Newton Method For Complex Compressive Sensing

In the 5G era,compressive sensing technology is ubiquitous whether in the fields of network communication,face recognition,autopilot,or imaging technology,and one of their common characteristics is the sparsity of predictive variables.In real life,communication devices use complex numbers for information transmission,and a large number of complex-valued signals that are filled with problems in these fields are compressed.Therefore,predicting and restoring complex-valued variables is one of the main research contents in compressive sensing.Proposing a more effective and more accurate complex-valued compressive sensing signal recovery technology has become the focus of researches by scholars.Many recovery algorithms of different models have been designed and proposed one after another,which provides a lot of help to solve the problem of complex-valued compressive sensing signal recovery.However,because most of the current mainstream algorithms in this field only use gradient information for signal recovery,they might require a large amount of calculation and a long time to solve problems under high-dimensional data.With the development of science and technology,people's expectations for faster and more efficient methods have become greater,so the Newton method recovery technology using second-order information is worthy of our in-depth discussion and study.Based on the complex-valued compressive sensing model,this paper at first introduces the theory of compressive sensing and its application prospects in the context of communication,as well as the preparatory knowledge required in this paper;Secondly,the existing complex-valued compressive sensing algorithms are introduced,and important characteristics such as the framework of each algorithm and their efficiency are summarized;Thirdly,we utilize the projection on the sparse set and analyze theoretical properties based on the optimization model.And then combined with the hard-thresholding projection method,a Newton algorithm is designed to solve the complex-valued compressive sensing problem,and an algorithm framework is also given;Finally,in the numerical experiment analysis,the complex-valued compressive sensing Newton method is compared with the algorithm currently used in the communication field in terms of efficiency and accuracy of the recovery.A large number of numerical experiments show that the Newton algorithm designed in this paper is superior to the current mainstream algorithm in the field of compressive sensing in all aspects of experimental evaluation standards,indicating that our model and algorithm can cope with the actual communication signal recovery task.