Robustness Reserch Of Sparse Signal Recovery With Its Applications

Sparse signal recovery is a key point in compressive sensing and is widely used in the fields such as machine learning,pattern recognition,image processing,array signal processing,and communication signal processing,etc.Consequently,for theoretical and practical account,it is important to study the problem of sparse signal recovery.Since in the real environment the noise can not be ignored,it is necessary to study the robustness of the sparse signal recovery.This dissertation provides a research on the robust sparse signal recovery with its applications in the presence of noise.The main contributions of the research are listed as follows.1.An improved block-sparse signal recovery algorithm,namely,the block-sparse orthogonal matching pursuit with threshold(B-OMPT)algorithm is proposed.By properly selecting the threshold,the efficiency of searching the support of block-sparse signal is improved.It is pointed out that the performance of the proposed algorithm depends on the setting of the threshold,and the proposed algorithm has some robustness for the support estimation.Simulation results demonstrate the validity of the proposed algorithm2.For the problem of sparse support recovery,a correlation information based model is studied.The sparse support recoverability via Least Absolute Shrinkage and Selection Operator(LASSO)regression and the adjustment of the regularization parameters in the noisy case are analyzed.The noise-related conditions to guarantee the sparse support recovery are provided.It is shown that the correlation information based model also has asymptotic robustness against the noise.3.To solve the problem of robust sparse signal recovery in the presence of impulsive noise,a robust reconstruction method is proposed using the theory of M-estimate.Specifically,the symmetric a-stable(S a S)distribution is used to model the impulsive noise.The maximum likelihood(ML)estimation is approximated by approximating the location score function of noise.A reweighted iterative hard threshold algorithm is proposed to solve the proposed model.The choosing of the basis function and the setting of the step size are also discussed.Moreover,the Cramér-Rao bound of the Oracle estimator is derived for the comparison in the simulation.4.For the robust complex-valued sparse signal reconstruction,signal modeling and optimization are investigated.Based on the assumption that the elements of the complex-valued noise are rotation invariant distributed,a generalized Lorentzian-norm based iterative hard thresholding algorithm is proposed.To show the validity of the proposed algorithm,some simulations are provided in which both the signal reconstruction and the application of direction-of-arrival(DOA)estimation are considered.5.For the application of sparse signal reconstruction,a robust DOA estimation algorithm is proposed.By properly representing the complex-valued measurement model as an augmented complex-valued measurement model,a robust DOA estimation model is proposed.Simulation results are provided to show the validity and superiority of the proposed algorithm.