnd H^GAre all positive integers;

2.6 Generation of random sequences rn from 1 to N Using random sequence Generation function₁…,rn_n,…,rn_NUsing random sequence as index, for G₁,…G_n,…G_N，L₁,…L_n,…L_NReading is performed to make the random image readRandom class label for readingObtaining a random image sequence G'₁,…G′_n,…,G′_NAnd a random class tag L'₁,…,L′_n,…,L′_N；

2.7 to G'₁,…G′_n,…,G′_N，L′₁,…,L′_n,…,L′_NGrouping is carried out, the number of images and the number of labels in each group are in, and in is more than or equal to 1 and less than or equal to N and G'₁,…G′_n,…,G′_NIs totally BN group, L'₁,…,L′_n,…,L′_NAnd is also divided into a group BN, wherein,whereinRepresents rounding up;

third step, according to W^G×H^GConstructing a neural network model, wherein the method comprises the following steps:

3.1 initializing the layer number variable cn, setting the layer number variable cn of the convolutional layer to 1, setting the layer number variable pn of the pooling layer to 1, setting the layer number variable dn of the discarded layer to 1, and setting the layer number variable fn of the all-connected layer to 1;

3.2 calculating the size of the convolution layer output characteristic diagram, wherein the method comprises the following steps:

3.2.1 if cn is 1, let CW^cn＝W^G,CH^cn＝H^G,CD^cn1, otherwise, 3.2.2, where CW^cnAn input feature map CG for the cn-th convolution layer^cnWidth of (C, CH)^cnIs CG^cnHigh, CD^cnIs CG^cnDepth of (CW)^cn×CH^cn×CD^cnRepresentation CG^cnThe dimension size of (d);

3.2.2 pairs of CG^cnBuilding convolutional layers with the convolutional kernel of the cn convolutional layer of sizeThe number of convolution kernels of the cn convolution layer is KN^cnStep size of convolution kernel at sliding isThe zero element filling size is x^cn(ii) a Order toRepresenting the kn of the cn-th convolutional layer^cnA convolution kernel of 1 or more kn^cn≤KN^cn，Representing the kn of the cn-th convolutional layer^cnThe bias voltage is set to be equal to the bias voltage,representing the kn of the cn-th convolutional layer^cnThe weight of each convolution kernel; order toOutputting a feature map for a convolutional layerThe size of (d) is as follows:

3.3 construct pooling layer, calculate the size of the pooling layer output characteristic map, the method is:

3.3.1 input profile of pn-th pooling layerOrder toWherein PW^cnIs PG^pnWidth of (D), PH^cnIs PG^pnHigh, PD of^cnIs PG^pnDepth of (1), then PW^pn×PH^pn×PD^pnRepresents PG^pnThe dimension size of (d);

3.3.2 for PG^pnConstructing the pooling layer such that the size of the sliding window in the pn-th pooling layer isThe step size of the sliding window during sliding isOrder toOutputting a feature map for the pooling layerThe size of (d) is as follows:

3.4, constructing a discarding layer, and calculating the size of a feature map of the discarding layer, wherein the method comprises the following steps:

3.4.1 input feature map for the dn-th discard layerOrder toIn which DW^dnRepresents DG^dnWidth of (D), DH^dnRepresents DG^dnHigh, DD^dnRepresents DG^dnDepth of (2), then DW^dn×DH^dn×DD^dnRepresents DG^dnThe dimension size of (d);

3.4.2 pairs DG^dnBuild a discard layer, orderRepresents the drop probability of the dn-th drop layer, orderOrder toOutputting a feature map for a discard layerThe size of (d) is as follows:

3.5 determinationthf is the discard level output profileIf the first threshold value of (a) is a positive integer, let cn be cn +1, pn be pn +1, and dn be dn +1, and then letAnd orderTurning to step 3.2; if not, executing step 3.6;

3.6 calculate the size of the full-connection layer output feature vector:

3.6.1 let fn be 1, let the input feature vector FG for the fn-th fully-connected layer^fnDimension of (2)

3.6.2 FW for dimension size^fnFG of (1)^fnConstructing a full connection layer, and making a weight matrix A of the full connection layer^fnHas a dimension ofOffset fb^fnHas a dimension ofWhereinOutputting feature vectors for full connection layersSize, setting of

3.7 calculate the eigenvector size of the discarded layer:

3.7.1 let dn be dn + 1;

