THE STABLE RECONSTRUCTION OF STRONGLY-DECAYING BLOCK SPARSE SIGNALS

In this paper,we reconstruct strongly-decaying block sparse signals by the block generalized orthogonal matching pursuit(BgOMP)algorithm in the l2-bounded noise case.Under some restraints on the minimum magnitude of the nonzero elements of the strongly-decaying block sparse signal,if the sensing matrix satisfies the the block restricted isometry property(block-RIP),then arbitrary strongly-decaying block sparse signals can be accurately and steadily reconstructed by the BgOMP algorithm in iterations.Furthermore,we conjecture that this condition is sharp.

SRMD:Sparse Random Mode Decomposition

Signal decomposition and multiscale signal analysis provide many useful tools for timefrequency analysis.We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram.The randomization is both in the time window locations and the frequency sampling,which lowers the overall sampling and computational cost.The sparsification of the spectrogram leads to a sharp separation between time-frequency clusters which makes it easier to identify intrinsic modes,and thus leads to a new data-driven mode decomposition.The applications include signal representation,outlier removal,and mode decomposition.On benchmark tests,we show that our approach outperforms other state-of-the-art decomposition methods.

Gearbox Fault Diagnosis using Adaptive Zero Phase Time-varying Filter Based on Multi-scale Chirplet Sparse Signal Decomposition

When used for separating multi-component non-stationary signals, the adaptive time-varying filter(ATF) based on multi-scale chirplet sparse signal decomposition(MCSSD) generates phase shift and signal distortion. To overcome this drawback, the zero phase filter is introduced to the mentioned filter, and a fault diagnosis method for speed-changing gearbox is proposed. Firstly, the gear meshing frequency of each gearbox is estimated by chirplet path pursuit. Then, according to the estimated gear meshing frequencies, an adaptive zero phase time-varying filter(AZPTF) is designed to filter the original signal. Finally, the basis for fault diagnosis is acquired by the envelope order analysis to the filtered signal. The signal consisting of two time-varying amplitude modulation and frequency modulation(AM-FM) signals is respectively analyzed by ATF and AZPTF based on MCSSD. The simulation results show the variances between the original signals and the filtered signals yielded by AZPTF based on MCSSD are 13.67 and 41.14, which are far less than variances (323.45 and 482.86) between the original signals and the filtered signals obtained by ATF based on MCSSD. The experiment results on the vibration signals of gearboxes indicate that the vibration signals of the two speed-changing gearboxes installed on one foundation bed can be separated by AZPTF effectively. Based on the demodulation information of the vibration signal of each gearbox, the fault diagnosis can be implemented. Both simulation and experiment examples prove that the proposed filter can extract a mono-component time-varying AM-FM signal from the multi-component time-varying AM-FM signal without distortion.

DOA estimation of coexisted noncoherent and coherent signals via sparse representation of cleaned array covariance matrix

A new direction finding method is presented to deal with coexisted noncoherent and co- herent signals without smoothing operation. First the direction-of-arrival （DOA） estimation task is herein reformulated as a sparse reconstruction problem of the cleaned array covariance matrix, which is processed to eliminate the affection of the noise. Then by using the block of matrices, the information of DOAs which we pursuit are implied in the sparse coefficient matrix. Finally, the sparse reconstruction problem is solved by the improved M-FOCUSS method, which is applied to the situation of block of matrices. This method outperforms its data domain counterpart in terms of noise suppression, and has a better performance in DOA estimation than the customary spatial smoothing technique. Simulation results verify the efficacy of the proposed method.

DOA estimation method for wideband signals by sparse recovery in frequency domain

The traditional super-resolution direction finding methods based on sparse recovery need to divide the estimation space into several discrete angle grids, which will bring the final result some error. To this problem, a novel method for wideband signals by sparse recovery in the frequency domain is proposed. The optimization functions are found and solved by the received data at every frequency, on this basis, the sparse support set is obtained, then the direction of arrival (DOA) is acquired by integrating the information of all frequency bins, and the initial signal can also be recovered. This method avoids the error caused by sparse recovery methods based on grid division, and the degree of freedom is also expanded by array transformation, especially it has a preferable performance under the circumstances of a small number of snapshots and a low signal to noise ratio (SNR).

