Research On Optimization Method And Application Of Compressed Sensing

With the rapid development of Internet of Things technology,the amount and the variety of the generated data are increasing rapidly in various application fields.How to efficiently collect and transmit the data has become the focus of current research.Compressed sensing,as an efficient data acquisition and compression method,has certain limitations,that is,the number of the columns of the measurement matrix must be equal to the number of the rows of the data to be compressed due to the limitation of the traditional matrix operation rules.Therefore,as the amount of the data increases,the dimension of the measurement matrix will also increase.The large measurement matrix will lead to the increment of storage space,computing and transmission resources.The practicability of the traditional compressed sensing is limited in the networks with low storage and computing resources,such as the wireless sensor networks.The introduction of the semi-tensor product theory and the P-tensor product theory solves the problem of dimension matching in the traditional compressed sensing,but it brings the loss of reconstruction effect,stability and reconstruction time.In view of the above problems,based on the tensor product theory and the non-correlation theory of the measurement matrix,this paper studies the optimization method and the application of the proposed compressed sensing method.The main research results and the innovations of this paper are shown as follows:(1)We proposed an optimization method of the measurement matrix for the semi-tensor compressed sensing based on the gradient descent method.Combined with the semi-tensor product theory and the non-correlation theory of the measurement matrix,this paper constructs the correlation coefficient representation method and the objective optimization function of the measurement matrix.By the gradient descent method,this paper solves the objective optimization function,derives the iterative updating formula of the measurement matrix,and finally gives the specific optimization steps.Through simulation experiments,reconstruction effect,storage space and optimization time are analyzed to verify the effectiveness and the advantage of the proposed method.(2)Aiming at P-tensor product theory and the properties of measurement matrix in P-tensor compressed sensing,an optimization method for P-tensor compressed sensing is proposed based on the gradient descent.The proposed method reduces the correlation coefficient of the high-dimensional measurement matrix by simultaneously optimizing the initial low-dimensional measurement matrix and the matrix P,and it can improve the recovery effect and the stability of P-tensor compressed sensing and reduce the reconstruction time.Based on the proposed optimization method,this paper designs an efficient data transmission scheme,which can be applied to wireless sensor networks.Simulation results show that the proposed scheme is feasible,which can reduce the storage and transmission resources occupied by the measurement matrix,improve the efficiency of data acquisition and reconstruction,and achieve a stable and good recovery effect.