Coherence Based Sufficient Condition for Support Recovery Using Generalized Orthogonal Matching Pursuit

In an underdetermined system,compressive sensing can be used to recover the support vector.Greedy algorithms will recover the support vector indices in an iterative manner.Generalized Orthogonal Matching Pursuit(GOMP)is the generalized form of the Orthogonal Matching Pursuit(OMP)algorithm where a number of indices selected per iteration will be greater than or equal to 1.To recover the support vector of unknown signal‘x’from the compressed measurements,the restricted isometric property should be satisfied as a sufficient condition.Finding the restricted isometric constant is a non-deterministic polynomial-time hardness problem due to that the coherence of the sensing matrix can be used to derive the sufficient condition for support recovery.In this paper a sufficient condition based on the coherence parameter to recover the support vector indices of an unknown sparse signal‘x’using GOMP has been derived.The derived sufficient condition will recover support vectors of P-sparse signal within‘P’iterations.The recovery guarantee for GOMP is less restrictive,and applies to OMP when the number of selection elements equals one.Simulation shows the superior performance of the GOMP algorithm compared with other greedy algorithms.

Based on Compressed Sensing of Orthogonal Matching Pursuit Algorithm Image Recovery

Compressive sensing theory mainly includes the sparsely of signal processing,the structure of the measurement matrix and reconstruction algorithm.Reconstruction algorithm is the core content of CS theory,that is,through the low dimensional sparse signal recovers the original signal accurately.This thesis based on the theory of CS to study further on seismic data reconstruction algorithm.We select orthogonal matching pursuit algorithm as a base reconstruction algorithm.Then do the specific research for the implementation principle,the structure of the algorithm of AOMP and make the signal simulation at the same time.In view of the OMP algorithm reconstruction speed is slow and the problems need to be a given number of iterations,which developed an improved scheme.We combine the optimized OMP algorithm of constraint the optimal matching of item selection strategy,the backwards gradient projection ideas of adaptive variance step gradient projection method and the original algorithm to improve it.Simulation experiments show that improved OMP algorithm is superior to traditional OMP algorithm of improvement in the reconstruction time and effect under the same condition.This paper introduces CS and most mature compressive sensing algorithm at present orthogonal matching pursuit algorithm.Through the program design realize basic orthogonal matching pursuit algorithms,and design realize basic orthogonal matching pursuit algorithm of one-dimensional,two-dimensional signal processing simulation.

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.

Robustness of orthogonal matching pursuit under restricted isometry property

Orthogonal matching pursuit （OMP） algorithm is an efficient method for the recovery of a sparse signal in compressed sensing, due to its ease implementation and low complexity. In this paper, the robustness of the OMP algorithm under the restricted isometry property （RIP） is presented. It is shown that 5K＋V/KOK,1 〈 1 is sufficient for the OMP algorithm to recover exactly the support of arbitrary /（-sparse signal if its nonzero components are large enough for both 12 bounded and lz~ bounded noises.

A new result on recovery sparse signals using orthogonal matching pursuit

Orthogonal matching pursuit(OMP)algorithm is a classical greedy algorithm widely used in compressed sensing.In this paper,by exploiting the Wielandt inequality and some properties of orthogonal projection matrix,we obtained a new number of iterations required for the OMP algorithm to perform exact recovery of sparse signals,which improves significantly upon the latest results as we know.

THE EXACT RECOVERY OF SPARSE SIGNALS VIA ORTHOGONAL MATCHING PURSUIT

This paper aims to investigate sufficient conditions for the recovery of sparse signals via the orthogonal matching pursuit （OMP） algorithm. In the noiseless case, we present a novel sufficient condition for the exact recovery of all k-sparse signals by the OMP algorithm, and demonstrate that this condition is sharp. In the noisy case, a sufficient condition for recovering the support of k-sparse signal is also presented. Generally, the computation for the restricted isometry constant （RIC） in these sufficient conditions is typically difficult, therefore we provide a new condition which is not only computable but also sufficient for the exact recovery of all k-sparse signals.

The Recovery Guarantee for Orthogonal Matching Pursuit Method to Reconstruct Sparse Polynomials

Orthogonal matching pursuit(OMP for short)algorithm is a popular method of sparse signal recovery in compressed sensing.This paper applies OMP to the sparse polynomial reconstruction problem.Distinguishing from classical research methods using mutual coherence or restricted isometry property of the measurement matrix,the recovery guarantee and the success probability of OMP are obtained directly by the greedy selection ratio and the probability theory.The results show that the failure probability of OMP given in this paper is exponential small with respect to the number of sampling points.In addition,the recovery guarantee of OMP obtained through classical methods is lager than that of ℓ_(1)-minimization whatever the sparsity of sparse polynomials is,while the recovery guarantee given in this paper is roughly the same as that of ℓ_(1)-minimization when the sparsity is less than 93.Finally,the numerical experiments verify the availability of the theoretical results.