Underwater Noise Target Recognition Based on Sparse Adversarial Co-Training Model with Vertical Line Array

The automatic identification of underwater noncooperative targets without label records remains an arduous task considering the marine noise interference and the shortage of labeled samples.In particular,the data-driven mechanism of deep learning cannot identify false samples,aggravating the difficulty in noncooperative underwater target recognition.A semi-supervised ensemble framework based on vertical line array fusion and the sparse adversarial co-training algorithm is proposed to identify noncooperative targets effectively.The sound field cross-correlation compression(SCC)feature is developed to reduce noise and computational redundancy.Starting from an incomplete dataset,a joint adversarial autoencoder is constructed to extract the sparse features with source depth sensitivity,aiming to discover the unknown underwater targets.The adversarial prediction label is converted to initialize the joint co-forest,whose evaluation function is optimized by introducing adaptive confidence.The experiments prove the strong denoising performance,low mean square error,and high separability of SCC features.Compared with several state-of-the-art approaches,the numerical results illustrate the superiorities of the proposed method due to feature compression,secondary recognition,and decision fusion.

2D DOA Estimation of Coherent Signals with a Separated Linear Acoustic Vector-Sensor Array

In this paper, a two-dimensional(2D) DOA estimation algorithm of coherent signals with a separated linear acoustic vector-sensor(AVS) array consisting of two sparse AVS arrays is proposed. Firstly,the partitioned spatial smoothing(PSS) technique is used to construct a block covariance matrix, so as to decorrelate the coherency of signals. Then a signal subspace can be obtained by singular value decomposition(SVD) of the covariance matrix. Using the signal subspace, two extended signal subspaces are constructed to compensate aperture loss caused by PSS.The elevation angles can be estimated by estimation of signal parameter via rotational invariance techniques(ESPRIT) algorithm. At last, the estimated elevation angles can be used to estimate automatically paired azimuth angles. Compared with some other ESPRIT algorithms, the proposed algorithm shows higher estimation accuracy, which can be proved through the simulation results.

Filtering noisy chaotic signal via sparse representation based on random frame dictionary

The denoising problem of impure chaotic signals is addressed in this paper. A method based on sparse representation is proposed, in which the random frame dictionary is generated by a chaotic random search algorithm. The numerical simulation shows the proposed algorithm outperforms those recently reported alternative denoising methods.

Chaotic signal denoising algorithm based on sparse decomposition

Denoising of chaotic signal is a challenge work due to its wide-band and noise-like characteristics.The algorithm should make the denoised signal have a high signal to noise ratio and retain the chaotic characteristics.We propose a denoising method of chaotic signals based on sparse decomposition and K-singular value decomposition(K-SVD)optimization.The observed signal is divided into segments and decomposed sparsely.The over-complete atomic library is constructed according to the differential equation of chaotic signals.The orthogonal matching pursuit algorithm is used to search the optimal matching atom.The atoms and coefficients are further processed to obtain the globally optimal atoms and coefficients by K-SVD.The simulation results show that the denoised signals have a higher signal to noise ratio and better preserve the chaotic characteristics.

Obtaining Prior Information for Ultrasonic Signal Reconstruction from FRI Sparse Sampling Data

Finite rate of innovation sampling is a novel sub-Nyquist sampling method that can reconstruct a signal from sparse sampling data.The application of this method in ultrasonic testing greatly reduces the signal sampling rate and the quantity of sampling data.However,the pulse number of the signal must be known beforehand for the signal reconstruction procedure.The accuracy of this prior information directly affects the accuracy of the estimated parameters of the signal and influences the assessment of flaws,leading to a lower defect detection ratio.Although the pulse number can be pre-given by theoretical analysis,the process is still unable to assess actual complex random orientation defects.Therefore,this paper proposes a new method that uses singular value decomposition(SVD) for estimating the pulse number from sparse sampling data and avoids the shortcoming of providing the pulse number in advance for signal reconstruction.When the sparse sampling data have been acquired from the ultrasonic signal,these data are transformed to discrete Fourier coefficients.A Hankel matrix is then constructed from these coefficients,and SVD is performed on the matrix.The decomposition coefficients reserve the information of the pulse number.When the decomposition coefficients generated by noise according to noise level are removed,the number of the remaining decomposition coefficients is the signal pulse number.The feasibility of the proposed method was verified through simulation experiments.The applicability was tested in ultrasonic experiments by using sample flawed pipelines.Results from simulations and real experiments demonstrated the efficiency of this method.