3.7.2 order DW^dn＝1,DH^dn＝1,Then DW^dn×DH^dn×DD^dnInput feature vector DG for the dnth discarded layer^dnOf size of (1), wherein

3.7.3 for dimension size DW^dn×DH^dn×DD^dnDG of (1)^dnConstruction ofDiscard the layer, orderRepresents the drop probability of the dn-th drop layer, orderOrder toOutputting a feature map for a discard layerThe size of (d) is as follows:

3.7.4 determinationthd is the discard layer output feature mapIf the second threshold value of (2) is a positive integer, let fn be fn +1, dn be dn +1,and orderTurning to step 3.6.1; if not, executing step 3.8;

3.8 for dimension size ofIs/are as followsConstructing a full connection layer, and making the weight moment of the full connection layerArray A^fnHas a dimension ofOffset fb^fnThe dimension of (a) is C;

3.9 make CN ═ PN, DN ═ DN, FN ═ FN, that is, the neural network model has CN convolution layers, PN pooling layers, DN discarding layers and FN +1 full connection layers;

fourthly, initializing model parameters of the neural network to obtain convolution kernels in the initialized convolution layerWeights of convolution kernels in initialized convolution layerWeight matrix A in initialized full connection layer¹,…,A^fn,…,A^FN+1Bias in initialized convolution kernelAnd offset fb in the full connection layer¹,…,fb^fn,…,fb^FN+1；

Fifthly, initializing the iteration number en as 1;

sixthly, initializing a group number bn to be 1;

seventhly, initializing a variable n which is (bn-1) x in + 1;

eighth step, to G'_nAdopting a forward propagation method to carry out forward propagation, namely carrying out forward propagation on the nth SAR image in the constructed neural network model to obtain a probability prediction value of the SAR image category, wherein the method comprises the following steps:

8.1 initializing the layer number variable, setting the layer number variable cn of the convolutional layer to 1, the layer number variable pn of the pooling layer to 1, the layer number variable dn of the discard layer to 1, and the layer number variable fn of the all-connected layer to 1;

8.2 calculating the output characteristic diagram of the convolution layer, the method is as follows:

8.2.1 if cn is 1, let us sayWhereinInputting the feature map of the nth input image at the cn convolution layer, otherwise, executing 8.2.2;

8.2.2 pairsCarrying out zero element filling to obtain a filled characteristic diagram

8.2.3 initializing kn^cn＝1；

8.2.4 calculating the kth^cnA convolution kernel andresult of convolution ofThe calculation method is as follows:

wherein,to representIn the coordinate (cw)^cn,ch^cn,kn^cn) The value of (a); (kw^cn,kh^cn) Is the position coordinate of the convolution kernel, (cw)^cn,ch^cn,cd^cn) For inputting feature mapsThe position coordinates of (a);

8.2.5 activation function σ (-) pairsThe value in (3) is subjected to nonlinear processing to obtain a convolution result after the nonlinear processing

8.2.6 will utilize an S-shaped functionMapping to 0-1 to obtain the weight of the mapped convolution kernel

8.2.7 utilizeTo pairWeighting to obtain the output of the convolution layer

8.3 calculating the output characteristic diagram of the pooling layer, wherein the method comprises the following steps:

8.3.1 input profile of the pn-th pooling layer

8.3.2 according to the size of the sliding WindowAnd step size of sliding window during slidingFor PG^pnPerforming a sliding window operation to obtainAn area;

8.3.3 pairsAre respectively pooled in whichThe position coordinates of the output characteristic diagram of the pooling layer are represented, and meanwhile, the coordinates are used for representing that the position of the output characteristic diagram corresponds to the area of the input characteristic diagram, and the specific operation is as follows:

wherein,as a coordinate relative to the sliding window area, as a function of taking the maximumOr taking the mean functionIf the maximum function is taken, the coordinates of the sliding window area at the position of the maximum are recordedRotating 8.4; if get the flatThe mean function is directly converted to 8.4;

8.4 calculating the output characteristic graph of the discarding layer, wherein the method comprises the following steps:

8.4.1 input feature map for the dn-th discard layer

8.4.2 Generation of 1 to DD Using random sequence Generation function^dnRandom sequence of (2)Random sequence is used as index, and dimension is DD^dnAssigning the one-dimensional matrix phi; order toIs 0, orderIs 1; whereinRepresents rounding down;

8.4.3 coupling phi with DG^dnMultiplying;

8.5 making CN ═ CN +1, pn ═ pn +1, dn ═ dn +1, judging CN ≦ CN, if yes, turning to 8.2, if no, executing 8.6;

