Nonlinear Sparse Signal Reconstruction Research Based On Samples And Polynomial Kernel Representation

The validity of the compressed sensing is premised on the sparsity of the signals.There is a known signal sparsity that there is a linear transformation that makes the signal sparse under the transformation.However,with the deepening of the compressed sensing research,the sparse structure is increasingly unable to meet the growing theoretical and application requirements.In order to deal with this challenge,this paper presents a new model based on the sample based on the nonlinear transformation to describe the sparseness of the sparse structure.Compared with the existing kernel principal component analysis and K-SVD nonlinear sparse representation model,our proposed model fully utilizes the sample data information to realize the robust reconstruction of complex signals.The main contents of this paper are as follows:The first chapter is the introduction,introduces the background and research status of traditional compressed sensing and nonlinear sparse signal reconstruction,that is,nonlinear compressed sensing.And then we give the full text of the organizational structure and the main content of the arrangement.In the second chapter,the reconstruction theory of sparse signal recovery in compressed sensing is briefly described,which mainly includes several main research directions.Respectively,signal sparse representation,measurement matrix design and reconstruction algorithm design.In this paper,a brief introduction to the current nonlinear compressed sensing is presented,that is,a preliminary study of nonlinear sparse signal representation.In the third chapter,we propose two assumptions about the nonlinear compressed sensing for the shortcomings of the existing sparse structure based on the linear representation and give the definition of the kernel sensing matrix K.According to the calculation of the nonlinear signal under the condition of kernel function,the original nonlinear sparse signal is solved indirectly by the kernel sensing matrix under the condition of obtaining the estimated value?? of the sparse vector ?.According to the traditional textbook on MIP,RIP,we give the definition of KMIP,KRIP in the meaning of the corresponding nonlinear compressed sensing theory,and the nonlinear compressed sensing model(3.4)is studied under the defined conditions.Solving the problem,we obtain the sufficient condition of the robust reconstruction of the problem,so we can finally get the exact reconstruction of the original nonlinear sparse signal.In the fourth chapter,we propose a new algorithm sample nonlinear compressed sensing(SNCS)for the third chapter.First,we choose different parameters c and d to restore one of the Sculpture Face images,compare the mean square error and kernel coherence KMIP we achieve the final selection of the parameters is c = 30,d = 3.And contrast with the existing KTCS,KCS algorithm,and the traditional ?1minimization algorithm.The experimental results indicate that: under the condition of appropriate selection of the measurement matrix A?the sample set X and the kernel function ?(x,y)= fk(?x,y?),SNCS has the ideal reconstruction effect.The results also show that the algorithm still has better reconstructing effect on the nonlinear sparse signal than the traditional compression sensor under the condition of lower measurement.The fifth chapter summarizes the work done in the text,and analyzes and prospects the direction that can be used as a follow-up study.