Gaussian-type activation function with learnable parameters in complex-valued convolutional neural network and its application for PolSAR classification

• Processing Complex-valued PolSAR Data Using Complex-valued Convolutional Neural Network (CV-CNN). • Uses a Gaussian-type activation function (GTAF) that preserves the integrity of complex-valued operations. • Introduces learnable Gaussian parameters for GTAF, and designs two multi-channel activation methods. • The classification accuracy is better than that of existing state-of-the-art methods in three datasets. To process complex-valued information such as SAR signals conveniently, the complex-valued convolutional neural network (CV-CNN) has been proposed in recent years, and it has achieved great success in SAR image recognition. This paper proposes an activation function with learnable parameters based on the Gaussian-type activation function (GTAF) in CV-CNN to improve the utilization of information in the real and imaginary parts of the neuro. For the multi-channel input of the feature map, this paper discusses two ways to set the parameters of the Gaussian-type activation function. One is that all channels share the same parameters, called the channel-sharing Gaussian-type activation function (CSGTAF). The other is that each channel has its independent parameters, called the channel-exclusive Gaussian-type activation function (CEGTAF). In addition, this paper derives the backpropagation formula of both CSGTAF and CEGTAF in detail for the training process of CV-CNN. This paper performs experimental analysis on three L-band standard PolSAR datasets. The experimental results show that, compared with the traditional method and the Gaussian activation function with fixed parameters, both CSGTAF and CEGTAF achieve higher recognition accuracy, and the difference in the recognition effect of different targets in the same dataset is little. Both show good recognition performance and have good stability and versatility.