| In recent years,generating images via a generative adversarial network(GAN)has attracted much attention in statistic learning.However,there are the following problems in generating images via a traditional GAN:(1)Traditional GAN can only produce low-dimensional images of simple structure.The training effect is not good for images with complex structures(such as human faces).(2)The traditional GAN has complex structure and high computational complexity,and the network is hard to train.There are two main reasons why it is difficult for a traditional GAN to generate high-dimensional images:(1)The gap between the low-dimensional prior distribution(i.e.input noise)and high-dimensional real distribution is too large,which makes it hard to directly learn a mapping between the prior distribution and the high-dimensional real distribution.(2)High-dimensional real data has noise information.The distribution of high-dimensional data that needs to be learned is too complex,so it is difficult to learn the distribution without additional conditional information.Therefore,based on the above issues,this research considers combining the dimensionality reduction with GAN.We reduce the high-dimensional real data to a low-dimensional space,then use GAN to generate low-dimensional embeddings in the low-dimensional space,and reconstruct the newly generated low-dimensional embeddings into high-dimensional images.We propose a method for generating complex structure images with a simple model architecture.This research proposes a GAN image generation method based on dimensionality reduction theory.It is divided into three steps:Firstly,we train a deep compressive sensing network to obtain the linear mapping embeddings.The deep compressive sensing network can linearly compress high-dimensional images into low-dimensional measurements and recover them to the original high-dimensional images with low loss.In this research,by training the deep compressive sensing network,we learn the linear compression mapping and recovery mapping between the high-dimensional images and the low-dimensional measurements,to obtain the linear mapping embeddings required in the second step.Secondly,generate the new low-dimensional embeddings.The linear mapping embeddings are transferred as the input to the GAN to generate new low-dimensional embeddings.Thirdly,generate the new high-dimensional images.The new low-dimensional embeddings are transferred to the recovery mapping which obtained in the first step,and the denoising training is carried out to obtain the new high-dimensional images.The main work of this research is as follows:Aiming at the problem of high-quality image reconstruction and the effectiveness of introducing low-dimensional manifolds,deep compressive sensing networks are studied.Combined with existing work,the SDA model,CSNET,and lite_net are proposed in this research.According experiments,we determine the optimal deep compressive sensing network on different data sets under different compression rates,laying a foundation for subsequent image generation.In response to the effectiveness issue of introducing low dimensional manifolds,experiments have verified the existence of low dimensional manifolds in the high-dimensional images that retain key feature information and spatial structure information in low-dimensional space.These low-dimensional manifolds have low dimensions and low noise,which are helpful for subsequent image generation.Using the method proposed in this research for image generation experiments on the above dataset,we propose two implementation details:not using the tanh function in the last layer of the generator and tensor conversion operations(RESHAPE,RECOVER).We design three experiments:"fully connected+fully connected","convolution+fully connected" and"convolution+convolution" to generate images and calculate FID values.We find that the method proposed in this research is superior to traditional GAN(fully connected GAN and DCGAN),and using this method can improve the image generation performance of small-scale GAN.Its visual effect and Frechet Inception Distance(FID)in generating images are superior to large-scale GAN,and it has advantages such as low network structure complexity,low computational cost,fast training speed,and high image generation quality.The innovation of this method lies in the following points:(1)Generating low-dimensional embeddings instead of directly generating high-dimensional images reduces the training difficulty of GAN.On the one hand,the dimension of the embeddings is greatly reduced after linear compression.which shortens the distance between prior distribution and high-dimensional real distribution and reduces the complexity of GAN network structure.On the other hand,after dimension reduction,the key structure information is retained,which reduces the learning difficulty of the generator.(2)The distribution of linear mapping embeddings becomes a posteriori distribution to provide additional information for GAN.Compared to the traditional GAN where the posterior distribution is the high-dimensional real distribution,the posterior distribution in this method is the distribution of low-dimensional embeddings generated by the compression process,which has lower dimensions and contains spatial structure information and feature information.It provides an additional information for GAN to help train and reduce the difficulty of learning the mapping between the prior distribution of the posterior distribution.(3)The model architecture of the deep compressive sensing network is simple.The compression module of the deep compressive sensing network used in this research is a single fully connected layer or a single convolutional layer,with fewer network parameters and lower computational complexity.In addition,CSNET used in this research only needs to be trained once for any fixed compression rate,which can be applied to images of different sizes,making the training convenient. |
