Sparse Reconstructive Evidential Clustering for Multi-View Data

Although many multi-view clustering(MVC) algorithms with acceptable performances have been presented, to the best of our knowledge, nearly all of them need to be fed with the correct number of clusters. In addition, these existing algorithms create only the hard and fuzzy partitions for multi-view objects,which are often located in highly-overlapping areas of multi-view feature space. The adoption of hard and fuzzy partition ignores the ambiguity and uncertainty in the assignment of objects, likely leading to performance degradation. To address these issues, we propose a novel sparse reconstructive multi-view evidential clustering algorithm(SRMVEC). Based on a sparse reconstructive procedure, SRMVEC learns a shared affinity matrix across views, and maps multi-view objects to a 2-dimensional humanreadable chart by calculating 2 newly defined mathematical metrics for each object. From this chart, users can detect the number of clusters and select several objects existing in the dataset as cluster centers. Then, SRMVEC derives a credal partition under the framework of evidence theory, improving the fault tolerance of clustering. Ablation studies show the benefits of adopting the sparse reconstructive procedure and evidence theory. Besides,SRMVEC delivers effectiveness on benchmark datasets by outperforming some state-of-the-art methods.

Geophysical data sparse reconstruction based on L0-norm minimization

Missing data are a problem in geophysical surveys, and interpolation and reconstruction of missing data is part of the data processing and interpretation. Based on the sparseness of the geophysical data or the transform domain, we can improve the accuracy and stability of the reconstruction by transforming it to a sparse optimization problem. In this paper, we propose a mathematical model for the sparse reconstruction of data based on the LO-norm minimization. Furthermore, we discuss two types of the approximation algorithm for the LO- norm minimization according to the size and characteristics of the geophysical data： namely, the iteratively reweighted least-squares algorithm and the fast iterative hard thresholding algorithm. Theoretical and numerical analysis showed that applying the iteratively reweighted least-squares algorithm to the reconstruction of potential field data exploits its fast convergence rate, short calculation time, and high precision, whereas the fast iterative hard thresholding algorithm is more suitable for processing seismic data, moreover, its computational efficiency is better than that of the traditional iterative hard thresholding algorithm.

一种基于迭代近端投影的被动声纳探测离网格DOA估计方法

Traditional direction of arrival(DOA)estimation methods based on sparse reconstruction commonly use convex or smooth functions to approximate non-convex and non-smooth sparse representation problems.This approach often introduces errors into the sparse representation model,necessitating the development of improved DOA estimation algorithms.Moreover,conventional DOA estimation methods typically assume that the signal coincides with a predetermined grid.However,in reality,this assumption often does not hold true.The likelihood of a signal not aligning precisely with the predefined grid is high,resulting in potential grid mismatch issues for the algorithm.To address the challenges associated with grid mismatch and errors in sparse representation models,this article proposes a novel high-performance off-grid DOA estimation approach based on iterative proximal projection(IPP).In the proposed method,we employ an alternating optimization strategy to jointly estimate sparse signals and grid offset parameters.A proximal function optimization model is utilized to address non-convex and non-smooth sparse representation problems in DOA estimation.Subsequently,we leverage the smoothly clipped absolute deviation penalty(SCAD)function to compute the proximal operator for solving the model.Simulation and sea trial experiments have validated the superiority of the proposed method in terms of higher resolution and more accurate DOA estimation performance when compared to both traditional sparse reconstruction methods and advanced off-grid techniques.

A FAST CONVERGING SPARSE RECONSTRUCTION ALGORITHM IN GHOST IMAGING

A fast converging sparse reconstruction algorithm in ghost imaging is presented. It utilizes total variation regularization and its formulation is based on the Karush-Kuhn-Tucker (KKT) theorem in the theory of convex optimization. Tests using experimental data show that, compared with the algorithm of Gradient Projection for Sparse Reconstruction (GPSR), the proposed algorithm yields better results with less computation work.

