The Study Of Characteristic-oriented Measurement Method Based On The Theory Of Compressive Sensing

In the current era of big data,the theory of compressive sensing(CS)has very high application value for the integration of signal sampling and compressing,so it has great significance to research the implementation of compressive sensing theory.In the theory of CS,the choice of measurement method will directly influence the quality of signal reconstruction.For an accurate signal reconstruction,most of the existing researches of the measurement method design the measurement matrix under the restricted isometric property.In this paper,with a small amount of prior about the signal,we study the implementation of measurement in CS based on the signal characteristic,aiming to greatly improve the efficiency of signal sampling.Firstly,this paper presents a measurement method for sparse signal in orthogonal base.Using the reversibility of orthogonal base matrix,the measurement matrix is computed by designing the sensing matrix which is the product of measurement matrix and sparse matrix.By this method,the relationship between sensing matrix and sparse matrix doesn't need to be considered but only restricted isometric property of the sensing matrix.Thus,the difficulty of the design of the measurement matrix is reduced.The presented method is suitable for sparse signal in any orthogonal base,and the feasibility and effectiveness both have been verified by simulation results.Secondly,the direct sampling of ultra wideband(UWB)signal has been a difficult issue in its application.In this paper,two methods for low rate measurement of UWB linear frequency modulate(LFM)signal in the framework of CS are presented: low-pass filtering compressive sampling method and correlate-modulate compressive sampling method.Both methods are realized by sampling in time-domain,to get measurements in frequency-domain.The low-pass filtering compressive sampling method samples in time-domain to get the measurements in low frequency coefficients by utilizing the characteristic of energy concentration in frequency domain of LFM signal.The method includes low-pass filtering,low-rate sampling and signal reconstruction.The correlate-modulate compressive sampling method is an improved version of low-pass filtering compressive sampling method.In this method,the signal energy is concentrated in low frequency by symbol modulation which utilizes the frequency characteristic of LFM signal.By this method,the measurements sampled in time-domain contain more signal information which can promote the quality of signal reconstruction.The simulation results verify the feasibility and superiority of both methods,especially the correlate-modulate compressive sampling method which has excellent performance on compressive sampling and robustness.In some cases,the signal can be reconstructed with the same amount of measurements as the sparse degree,which reaches the limit of compressive sampling.