Research On Sensing Strategy In Compressive Sensing

Traditional analog-to-digital converters based on the Shannon-Nyquist sampling theorem are incapable of dealing with the massive data and ultra-high transmission rates in the information age.They cannot meet the requirements in many application scenarios,and the collected data exist.Huge redundancy wastes a lot of computing resources and storage resources,and also imposes unnecessary burdens on the later data processing and transmission process.Compressive sensing makes the above problems well solved,has great application value,and has received extensive attention.Compressive sensing mainly includes three steps-signal sparsification,signal compression sampling and signal reconstruction recovery,corresponding to three theories-signal sparsity base and sparse representation,the nature and construction of the measurement matrix,signal reconstruction algorithm.On the basis of summarizing theories of compressive sensing,this paper focuses on the basis pursuit reconstruction algorithm with the most practical value and development prospects.The basic theory of the basis pursuit reconstruction algorithm is Lagrange multiplier method.Based on the content and feasibility analysis of the Lagrangian multiplier method,this paper concludes three points expansion of the application of the Lagrangian multiplier method:(1)Non-smooth objective function of Lagrangian multiplier method is applicable;(2)"Isolated touch" can be used in low dimension;(3)Lagrange multiplier method have annotation.Based on the three-point extension of the Lagrangian multiplier method and the combining with the characteristics of compressive sensing,this paper proposed a new compressive sensing strategy—indirect sensing strategy.In the indirect sensing strategy,instead of measuring the original sparse signal directly,another signal with some relation to the original sparse signal is measured,meaning ? .Then,at the signal reconstruction terminal,the basis pursuit reconstruction algorithm can accurately recover the original sparse signal.Through theoretical analysis and experimental verification,it is proved that the indirect sensing strategy has many advantages such as faster sensing speed,higher signal reconstruction accuracy,and wider application scenarios than the current direct sensing strategy.