Synthetic aperture radar imaging based on attributed scatter model using sparse recovery techniques

The sparse recovery algorithms formulate synthetic aperture radar （SAR） imaging problem in terms of sparse representation （SR） of a small number of strong scatters＇ positions among a much large number of potential scatters＇ positions, and provide an effective approach to improve the SAR image resolution. Based on the attributed scatter center model, several experiments were performed with different practical considerations to evaluate the performance of five representative SR techniques, namely, sparse Bayesian learning （SBL）, fast Bayesian matching pursuit （FBMP）, smoothed 10 norm method （SL0）, sparse reconstruction by separable approximation （SpaRSA）, fast iterative shrinkage-thresholding algorithm （FISTA）, and the parameter settings in five SR algorithms were discussed. In different situations, the performances of these algorithms were also discussed. Through the comparison of MSE and failure rate in each algorithm simulation, FBMP and SpaRSA are found suitable for dealing with problems in the SAR imaging based on attributed scattering center model. Although the SBL is time-consuming, it always get better performance when related to failure rate and high SNR.

Compressed sensing sparse reconstruction for coherent field imaging

Return signal processing and reconstruction plays a pivotal role in coherent field imaging, having a significant in- fluence on the quality of the reconstructed image. To reduce the required samples and accelerate the sampling process, we propose a genuine sparse reconstruction scheme based on compressed sensing theory. By analyzing the sparsity of the received signal in the Fourier spectrum domain, we accomplish an effective random projection and then reconstruct the return signal from as little as 10% of traditional samples, finally acquiring the target image precisely. The results of the numerical simulations and practical experiments verify the correctness of the proposed method, providing an efficient processing approach for imaging fast-moving targets in the future.

Maximal-minimal correlation atoms algorithm for sparse recovery

A new iterative algorithm is proposed to reconstruct an unknown sparse signal from a set of projected measurements. Unlike existing greedy pursuit methods which only consider the atoms having the highest correlation with the residual signal, the proposed algorithm not only considers the higher correlation atoms but also reserves the lower correlation atoms with the residual signal. In the lower correlation atoms, only a few are correct which usually impact the reconstructive performance and decide the reconstruction dynamic range of greedy pursuit methods. The others are redundant. In order to avoid redundant atoms impacting the reconstructive accuracy, the Bayesian pursuit algorithm is used to eliminate them. Simulation results show that the proposed algorithm can improve the reconstructive dynamic range and the reconstructive accuracy. Furthermore, better noise immunity compared with the existing greedy pursuit methods can be obtained.

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.

Radar Imaging of Sidelobe Suppression Based on Sparse Regularization

Synthetic aperture radar based on the matched filter theory has the ability of obtaining two-di- mensional image of the scattering areas. Nevertheless, the resolution and sidelobe level of SAR imaging is limited by the antenna length and bandwidth of transmitted signal. However, for sparse signals (direct or indirect), sparse imaging methods can break through limitations of the conventional SAR methods. In this paper, we introduce the basic theory of sparse representation and reconstruction, and then analyze several common sparse imaging algorithms: the greed algorithm, the convex optimization algorithm. We apply some of these algorithms into SAR imaging using RadBasedata. The results show the presented method based on sparse construction theory outperforms the conventional SAR method based on MF theory.

Target parameter estimation for OTFS-integrated radar and communications based on sparse reconstruction preprocessing

Orthogonal time-frequency space(OTFS)is a new modulation technique proposed in recent years for high Doppler wireless scenes.To solve the parameter estimation problem of the OTFS-integrated radar and communications system,we propose a parameter estimation method based on sparse reconstruction preprocessing to reduce the computational effort of the traditional weighted subspace fitting(WSF)algorithm.First,an OTFS-integrated echo signal model is constructed.Then,the echo signal is transformed to the time domain to separate the target angle from the range,and the range and angle of the detected target are coarsely estimated by using the sparse reconstruction algorithm.Finally,the WSF algorithm is used to refine the search with the coarse estimate at the center to obtain an accurate estimate.The simulations demonstrate the effectiveness and superiority of the proposed parameterestimation algorithm.

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.

Algorithm for reconstructing compressed sensing color imaging using the quaternion total variation

A new method for reconstructing the compressed sensing color image by solving an optimization problem based on total variation in the quaternion field is proposed, which can effectively improve the reconstructing ability of the color image. First, the color image is converted from RGB （red, green, blue） space to CMYK （cyan, magenta, yellow, black） space, which is assigned to a quaternion matrix. Meanwhile, the quaternion matrix is converted into the information of the phase and amplitude by the Euler form of the quatemion. Secondly, the phase and amplitude of the quatemion matrix are used as the smoothness constraints for the compressed sensing （CS） problem to make the reconstructing results more accurate. Finally, an iterative method based on gradient is used to solve the CS problem. Experimental results show that by considering the information of the phase and amplitude, the proposed method can achieve better performance than the existing method that treats the three components of the color image as independent parts.

