Matrix Recovery Modeling Based On Deep Generative Models And Its Application

With the vigorous development of Internet technology and the continuous progress of big data technology,people’s demand for streaming data such as images and videos is increasingly high,which poses a significant challenge to data transmission and processing.The traditional signal sampling mode faces the pressure of massive data transmission and data processing.As an extension of compressed sensing in high-dimensional data,matrix recovery can accurately recover data from undersampling data,not only more suitable for data structures such as images that take the form of matrix data,but also significantly reduce the cost of data storage and transmission.In this article,we creatively combine the deep generative models in deep learning with matrix recovery.Taking deviation modeling as the core idea,we use the deep generation model to mine the prior properties of data and incorporate matrix recovery.We propose a ’LowRank-Gen’ matrix recovery framework,which successfully reduces the sampling requirements required for matrix recovery and improves the recovery cleanliness.The main contents of this article include:1.This paper briefly outlines the research background of matrix recovery,as well as different modeling ideas for current matrix recovery issues.Considering that the deep generation model can effectively capture and mine low dimensional representations of target data,and can provide complete and intuitive prior information,it goes beyond traditional prior assumptions to a certain extent.Therefore,we use the idea of low-rank deviation modeling,combine matrix recovery and deep generative models,and present a Low-Rank-Gen model.2.Theoretical analysis of the model Low-Rank-Gen for matrix recovery based on a priori deep generative model.We propose a matrix set restricted singular value condition(M-S-REC condition),and combine it with the matrix restricted isometric condition(M-RIP condition)to prove the existence theorem of decoders,sampling operator theorem,and recoverability theorem under the Low-Rank-Gen framework.The theorem indicates that when the sampling number satisfies m=O(?),the random Gaussian sampling operator can successfully recover the original matrix signal with a high probability.The theorem also shows the rationality of splitting the recovery matrix into a generating prior and a low rank deviation matrix.The Low-Rank-Gen method is more reasonable and effective in characterizing the internal structural information of the deviation matrix.3.For applications in real scenes,we have pre trained a Variational Auto-encoder(VAE)or Deep Convolutional Adversarial Networks(DCGAN)model on five real datasets as a model priori,and conducted four types of experiments,including image reconstruction,under-training reconstruction,transfer reconstruction,and noise tolerance testing.Experiments show that the reconstruction accuracy of the algorithm is significantly better than that of the classical matrix recovery algorithm in scenes with low measurement counts.In particular,it has great advantages over other scenes in depicting large deviation scenes.Transfer reconstruction shows that our method has great potential in cross domain reconstruction,and has stronger robustness against noise.The experimental results agree with the modeling ideas and theoretical analysis results of the model.