QBFO-BOMP Based Channel Estimation Algorithm for mmWave Massive MIMO Systems

At present,the traditional channel estimation algorithms have the disadvantages of over-reliance on initial conditions and high complexity.The bacterial foraging optimization(BFO)-based algorithm has been applied in wireless communication and signal processing because of its simple operation and strong self-organization ability.But the BFO-based algorithm is easy to fall into local optimum.Therefore,this paper proposes the quantum bacterial foraging optimization(QBFO)-binary orthogonal matching pursuit(BOMP)channel estimation algorithm to the problem of local optimization.Firstly,the binary matrix is constructed according to whether atoms are selected or not.And the support set of the sparse signal is recovered according to the BOMP-based algorithm.Then,the QBFO-based algorithm is used to obtain the estimated channel matrix.The optimization function of the least squares method is taken as the fitness function.Based on the communication between the quantum bacteria and the fitness function value,chemotaxis,reproduction and dispersion operations are carried out to update the bacteria position.Simulation results showthat compared with other algorithms,the estimationmechanism based onQBFOBOMP algorithm can effectively improve the channel estimation performance of millimeter wave(mmWave)massive multiple input multiple output(MIMO)systems.Meanwhile,the analysis of the time ratio shows that the quantization of the bacteria does not significantly increase the complexity.

Analysis of orthogonal multi-matching pursuit under restricted isometry property

Orthogonal multi-matching pursuit（OMMP）is a natural extension of orthogonal matching pursuit（OMP）in the sense that N（N≥1）indices are selected per iteration instead of 1.In this paper,the theoretical performance of OMMP under the restricted isometry property（RIP）is presented.We demonstrate that OMMP can exactly recover any K-sparse signal from fewer observations y=φx,provided that the sampling matrixφsatisfiesδKN-N＋1＋√K/NθKN-N＋1,N〈1.Moreover,the performance of OMMP for support recovery from noisy observations is also discussed.It is shown that,for l_2 bounded and l_∞bounded noisy cases,OMMP can recover the true support of any K-sparse signal under conditions on the restricted isometry property of the sampling matrixφand the minimum magnitude of the nonzero components of the signal.

A modified OMP method for multi-orbit three dimensional ISAR imaging of the space target

The conventional two dimensional(2D)inverse synthetic aperture radar(ISAR)imaging fails to provide the targets'three dimensional(3D)information.In this paper,a 3D ISAR imaging method for the space target is proposed based on mutliorbit observation data and an improved orthogonal matching pursuit(OMP)algorithm.Firstly,the 3D scattered field data is converted into a set of 2D matrix by stacking slices of the 3D data along the elevation direction dimension.Then,an improved OMP algorithm is applied to recover the space target's amplitude information via the 2D matrix data.Finally,scattering centers can be reconstructed with specific three dimensional locations.Numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed 3D imaging method.

A Novel Efficient and Effective Preprocessing Algorithm for Text Classification

Text classification is an essential task of natural language processing. Preprocessing, which determines the representation of text features, is one of the key steps of text classification architecture. It proposed a novel efficient and effective preprocessing algorithm with three methods for text classification combining the Orthogonal Matching Pursuit algorithm to perform the classification. The main idea of the novel preprocessing strategy is that it combined stopword removal and/or regular filtering with tokenization and lowercase conversion, which can effectively reduce the feature dimension and improve the text feature matrix quality. Simulation tests on the 20 newsgroups dataset show that compared with the existing state-of-the-art method, the new method reduces the number of features by 19.85%, 34.35%, 26.25% and 38.67%, improves accuracy by 7.36%, 8.8%, 5.71% and 7.73%, and increases the speed of text classification by 17.38%, 25.64%, 23.76% and 33.38% on the four data, respectively.

GS-orthogonalization OMP method for space target detection via bistatic space-based radar

A space-based bistatic radar system composed of two space-based radars as the transmitter and the receiver respectively has a wider surveillance region and a better early warning capability for high-speed targets,and it can detect focused space targets more flexibly than the monostatic radar system or the ground-based radar system.However,the target echo signal is more difficult to process due to the high-speed motion of both space-based radars and space targets.To be specific,it will encounter the problems of Range Cell Migration(RCM)and Doppler Frequency Migration(DFM),which degrade the long-time coherent integration performance for target detection and localization inevitably.To solve this problem,a novel target detection method based on an improved Gram Schmidt(GS)-orthogonalization Orthogonal Matching Pursuit(OMP)algorithm is proposed in this paper.First,the echo model for bistatic space-based radar is constructed and the conditions for RCM and DFM are analyzed.Then,the proposed GS-orthogonalization OMP method is applied to estimate the equivalent motion parameters of space targets.Thereafter,the RCM and DFM are corrected by the compensation function correlated with the estimated motion parameters.Finally,coherent integration can be achieved by performing the Fast Fourier Transform(FFT)operation along the slow time direction on compensated echo signal.Numerical simulations and real raw data results validate that the proposed GS-orthogonalization OMP algorithm achieves better motion parameter estimation performance and higher detection probability for space targets detection.

