DOA estimation method for wideband signals by block sparse reconstruction

For the direction of arrival（DOA） estimation,traditional sparse reconstruction methods for wideband signals usually need many iteration times.For this problem,a new method for two-dimensional wideband signals based on block sparse reconstruction is proposed.First,a prolate spheroidal wave function（PSWF） is used to fit the wideband signals,then the block sparse reconstruction technology is employed for DOA estimation.The proposed method uses orthogonalization to choose the matching atoms,ensuring that the residual components correspond to the minimum absolute value.Meanwhile,the vectors obtained by iteration are back-disposed according to the corresponding atomic matching rules,so the extra atoms are abandoned in the course of iteration,and the residual components of current iteration are reduced.Thus the original sparse signals are reconstructed.The proposed method reduces iteration times comparing with the traditional reconstruction methods,and the estimation precision is better than the classical two-sided correlation transformation（TCT）algorithm when the snapshot is small or the signal-to-noise ratio（SNR） is low.

Iterative sparse reconstruction of spectral domain OCT signal

We propose and study an iterative sparse reconstruction for Fourier domain optical coherence tomography （FD OCT） image by solving a constrained optimization problem that minimizes L-1 norm. Our method takes the spectral shape of the OCT light source into consideration in the iterative image reconstruction procedure that allows deconvolution of the axial point spread function from the blurred image during reconstruction rather than after reconstruction. By minimizing the L-1 norm, the axial resolution and the signal to noise ratio of image can both be enhanced. The effectiveness of our method is validated using numerical simulation and experiment.

An improved sparsity estimation variable step-size matching pursuit algorithm

To improve the reconstruction performance of the greedy algorithm for sparse signals, an improved greedy algorithm, called sparsity estimation variable step-size matching pursuit, is proposed. Compared with state-of-the-art greedy algorithms, the proposed algorithm incorporates the restricted isometry property and variable step-size, which is utilized for sparsity estimation and reduces the reconstruction time, respectively. Based on the sparsity estimation, the initial value including sparsity level and support set is computed at the beginning of the reconstruction, which provides preliminary sparsity information for signal reconstruction. Then, the residual and correlation are calculated according to the initial value and the support set is refined at the next iteration associated with variable step-size and backtracking. Finally, the correct support set is obtained when the halting condition is reached and the original signal is reconstructed accurately. The simulation results demonstrate that the proposed algorithm improves the recovery performance and considerably outperforms the existing algorithm in terms of the running time in sparse signal reconstruction.

Direction-of-Arrival Method Based on Randomize-Then-Optimize Approach

The direction-of-arrival(DOA)estimation problem can be solved by the methods based on sparse Bayesian learning(SBL).To assure the accuracy,SBL needs massive amounts of snapshots which may lead to a huge computational workload.In order to reduce the snapshot number and computational complexity,a randomize-then-optimize(RTO)algorithm based DOA estimation method is proposed.The“learning”process for updating hyperparameters in SBL can be avoided by using the optimization and Metropolis-Hastings process in the RTO algorithm.To apply the RTO algorithm for a Laplace prior,a prior transformation technique is induced.To demonstrate the effectiveness of the proposed method,several simulations are proceeded,which verifies that the proposed method has better accuracy with 1 snapshot and shorter processing time than conventional compressive sensing(CS)based DOA methods.

Coherence-based performance analysis of the generalized orthogonal matching pursuit algorithm

The performance guarantees of generalized orthogonal matching pursuit（ gOMP） are considered in the framework of mutual coherence. The gOMP algorithmis an extension of the well-known OMP greed algorithmfor compressed sensing. It identifies multiple N indices per iteration to reconstruct sparse signals.The gOMP with N≥2 can perfectly reconstruct any K-sparse signals frommeasurement y = Φx if K 〈1/N（1/μ-1） ＋1,where μ is coherence parameter of measurement matrix Φ. Furthermore,the performance of the gOMP in the case of y = Φx ＋ e with bounded noise ‖e‖2≤ε is analyzed and the sufficient condition ensuring identification of correct indices of sparse signals via the gOMP is derived,i. e.,K 〈1/N（1/μ-1）＋1-（2ε/Nμxmin） ,where x min denotes the minimummagnitude of the nonzero elements of x. Similarly,the sufficient condition in the case of G aussian noise is also given.

Method for denoising and reconstructing radar HRRP using modified sparse auto-encoder

A high resolution range profile(HRRP) is a summation vector of the sub-echoes of the target scattering points acquired by a wide-band radar.Generally, HRRPs obtained in a noncooperative complex electromagnetic environment are contaminated by strong noise.Effective pre-processing of the HRRP data can greatly improve the accuracy of target recognition.In this paper, a denoising and reconstruction method for HRRP is proposed based on a Modified Sparse Auto-Encoder, which is a representative non-linear model.To better reconstruct the HRRP, a sparse constraint is added to the proposed model and the sparse coefficient is calculated based on the intrinsic dimension of HRRP.The denoising of the HRRP is performed by adding random noise to the input HRRP data during the training process and fine-tuning the weight matrix through singular-value decomposition.The results of simulations showed that the proposed method can both reconstruct the signal with fidelity and suppress noise effectively, significantly outperforming other methods, especially in low Signal-to-Noise Ratio conditions.