8.6 calculating the output characteristic vector of the full connection layer, the method is as follows:

8.6.1 feature map output by the dn-1 st layer drop layer if fn is 1Converting into one-dimensional feature vector as input feature vector FG of full connection layer^fn；

8.6.2 calculating the weight matrix A^fnAnd FG^fnAnd with an offset fb^fnAdding to obtain a feature vector FG between convolution layers^fn′The calculation method is as follows:

FG^fn′＝A^fn×FG^fn+fb^fn (11)；

8.6.3 Using the activation function σ (-) on FG^fn′The value in (3) is subjected to nonlinear processing to obtain a characteristic vector after the nonlinear processing

8.7 calculating the output feature vector of the discarding layer, the method is:

8.7.1 input feature map for the dn-th discard level

8.7.2 use random sequence generation function to generate 1 to DD^dnRandom sequence of (2)Random sequence is used as index, and dimension is DD^dnAssigning the one-dimensional matrix phi; order toIs 0, orderIs 1;

8.7.3 will phi and DG^dnMultiplication, specifically:

8.7.3.1 initialize dd^dn＝1；

8.7.3.2 order

8.7.3.3 order dd^dn＝dd^dn+1, decision dd^dn≤DD^dnIf yes, 8.7.3.2 is turned to, if no, the assignment is finished, and 8.8 is executed;

8.8 making FN ═ FN +1 and dn ═ dn +1, judging FN is less than or equal to FN, if it is satisfied, turning to 8.6, if it is not satisfied, executing 8.9;

8.9 calculating the output characteristic vector of the full connection layer, the method is as follows:

8.9.1 calculating the weight matrix A^fnAnd FG^fnAnd with an offset fb^fnAdding to obtain feature vector (FG) in the middle of the full connection layer^fn) ', the calculation is as follows:

(FG^fn)′＝A^fn×FG^fn+fb^fn (12)

8.9.2 utilize a softmax function pair (FG)^fn) ' the values in (1) are non-linearized to obtain a fully connected layer result The calculation method of (c) is as follows:

the probability prediction value of the image as the class c is obtained;

the ninth step is based onAnd L'_nCalculating a loss function J of the nth SAR image_n：

L′_n(cc) represents L'_nThe cc element of (1);

9.1, let n be n +1, judge BN be BN, if satisfied, execute 9.2; if not, executing 9.3;

9.2 judging that N is less than or equal to N, if so, turning to the eighth step; if not, executing the tenth step;

9.3 judging that n is less than or equal to bn x in, if so, turning to the eighth step, and if not, executing the tenth step;

the tenth step is that the loss functions obtained by the SAR images in the bn group are averaged, and the loss function JJ of the bn group in the en iteration is calculated_{(en-1)×in+bn}If so, turning to 10.1, and if not, turning to 10.2;

10.1

10.2

the tenth step, determining the loss function JJ of the bn th group in the en-th iteration_{(en-1)×in+bn}JJM, wherein JJM is a loss function threshold, if yes, the forward propagation is completed, the seventeenth step is carried out, and if not, the twelfth step is carried out;

a twelfth step of mixing J_nBackward propagation is carried out in the network, neural network model parameters of convolution kernels and weights and offsets of the convolution kernels in the convolution layers and weight matrixes and offsets in the full-connection layers are adjusted, and the method specifically comprises the following steps:

12.1 initializing a layer number variable, wherein the layer number variable CN of the convolutional layer is CN, the layer number variable PN of the pooling layer is PN, the layer number variable DN of the discarded layer is DN, and the layer number variable FN of the fully-connected layer is FN + 1;

12.2 calculation of J_nFor weight matrix A in the full connection layer¹,…,A^fn,…,A^FN+1And an offset fb¹,…,fb^fn,…,fb^FN+1Partial derivatives of (d);

12.2.1 if FN ═ FN +1, thenIf not, then,wherein T represents a matrix A^(fn+1)Transpose of (1), softmax 'and S' represent derivatives of the softmax function and sigmoid function;

12.2.2 calculating J_nFor weight matrix A^fnAnd J_nTo offset fb^fnPartial derivatives of (a):

12.2.3, making fn equal to fn-1, judging that fn is equal to or more than 1, if so, converting to 12.2; if not, turning to 12.3;

12.3 if PN ═ PN, converting J into_nFor FG^fn+1Partial derivatives ofConversion into three dimensions12.4, turning; otherwise, directly rotating to 12.4;

