Algorithms For Sparse Recovery With The Nearest Neighbor Mapping And Generative Adversarial Networks Via Manifold Constraints

In recent years,the Nyquist sampling theorem has always been the foundation of traditional signal sampling.However,the theorem requires that the signal can be recovered accurately when the sampling rate is more than twice of the bandwidth of the signal.Therefore,the compressed sensing theory has emerged,and is the latest but most effective-compressed processing technology on signal sampling instead of the Nyquist sampling theorem.It is also called as the compressed sensing theory.The theory is based on the sparse and compression of the signal.The compression and sampling of the signal has been realized at the same time.It has been applied to many fields of science and engineering successfully.It has become a research hotspot of scholars at home and abroad in recent years.The theory mainly includes the following three basic problems,sparse representation of the signal,construction of the sampling matrix and establishment of the recovery algorithm.More recently,the research of machine learning has made great progress.However,the early generation model is not very prosperous.A new model,called generative adversarial networks,has become a popular topic in the field of artificial intelligence.In this dissertation,we devote ourself to research on the sparse recovery algorithms based on proximal mapping for solving the problem of sparse recovery for compressed sensing and Nesterov accelerated algorithm on generative adversarial networks via manifold constraints about deep learning.Firstly,the classical algorithms of sparse recovery in compressed sensing theory are intro-duced,including three kinds of algorithms,convex relaxation algorithms,greedy pursuit algorithms and non convex optimization algorithms.In addition the proximal mapping and generative adversarial networks are also introduced.Secondly,based on the Semi-Iterative algorithm and combining the hard threshold theory,a new semi-iterative hard threshold s-parse recovery algorithm is proposed,and the performance of the algorithm is verified by a large number of experiments.Then,for the sparse signal recovery problem when the spar-sity is unknown for compressed sensing recovery algorithms,a new algorithm is proposed where the first outer loop is carried out to estimate the sparsity of the signal adaptively,and the inner loop is carried out for our adaptive quasi-Newton projection recovery algorithm based on the combination of hard threshold function and the quasi-Newton method.Thus,the approximation recovered signal is better than other algorithms,which has been verified by our experimental results.Finally,in view of the difficulty to obtain labeled samples for polarimetric synthetic aperture radar data,we propose a new Nesterov accelerated algorithm on generative adversarial networks based on manifold constraints.The experimental results show that the classification accuracy of the polarimetric synthetic aperture radar data is dra-matically enhanced compared with the conventional algorithms.The main contributions of this dissertation are as follows:1.Since the negative gradient direction is used as the search direction in hard threshold algorithms for sparse recovery of compressed sensing,it leads to the disadvantages of the"zigzag" effect and a slow convergence speed.Based on this observation,according to the semi-iterative theory about our semi-iterative method and a two-step iterative method of Landweber and threshold theory about hard threshold mapping and soft threshold mapping,under the background of compressed sensing theory,and sparsity or compressibility of sig-nals,a semi-iterative hard threshold sparse recovery algorithm is proposed.The algorithm uses the linear combination of the previous search direction and the current negative gradient direction as the iterative search direction of the current step.Combined with hard threshold theory,it not only avoids the generation of zigzag effect,and but also speeds up the conver-gence rate.By comparing in terms of the choice of parameters,the calculation of recovery rate,the computation time of recovery,the comparison of sparsity,and the calculation of iteration times,a large number of experiments show that the proposed algorithm has many advantages compared with other algorithms,such as a short recovery time,fewer iterations and high accuracy.And it has a better performance.2.Greedy algorithms are sparse recovery algorithms in compressed sensing and require to know the sparsity of signal in advance,which is difficult to achieve in practice.In view of this situation,based on quasi-Newton projection sparse recovery algorithms and estimating the sparsity of the signal,an adaptive quasi-Newton projection sparse recovery algorithm is proposed.The algorithm is divided into two loops:the sparsity of the signal is estimated by using a thresholding operator in the outer loop,and the sparse signal is recovered based on a quasi-Newton projection algorithm under the current sparsity of the outer iterative es-timation in the inner loop.The algorithm with the quasi-Newton direction avoids the need to calculate the inverse matrix of the Hessian matrix,and thus the calculation is simple and fast.Experimental results show that our proposed method can have a better approximation performance and recovery rate of sparse signals with unknown sparsity compared with the greedy algorithms with known sparsity in advance.And the estimated sparsity is very close to the actual sparsity.3.Traditional generation network training algorithm use the random gradient descent algo-rithm to network training.The training algorithms have some shortcomings of high com-plexity,long training time,low classification accuracy.As a generation model of unsu-pervised learning,GAN has become one of the new research hotspots in the field of deep learning.In order to overcome the difficulty to obtain labeled samples for polarimetric syn-thetic aperture radar data and classification accuracy is low,we propose a new generative adversarial networks algorithm based on manifold constraints.Using a large number of unlabeled generated samples,the algorithm not only can get the intrinsic characteristics of data,but also make the network training algorithm more stable.Based on this algorithm,the ground feature classification experiments of the polarimetric Synthetic Aperture Radar data are completed.The experimental results show that the classification accuracy is dramatically enhanced compared with the conventional algorithms.The experimental results show that the algorithm compared with the mainstream algorithms has the significant improvement in the classification accuracy with a small amount of titled data.