Research On Convolutional Neural Network Algorithms In Complex Domain

Artificial intelligence has become one of the hot topics in today's society,mainly due to the rapid development of deep learning,and Convolutional Neural Networks(CNN)is an important model of deep learning.CNN is mainly applied in the field of computer vision and has achieved many excellent results in this field.Most CNN representations are based on real numbers,and very few are based on complex numbers.Recent studies have shown that networks based on complex numbers representation have better representation ability than networks based on real numbers representation,but there are some problems with the existing complex-valued CNN(c CNN)model.Most of the models are two-branch structure where one branch is shortcut connection.Compared to this structure,each branch of multi-branch structure can learn a transformation.In addition,the existing models do not pay attention to the relationship between complex feature maps,and the contribution of each complex feature map to the current task is not consistent.Aiming at these problems,this paper proposes new c CNN models.The main work is as follows:(1)In this paper,the split-transform-merge scheme in the complex domain is proposed,and a new network model is constructed: Complex-valued Aggregated Residual Network(c Res Ne Xt).The performance of the network is improved by increasing the number of branches while maintaining the complexity of the model.The core module of the network is a multi-branch structure,and each branch contains three three convolution layers.First of all,the first complex convolution layer splits the high-dimensional complex feature maps into the low-dimensional complex feature maps.Then the second complex convolution layer transforms the low-dimensional feature maps to obtain the complex feature maps of the same dimension,the third complex convolution layer increases the dimension of the low-dimensional feature maps to obtain the high-dimensional complex feature maps.Finally,the complex feature maps of each branch is added in the same dimension.In addition,a shortcut connection is added into the module,which can build a deep network.In order to make the structure of the module more convenient,the scheme of complex group convolution is applied in this module,and a new module is formed.The multi-branch structure of the module contains only the second complex convolution layer,and the dimensions of the input and output of the branch are the same.(2)In this paper,the scheme of feature recalibration in the Complex domain is proposed and applied to the network to construct Complex-valued Channel-Weighted Networks(c SENet).By learning the corresponding weight values of each complex feature map,the complex feature maps with higher contribution to the current task can be enhanced and the complex feature maps with lower contribution can be suppressed.The specific operation of the core module of the network is as follows: firstly,the global information is obtained through global average pooling.Then the global information is passed through the complex domain gating mechanism to obtain each input complex feature map of the complex weight value.Finally,each input complex feature map is calculated with the corresponding complex weight value to get the output complex feature map.The first 1×1 complex convolution layer is used to reduce the dimension,which can reduce the computational effort.The second 1×1 complex convolution layer has a Sigmoid activation function that maps both the real and imaginary parts of the complex weight values between 0 and 1.(3)Combining the above two schemes,c SENet is integrated into c Res Ne Xt in this paper to form a Complex-valued Channel-Weighted Aggregated Residual Networks(c SE-Res Ne Xt).Its core component is to intergrate c SENet block to the last complex convolution layer of the c Res Ne Xt block.A shortcut connection is used to connect the input of the c Res Ne Xt block to the output complex feature maps of the c SENet block.The specific process is as follows: Firstly,complex input feature maps x is passed through multi-branch structure to obtain z.Then,z is obtained through global average pooling and complex domain gating mechanism to obtain weight c,which is then calculated with complex feature maps z to obtain s.Finally,complex input feature maps x and s for the same dimension addition operation to get the output complex feature maps.