# A Joint Denoising Learning Model for Weight Update Space-Time Diversity Method +
## 4 A Joint Denoising Learning Model for Weight Update STD Method
### Noise-Reduction Learning Models Based on Complex-CGAN  
As one of the KBM adaptive filters, the algorithm represented by KRLS cannot effectively cope with the UWA signal with complex structural characteristics. The core of the KRLS algorithm is an iterative learning mechanism by which a nonlinear mapping is created between the received signal and the acquisition noise. A radial basis function (RBF) neural network, similar to KRLS, is a single hidden layer feedforward neural network that accomplishes online learning by using RBF as the activation function. RBFNN has more adjustable parameters than the KRLS algorithm. RBFNN, with the addition of complex convolutional units, can handle complex-type data, but still has the problems of simple structure and easy structure loss of feedback information. Although CNNs have been successfully applied in image noise-reduction processing, there is a drawback of unstable convergence for UWA data because such network models do not have a judgment feedback mechanism. In recent years, GAN models have improved noise-reduction performance for nonlinear and nonstationary signals by introducing the structure of generation-discrimination. The GAN consists of a generative model (GM) and a discriminative model (DM), alternately optimized and trained until they reach a steady equilibrium state [64]. The CGAN is a derivative upgrade from the GAN that can add conditional attributes to the samples, further increasing the accuracy of the parameters in the feedback mechanism. Figure 7: Convolutional structure of complex processing module. Inspired by the above algorithm structure, this paper proposes a noise-reduction learning model dedicated to UWA data features. Specifically, the model is a complex-CGAN noise-reduction network based on residual cancellation learning (RCL). The structural composition of the noise-reduction model is shown in Figure 8. In the following, we illustrate the operation process of the noise-reduction model with the learning process of the real part in the complex-type signal. We added a complex convolutional kernel unit to the original CGAN, which can turn the DM into the complex-DM. The complex-DM is combined with the complex activation function CReLU to form the basic structure of the complex-CGAN, which is capable of handling complex-type data. The GM can be considered a feature generation network by which noise-reducing features are generated that are realistic. The DM is a discriminative network that constantly feeds back to correct the generation quality of the GM by discriminating the differences between noise-bearing features and denoised reference features. The model is alternatively optimized and trained until a Nash equilibrium is reached and the final noise-reduced estimate is output. Specifically, for the complex-CGAN, its input is the pre-processing result \(\mathbf{TR}_{y}\). After \(\mathbf{TR}_{y}\) enters the GM for the first time, it generates an initialization value, which will be constantly compared and fed back to \(\mathbf{TR}_{n}\) for learning. The GM contains the encoding part Gen and the decoding part Gde [65]. Gen gradually discards the redundant information in the original high-dimensional data by the dimensionality reduction of \(\mathbf{TR}_{y}\), outputs the valuable information in the signal as a low-dimensional vector, and then, reconstructs the high-dimensional features by Gde. Figure 9 shows the detailed structural setup of the GM in the complex-CGAN. Then, \(\mathbf{TR}_{y}\) and \(\mathbf{TR}_{n}\) are sequentially input into the DM for determination and identification until a steady-state mapping distribution is reached. By feedback learning through  
Figure 8: Structural components of the noise-reduction learning model. Figure 9: The detailed structural setup of the GM in the complex-CGAN. error reflection propagation between \(\mathbf{TR}_{y}\) and \(\mathbf{TR}_{hi}\), the accuracy of adversarial training is continuously enhanced [66].