Research On Adaptive Compressed Sensing Algorithm With Limited Sense Energy

Compressive sensing has received extensive attention from researchers due to its efficient information sampling mechanism.It has great potential for application in practice.Traditional compressed sensing disperses the sensing energy in the entire signal range,which results in relatively low utilization efficiency,especially in the case of sensing energy confinement.This results in traditional compressed sensing algorithms being more susceptible to observation noise.Adaptive Compressed Sensing enables subsequent observation vectors to be adaptively designed based on previous observations,and distributes the sensing energy as much as possible at the support position to improve the observed signal-to-noise ratio.This paper considers the situation of sensing energy limitation,studies adaptive compressive sensing algorithms,and decomposes the adaptive observation problem into two sub-problems,namely the new observation vector sparse item update method and the new observation vector support set acquisition method.To solve these two problem,the main work of this paper is as follows:(1)Aiming at the problem of updating the sparse items of new observation vectors,it is found that the current optimization methods of the observation matrix based on Gram matrix can reduce the coherence coefficient of the observation matrix to improve the quality of reconstruction.This idea is introduced into adaptive compressive sensing.There is an optimization problem for the nenw observation vector if the traditional reconstruction algorithm is used to obtain estimated support set and constrains the sensing energy of each observation vector.The optimal observation vector with matrix optimization significance can be acquired by solving the above matrix optimization problem.Using the backtracking method instead of the complete reconstruction algorithm to obtain the estimated support set,the internal iteration of the reconstruction algorithm is transferred to the adaptive iteration in the observation process,thereby reducing the computational complexity to the extent of the traditional greedy algorithm.The simulation experiments show that the proposed algorithm can effectively improve the SNR of the observation and reduce the non-diagonal elemental energy of the Gram matrix.It has lower reconstruction error than the traditional compressed sensing algorithm,the observation matrix optimization algorithm and the adaptive algorithm.(2)For the problem of new observation vector support set acquisition method,under the multi-measurement vector observation model,it was found through research that multiple signal classification algorithm(MUSIC)can achieve good reconstruction effect in fewer observations.This is conincidence with the requirement of adaptive compressed sensing for initial observations.The idea of MUSIC algorithm is introduced into adaptive compressive sensing,and the applicable condition of MUSIC algorithm is extended theoretically.A modified MUSIC spectral function is proposed,which is used to deal with support set recovery problems when the number of snapshots is insufficient.The estimated support set can be obtained more accurately,so that the sensing energy distribution is more effective.Simulation experiments show that the proposed improved MUSIC spectral method can obtain a higher support set estimation accuracy than the traditional algorithm,and the corresponding adaptive observation solution also has a lower reconstruction error than the traditional greedy algorithm and MUSIC-like algorithm.