Source Recovery in Underdetermined Blind Source Separation Based on Artificial Neural Network

We propose a novel source recovery algorithm for underdetermined blind source separation, which can result in better accuracy and lower computational cost. On the basis of the model of underdetermined blind source separation, the artificial neural network with single-layer perceptron is introduced into the proposed algorithm. Source signals are regarded as the weight vector of single-layer perceptron, and approximate ι~0-norm is taken into account for output error decision rule of the perceptron, which leads to the sparse recovery. Then the procedure of source recovery is adjusting the weight vector of the perceptron. What's more, the optimal learning factor is calculated and a descent sequence of smoothed parameter is used during iteration, which improves the performance and significantly decreases computational complexity of the proposed algorithm. The simulation results reveal that the algorithm proposed can recover the source signal with high precision, while it requires lower computational cost.

Imaging algorithm of multi-ship motion target based on compressed sensing

An imaging algorithm based on compressed sensing（CS） for the multi-ship motion target is presented. In order to reduce the quantity of data transmission in searching the ships on a large sea area, both range and azimuth of the moving ship targets are converted into sparse representation under certain signal basis. The signal reconstruction algorithm based on CS at a distant calculation station, and the Keystone and fractional Fourier transform（FRFT） algorithm are used to compensate range migration and obtain Doppler frequency. When the sea ships satisfy the sparsity, the algorithm can obtain higher resolution in both range and azimuth than the conventional imaging algorithm. Some simulations are performed to verify the reliability and stability.

Primary Research of EIT Inverse Problem Based on CS （Compressed Sensing） Technique

EIT （electrical impedance tomography） problem should be represented by a group of partial differential equation, in numerical calculation： the nonlinear problem should be linearization approximately, and then linear equations set is obtained, so EIT image reconstruct problem should be considered as a classical ill-posed, ill-conditioned, linear inverse problem. Its biggest problem is the number of unknown is much more than the number of the equations, this result in the low imaging quality. Especially, it can not imaging in center area. For this problem, we induce the CS technique into EIT image reconstruction algorithm. The main contributions in this paper are： firstly, built up the relationship between CS and EIT definitely; secondly, sparse reconstruction is a critical step in CS, built up a general sparse regularization model based on EIT; finally, gives out some EIT imaging models based on sparse regularization method. For different scenarios, compared with traditional Tikhonov regularization （smooth regularization） method, sparse reconstruction method is not only better at anti-noise, and imaging in center area, but also faster and better resolution.

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.

RECONSTRUCTION OF SPARSE POLYNOMIALS VIA QUASI-ORTHOGONAL MATCHING PURSUIT METHOD

In this paper,we propose a Quasi-Orthogonal Matching Pursuit(QOMP)algorithm for constructing a sparse approximation of functions in terms of expansion by orthonormal polynomials.For the two kinds of sampled data,data with noises and without noises,we apply the mutual coherence of measurement matrix to establish the convergence of the QOMP algorithm which can reconstruct s-sparse Legendre polynomials,Chebyshev polynomials and trigonometric polynomials in s step iterations.The results are also extended to general bounded orthogonal system including tensor product of these three univariate orthogonal polynomials.Finally,numerical experiments will be presented to verify the effectiveness of the QOMP method.

RM-CSTV:An effective high-resolution method of non-line-of-sight millimeter-wave radar 3-D imaging

Non-line-of-sight(NLOS)imaging is a novel radar sensing technology that enables the reconstruction of hidden targets.However,it may suffer from synthetic aperture length reduction caused by ambient occlusion.In this study,a complex total variation(CTV)regularization-based sparse reconstruction method for NLOS three-dimensional(3-D)imaging by millimeter-wave(mm W)radar,named RM-CSTV method,is proposed to improve imaging quality and speed.In this scheme,the NLOS imaging model is first introduced,and associated geometric constraints for NLOS objects are established.Second,an effective high-resolution NLOS imaging method based on the range migration(RM)kernel and complex sparse joint total variation constraint,dubbed as modified RM-CSTV,is proposed for 3-D high-resolution imaging with edge information.The experiments with multi-type NLOS targets show that the proposed RM-CSTV method can provide effective and high-resolution NLOS targets 3-D imaging.

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.