12.4 use of J_nTo pairPartial derivatives ofCalculating a loss function J_nFor PG^pnInPartial derivatives of the elements;

12.4.1 if in 8.3.2The maximum function is taken, and the operation is switched to 12.4.2, and if the maximum function is taken as the average function, the operation is switched to 12.4.3;

12.4.2 order J_nFor PG^pnThe middle position isThe partial derivatives of the elements of (a) are:

J_nfor PG^pnThe partial derivatives of the other elements are 0;

12.4.3 order J_nFor PG^pnPartial derivatives of all elements in

12.5 order

12.6 calculation of J_nFor convolution kernel in convolution layerWeights of convolution kernelsAnd bias in convolution kernelThe method comprises the following steps:

12.6.1 calculating J_nFor convolution kernelWhere σ' (. cndot.) is the derivative of the activation function σ ():

12.6.2 calculating J_nWeight to convolution kernelPartial derivatives of (a):

12.6.3 calculating J_nFor bias in convolution kernelPartial derivatives of (a):

12.6.4, making cn ═ cn-1, pn ═ pn-1, dn ═ dn-1, judging cn ≥ 1, if not, it is said that propagation is completed, and going to the thirteenth step; if so, go to 12.6.5;

12.6.5 calculating J_nTo pairPartial derivatives ofThe calculation method is as follows:

12.6.5.1 pairsCarrying out zero element filling;

12.6.5.2 will beRotate clockwise by 180 degrees to obtainRotated matrix

12.6.5.3 calculates:

12.6.5.4 to 12.4;

thirteenth, let n be n +1, judge BN be BN, if satisfy, go to 13.1; if not, 13.2 is switched;

13.1 judging that N is less than or equal to N, and if the N is less than or equal to N, turning to 12.1.2; if not, turning to 13.3;

13.2 judging that n is less than or equal to bn x in, if so, turning to 12.1.2; if not, turning to 13.3;

13.3 obtaining loss function for SAR images in the bn group vs. convolution kernel in convolution layerWeights of convolution kernels in convolutional layersBias in convolution kernelsWeight matrix A in full connection layer¹,…,A^fn,…,A^FN+1Bias fb in the full connection layer¹,…,fb^fn,…,fb^FN+1Respectively averaging partial derivatives of (A) by the following steps:

13.3.1, judging BN is BN, if so, turning to 13.3.2; if not, go to 13.3.3;

13.3.2

turning to the fourteenth step;

13.3.3

fourteenth, updating the convolution kernel using the output of the thirteenth stepWeights of convolution kernelsBias in convolution kernelsWeight matrix A in full connection layer¹,…,A^fn,…,A^FN+1Bias fb in the full connection layer¹,…,fb^fn,…,fb^FN+1The method specifically comprises the following steps:

14.1 order

Wherein beta is₁Is a given first hyper-parameter;

14.2 order

Wherein beta is₂Is a given second hyperparameter;

14.3 order

14.4 updateA^fnAnd fb^fnOrder:

wherein η is the initial learning rate;

the fifteenth step, making BN be BN +1, judging that BN is less than or equal to BN, and if so, turning to the seventh step; if not, turning to the sixteenth step;

sixthly, making EN equal to EN +1, judging that EN is less than or equal to EN, and if the EN is less than or equal to EN, turning to the sixth step; if not, indicating that the training is finished, and executing a seventeenth step;

seventeenth step, using the trained neural network model to identify the SAR image TG to be identified, wherein the method comprises the following steps:

17.1 forward-propagating the image in the network:

17.1.1 initializing the layer number variable dn of the discarded layer to 1;

17.1.2 orderAre all 0;

17.2 adopting the forward propagation method of the eighth step to forward propagate TG in the network to obtain

17.3 searchThe position cm of the medium maximum, i.e.:

and 17.4, outputting the cm-th category in the C categories in the label as the identification result.

2. The method of claim 1, wherein step 2.3 is performed by using G_nW of (2)_n×H_nThe method for respectively converting each pixel into a real number comprises the following steps:

2.3.1 let the row variable p be 1;

2.3.2 let column variable q be 1;

2.3.3 orderG_n(p, q) is G_nThe value of the upper (p, q) point, a is G_n(p, q) the real part of the complex data, b being G_n(p, q) an imaginary part of the complex data;

2.3.4q＝q+1；

2.3.5 determining whether q is equal to or less than W_nIf yes, turning to 2.3.3; if not, go to 2.3.6;

2.3.6p＝p+1；

2.3.7 determining whether p is equal to or less than H_nIf yes, turning to 2.3.2; if not, G will be described_nThe conversion is finished for a real image.

