In recent years， Generative Adversarial Networks （GANs） have been widely used for data augmentation， which can solve the problem of insufficient training samples effectively and has important research significance for model training. However， the existing GAN models for data augmentation have problems such as high requirements for datasets and unstable model convergence， which can lead to distortion and deformation of the generated images. Therefore， a lightweight GAN based on dynamic-upsample — DU-FastGAN （Dynamic-Upsample-FastGAN） was proposed for data augmentation. Firstly， a generator was constructed through a dynamic-upsample module， which enables the generator to use upsampling methods of different granularities based on the size of the current feature map， thereby reconstructing textures， and enhancing overall structure and local detail quality of the synthesis. Secondly， in order to enable the model to better obtain global information flow of images， a weight information skip connection module was proposed to reduce the disturbance of convolution and pooling operations on features， thereby improving the model’s learning ability for different features， and making details of the generated images more realistic. Finally， a feature loss function was given to improve the quality of the model generation by calculating relative distance between the corresponding feature maps during the sampling process. Experimental results show that compared with methods such as FastGAN， MixDL （Mixup-based Distance Learning）， and RCL-master （Reverse Contrastive Learning-master）， DU-FastGAN achieves a maximum reduction of 23.47% in FID （Fréchet Inception Distance） on 10 small datasets， thereby reducing distortion and deformation problems in the generated images effectively， and improving the quality of the generated images. At the same time， DU-FastGAN achieves lightweight overhead with model training time within 600 min.

The effect of the existing Total Variation (TV) method for image denoising is not ideal, and it is not good at keeping the characteristics of image edge and texture details. A new method of image denoising based on rational-order differential was proposed in this paper. First, the advantages and disadvantages of the present image denoising methods of TV and fractional differential were discussed in detail, respectively. Then, combining the model of TV with fractional differential theory, the new method of image denoising was obtained, and a rational differential mask in eight directions was drawn. The experimental results demonstrate that compared with the existing denoising methods, Signal Noise Ratio (SNR) is increased about 2 percents, and the method retains effectively the advantages of integer and fractional differential methods, respectively. In aspects of improving significantly high frequency of image and keeping effectively the details of image texture, it is also an effective, superior image denoising method. Therefore, it is an effective method for edge detection.