Compression techniques of mechanical vibration signals based on optimal sparse representations

This paper presents the result of an experimental study on the compression of mechanical vibration signals. The signals are collected from both rotating and reciprocating machineries by the accelerometers and a data acquisition （DAQ） system. Four optimal sparse representation methods for compression have been considered including the method of frames （ MOF）, best orthogonal basis （ BOB）, matching pursuit （MP） and basis pursuit （BP）. Furthermore, several indicators including compression ratio （CR）, mean square error （MSE）, energy retained （ER） and Kurtosis are taken to evaluate the performance of the above methods. Experimental results show that MP outperforms other three methods.

Finite rate of innovation sparse sampling for a binary frequency-coded ultrasonic signal

To achieve sparse sampling on a coded ultrasonic signal,the finite rate of innovation(FRI)sparse sampling technique is proposed on a binary frequency-coded(BFC)ultrasonic signal.A framework of FRI-based sparse sampling for an ultrasonic signal pulse is presented.Differences between the pulse and the coded ultrasonic signal are analyzed,and a response mathematical model of the coded ultrasonic signal is established.A time-domain transform algorithm,called the high-order moment method,is applied to obtain a pulse stream signal to assist BFC ultrasonic signal sparse sampling.A sampling of the output signal with a uniform interval is then performed after modulating the pulse stream signal by a sampling kernel.FRI-based sparse sampling is performed using a self-made circuit on an aluminum alloy sample.Experimental results show that the sampling rate reduces to 0.5 MHz,which is at least 12.8 MHz in the Nyquist sampling mode.The echo peak amplitude and the time of flight are estimated from the sparse sampling data with maximum errors of 9.324%and 0.031%,respectively.This research can provide a theoretical basis and practical application reference for reducing the sampling rate and data volume in coded ultrasonic testing.

Pulse Signal Recovery Method Based on Sparse Representation

Pulse signal recovery is to extract useful amplitude and time information from the pulse signal contaminated by noise. It is a great challenge to precisely recover the pulse signal in loud background noise. The conventional approaches,which are mostly based on the distribution of the pulse energy spectrum,do not well determine the locations and shapes of the pulses. In this paper,we propose a time domain method to reconstruct pulse signals. In the proposed approach,a sparse representation model is established to deal with the issue of the pulse signal recovery under noise conditions. The corresponding problem based on the sparse optimization model is solved by a matching pursuit algorithm. Simulations and experiments validate the effectiveness of the proposed approach on pulse signal recovery.

Parametrically Optimal, Robust and Tree-Search Detection of Sparse Signals

We consider sparse signals embedded in additive white noise. We study parametrically optimal as well as tree-search sub-optimal signal detection policies. As a special case, we consider a constant signal and Gaussian noise, with and without data outliers present. In the presence of outliers, we study outlier resistant robust detection techniques. We compare the studied policies in terms of error performance, complexity and resistance to outliers.

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.

Numerical Studies of the Generalized <i>l</i>₁Greedy Algorithm for Sparse Signals

The generalized l1 greedy algorithm was recently introduced and used to reconstruct medical images in computerized tomography in the compressed sensing framework via total variation minimization. Experimental results showed that this algorithm is superior to the reweighted l1-minimization and l1 greedy algorithms in reconstructing these medical images. In this paper the effectiveness of the generalized l1 greedy algorithm in finding random sparse signals from underdetermined linear systems is investigated. A series of numerical experiments demonstrate that the generalized l1 greedy algorithm is superior to the reweighted l1-minimization and l1 greedy algorithms in the successful recovery of randomly generated Gaussian sparse signals from data generated by Gaussian random matrices. In particular, the generalized l1 greedy algorithm performs extraordinarily well in recovering random sparse signals with nonzero small entries. The stability of the generalized l1 greedy algorithm with respect to its parameters and the impact of noise on the recovery of Gaussian sparse signals are also studied.