3. The method of claim 1, wherein 2.5 of the pairs G₁,…G_n,…G_NThe method for cutting comprises the following steps: get1.1 to 2 times the maximum value of (A) as W^GGet it1.1 to 2 times the maximum value of (A) as H^GWith the object as the center, press W on the image^G×H^GAnd (5) cutting.

4. The method according to claim 1, wherein the random sequence generating function refers to randderm function in MATLAB; random functions refer to rand functions in MATLAB.

5. The synthetic aperture radar image recognition method of claim 1, wherein in the convolutional layer,has a value range ofAnd isAnd isKN when cn is 1^cnHas a value range of KN^cn∈[10,20]When cn ≠ 1, KN^cnHas a value range of KN^cn∈[KN^cn-1,2×KN^cn-1](ii) a Step size of convolution kernel during slidingSet to 1 or 2, zero element fill sizeIn the above-mentioned pooling layer the water is added,set to 2 or 3, step size

6. The synthetic aperture radar image recognition method of claim 1, wherein in e [1,64 ∈ is said](ii) a The discard layer outputs a feature mapIs set to 3000, the layer output profile is discardedSet to 1000; the loss function threshold JJM is less than 0.01; beta is the same as₁0.9; beta is the same as₂0.999; eta is less than or equal to 0.01.

7. The synthetic aperture radar image recognition method of claim 1, wherein the fourth step initializes model parameters of the neural network using an Xavier method by:

4.1 convolution kernels in pairs of convolution layersAnd (3) initializing:

4.1.1 initializing the number of layers of the convolutional layer variable cn to 1;

4.1.2 initializing the number variable kn of the convolution kernel of the cn-th convolution layer^cn＝1；

4.1.3 Generation of random matrices Using random functionsWherein the value range of each element is within (0,1),has a dimension of

4.1.4 pairsInitializing to enable:

wherein, the formula (5) representsIs initialized toThe element at the corresponding position is subtracted by 0.5 and multiplied byAll matrix operations are in this sense;

4.1.5 order kn^cn＝kn^cn+1, decision kn^cn≤KN^cnIf yes, turning to 4.1.3, and if not, turning to 4.1.6;

4.1.6 making CN ═ CN +1, judging CN ≤ CN, if yes, turning to 4.1.2; if not, indicating the convolution kernelAfter the initialization is finished, 4.2 is switched;

4.2 weights for convolution kernels in convolutional layerAnd (3) initializing:

4.2.1 initializing the number of layers of the convolutional layer variable cn to 1;

4.2.2 initializing kn^cn＝1；

4.2.3 Generation of random number matrix Using random functionThe value range of each element in the (1) is within (0);

4.2.4 pairsInitializing to enable:

4.2.5 order kn^cn＝kn^cn+1, decision kn^cn≤KN^cnIf yes, turning to 4.2.3; if not, 4.2.6 is executed;

4.2.6 making CN equal to CN +1, judging CN less than or equal to CN, if yes, turning to 4.2.2; if not, the initialization of the weight value of the convolution kernel is completed, and 4.3 is executed;

4.3 weight matrix A in full connection layer¹,…,A^fn,…,A^FN+1And (3) initializing:

4.3.1 initialize fn to 1;

4.3.2 Generation of random number matrix RA Using random function^fn，RA^fnThe value range of each element in the (1) is within (0);

4.3.3 pairs of A^fnInitializing to enable:

4.3.4, making FN be FN +1, judging FN to be not more than FN +1, if yes, turning to 4.3.2, if not, turning to 4.4;

4.4 bias in the pairs of convolution kernelsAnd offset fb in the full connection layer¹,…,fb^fn,…,fb^{FN +1}Initialization is performed to assign all biases to 0.

8. A synthetic aperture radar image recognition method according to claim 1, wherein the pair of steps 8.2.2The method for carrying out zero element filling comprises the following steps:

8.2.2.1 initialize a size of (CW)^cn+2×χ^cn)×(CH^cn+2×χ^cn)×CD^cnIs/are as followsThe matrix is all zero;

8.2.2.2 initializing cd^cn＝1，cd^cnCoordinates of a third dimension on the feature map;

8.2.2.3 initialize ch^cn＝1，ch^cnCoordinates for a second dimension on the feature map;

8.2.2.4 initializing cw^cn＝1，cw^cnCoordinates that are a first dimension on the feature map;

8.2.2.5 orderWhereinTo representIn the coordinate (cw)^cn+χ^cn,ch^cn+χ^cn,cd^cn) The value of (a);

8.2.2.6 order cw^cn＝cw^cn+1, decision cw^cn≤CW^cnIf yes, go to 8.2.2.5, if not, go to 8.2.2.7;

8.2.2.7 order ch^cn＝ch^cn+1, determining ch^cn≤CH^cnIf yes, go to 8.2.2.4, if not, go to 8.2.2.8;

8.2.2.8 order cd^cn＝cd^cn+1, decision cd^cn≤CD^cnIf yes, go to 8.2.2.3, otherwise, end.

9. The method of claim 1, wherein 8.2.7 said pairs are used for image recognitionWeighting to obtain the output of the convolution layerThe method comprises the following steps:

8.2.7.1 initializing kn^cn＝1；

8.2.7.2 initialize ch^cn＝1；

8.2.7.3Initializing cw^cn＝1；

8.2.7.4 order

8.2.7.5 order cw^cn＝cw^cn+1, decision cw^cn≤CW^cn+2×χ^cnIf yes, go to 8.2.7.4, if not, go to 8.2.7.6;

8.2.7.6 order ch^cn＝ch^cn+1, determining ch^cn≤CH^cn+2×χ^cnIf yes, go to 8.2.7.3, if not, go to 8.2.7.7;

8.2.7.7 order kn^cn＝kn^cn+1, decision kn^cn≤KN^cnIf yes, go to 8.2.7.2, otherwise, end.

10. The method of claim 1, wherein the step of 8.4.3 is performed by combining Φ and DG^dnThe multiplication method comprises the following steps:

8.4.3.1 initialize dd^dn＝1；

8.4.3.2 initialize dh^dn＝1；

8.4.3.3 initialize dw^dn＝1；

8.4.3.4 order

8.4.3.5 order dw^dn＝dw^dn+1, decision dw^dn≤DW^dnIf yes, go to 8.4.3.4, if not, go to 8.4.3.6;

8.4.3.6 order dh^dn＝dh^dn+1, decision dh^dn≤DH^dnIf yes, go to 8.4.3.3, if not, go to 8.4.3.7;

8.4.3.7 order dd^dn＝dd^dn+1, decision dd^dn≤DD^dnIf yes, go to 8.4.3.2, otherwise, end.

11.The method of claim 1, wherein the step 8.6.1 is implemented by outputting the feature map of the layer dn-1 discarding layerThe method of converting into a one-dimensional feature vector is:

8.6.1.1 initialization

8.6.1.2 initialization

8.6.1.3 initialization

8.6.1.4 order:

8.6.1.5 orderDeterminationIf yes, go to 8.6.1.4, if not, execute 8.6.1.6;

8.6.1.6 orderDeterminationIf yes, go to 8.6.1.3, if not, execute 8.6.1.7;

8.6.1.7 orderDeterminationIf so, the routine proceeds to 8.6.1.2, and if not, the routine ends.

12. The method of claim 1, wherein step 12.3 is performed by using J_nFor FG^fn+1Partial derivatives ofConversion into three dimensionsThe method comprises the following steps:

12.3.1 initialization

12.3.2 initialization

12.3.3 initialization

12.3.4 order:

12.3.5determinationIf so, go to 12.3.4; if not, go to 12.3.6;

12.3.6determinationIf so, go to 12.3.3; if not, go to 12.3.7;

12.3.7determinationIf so, go to 12.3.2; if not, ending.

13. The method of claim 1, wherein 12.6.5.1 said pairs are used for image recognitionThe method for carrying out zero element filling comprises the following steps:

12.6.5.1.1 initialize a size ofAll-zero matrix JC of^cn+1；

12.6.5.1.2 initialization Is composed ofCoordinates of a third dimension above;

12.6.5.1.3 initialization Is composed ofA second dimension of coordinates of;

12.6.5.1.4 initialization Is composed ofA coordinate of a first dimension above;

12.6.5.1.5 order

12.6.5.1.6DeterminationIf yes, go to 12.6.5.1.5, if not, go to 12.6.5.1.7;

12.6.5.1.7determinationIf yes, go to 12.6.5.1.4, if not, go to 12.6.5.1.8;

12.6.5.1.8determinationIf so, the routine proceeds to 12.6.5.1.3, and if not, the routine ends.