Application of sparse time-frequency decomposition to seismic data

The Gabor and S transforms are frequently used in time-frequency decomposition methods. Constrained by the uncertainty principle, both transforms produce low-resolution time-frequency decomposition results in the time and frequency domains. To improve the resolution of the time-frequency decomposition results, we use the instantaneous frequency distribution function（IFDF） to express the seismic signal. When the instantaneous frequencies of the nonstationary signal satisfy the requirements of the uncertainty principle, the support of IFDF is just the support of the amplitude ridges in the signal obtained using the short-time Fourier transform. Based on this feature, we propose a new iteration algorithm to achieve the sparse time-frequency decomposition of the signal. The iteration algorithm uses the support of the amplitude ridges of the residual signal obtained with the short-time Fourier transform to update the time-frequency components of the signal. The summation of the updated time-frequency components in each iteration is the result of the sparse timefrequency decomposition. Numerical examples show that the proposed method improves the resolution of the time-frequency decomposition results and the accuracy of the analysis of the nonstationary signal. We also use the proposed method to attenuate the ground roll of field seismic data with good results.

A fast decoupled ISAR high-resolution imaging method using structural sparse information under low SNR

Inverse synthetic aperture radar (ISAR) image can be represented and reconstructed by sparse recovery (SR) approaches. However, the existing SR algorithms, which are used for ISAR imaging, have suffered from high computational cost and poor imaging quality under a low signal to noise ratio (SNR) condition. This paper proposes a fast decoupled ISAR imaging method by exploiting the inherent structural sparse information of the targets. Firstly, the ISAR imaging problem is decoupled into two sub-problems. One is range direction imaging and the other is azimuth direction focusing. Secondly, an efficient two-stage SR method is proposed to obtain higher resolution range profiles by using jointly sparse information. Finally, the residual linear Bregman iteration via fast Fourier transforms (RLBI-FFT) is proposed to perform the azimuth focusing on low SNR efficiently. Theoretical analysis and simulation results show that the proposed method has better performence to efficiently implement higher-resolution ISAR imaging under the low SNR condition.

Power-line interference suppression of MT data based on frequency domain sparse decomposition

Power-line interference is one of the most common noises in magnetotelluric(MT)data.It usually causes distortion at the fundamental frequency and its odd harmonics,and may also affect other frequency bands.Although trap circuits are designed to suppress such noise in most of the modern acquisition devices,strong interferences are still found in MT data,and the power-line interference will fluctuate with the changing of load current.The fixed trap circuits often fail to deal with it.This paper proposes an alternative scheme for power-line interference removal based on frequency-domain sparse decomposition.Firstly,the fast Fourier transform of the acquired MT signal is performed.Subsequently,a redundant dictionary is designed to match with the power-line interference which is insensitive to the useful signal.Power-line interference is separated by using the dictionary and a signal reconstruction algorithm of compressive sensing called improved orthogonal matching pursuit(IOMP).Finally,the frequency domain data are switched back to the time domain by the inverse fast Fourier transform.Simulation experiments and real data examples from Lu-Zong ore district illustrate that this scheme can effectively suppress the power-line interference and significantly improve data quality.Compared with time domain sparse decomposition,this scheme takes less time consumption and acquires better results.

A robust clustering algorithm for underdetermined blind separation of sparse sources

In underdetermined blind source separation, more sources are to be estimated from less observed mixtures without knowing source signals and the mixing matrix. This paper presents a robust clustering algorithm for underdetermined blind separation of sparse sources with unknown number of sources in the presence of noise. It uses the robust competitive agglomeration （RCA） algorithm to estimate the source number and the mixing matrix, and the source signals then are recovered by using the interior point linear programming. Simulation results show good performance of the proposed algorithm for underdetermined blind sources separation （UBSS）.