Infrared small target detection using sparse representation

Sparse representation has recently been proved to be a powerful tool in image processing and object recognition.This paper proposes a novel small target detection algorithm based on this technique.By modelling a small target as a linear combination of certain target samples and then solving a sparse 0-minimization problem,the proposed apporach successfully improves and optimizes the small target representation with innovation.Furthermore,the sparsity concentration index（SCI） is creatively employed to evaluate the coefficients of each block representation and simpfy target identification.In the detection frame,target samples are firstly generated to constitute an over-complete dictionary matrix using Gaussian intensity model（GIM）,and then sparse model solvers are applied to finding sparse representation for each sub-image block.Finally,SCI lexicographical evalution of the entire image incorparates with a simple threshold locate target position.The effectiveness and robustness of the proposed algorithm are demonstrated by the exprimental results.

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.

OMHT method for weak signal processing of GPR and its application in identification of concrete micro-crack

In the light of the problem of weak reflection signals shielded by strong reflections from the concrete surface,the detection and the recognition of hidden micro-cracks in the shield tunnel lining were studied using the orthogonal matching pursuit and the Hilbert transform(OMHT method).First,according to the matching pursuit algorithm and the strong reflection-forming mechanism,and based on the sparse representation theory,a sparse dictionary,adapted to the characteristics of the strong reflection signal,was selected,and a matching decomposition of each signal was performed so that the weak target signal submerged in the strong reflection was displayed more strongly.Second,the Hilbert transform was used to extract multiple parameters,such as the instantaneous amplitude,the instantaneous frequency,and the instantaneous phase,from the processed signal,and the ground penetrating radar(GPR)image was comprehensively analyzed and determined from multiple angles.The results show that the OMHT method can accurately weaken the effect of the strong impedance interface and effectively enhance the weak reflected signal energy of hidden micro-crack in the shield tunnel segment.The resolution of the processed GPR image is greatly improved,and the reflected signal of the hidden micro-crack is easily visible,which proves the validity and accuracy of the analysis method.

Root imaging from ground penetrating radar data by CPSO-OMP compressed sensing

As the amount of data produced by ground penetrating radar （GPR） for roots is large, the transmission and the storage of data consumes great resources. To alleviate this problem, we propose here a root imaging algorithm using chaotic particle swarm optimal （CPSO） compressed sensing based on GPR data according to the sparsity of root space. Radar data are decomposed, observed, measured and represented in sparse manner, so roots image can be reconstructed with limited data. Firstly, radar signal measurement and sparse representation are implemented, and the solution space is established by wavelet basis and Gauss random matrix; secondly, the matching function is considered as the fitness function, and the best fitness value is found by a PSO algorithm; then, a chaotic search was used to obtain the global optimal operator; finally, the root image is reconstructed by the optimal operators. A-scan data, B-scan data, and complex data from American GSSI GPR is used, respectively, in the experimental test. For B-scan data, the computation time was reduced 60 % and PSNR was improved 5.539 dB; for actual root data imaging, the reconstruction PSNR was 26.300 dB, and total computation time was only 67.210 s. The CPSO-OMP algorithm overcomes the problem of local optimum trapping and comprehensively enhances the precision during reconstruction.

Modified OMP method for multi-target parameter estimation in frequency-agile distributed MIMO radar

Introducing frequency agility into a distributed multipleinput multiple-output(MIMO)radar can significantly enhance its anti-jamming ability.However,it would cause the sidelobe pedestal problem in multi-target parameter estimation.Sparse recovery is an effective way to address this problem,but it cannot be directly utilized for multi-target parameter estimation in frequency-agile distributed MIMO radars due to spatial diversity.In this paper,we propose an algorithm for multi-target parameter estimation according to the signal model of frequency-agile distributed MIMO radars,by modifying the orthogonal matching pursuit(OMP)algorithm.The effectiveness of the proposed method is then verified by simulation results.

A Novel Training Sequence Applied to DCS-Based Channel Estimation

Studies have indicated that the distributed compressed sensing based(DCSbased) channel estimation can decrease the length of the reference signals effectively. In block transmission, a unique word(UW) can be used as a cyclic prefix and reference signal. However, the DCS-based channel estimation requires diversity sequences instead of UW. In this paper, we proposed a novel method that employs a training sequence(TS) whose duration time is slightly longer than the maximum delay spread time. Based on proposed TS, the DCS approach perform perfectly in multipath channel estimation. Meanwhile, a cyclic prefix construct could be formed, which reduces the complexity of the frequency domain equalization(FDE) directly. Simulation results demonstrate that, by using the method of simultaneous orthogonal matching pursuit(SOMP), the required channel overhead has been reduced thanks to the proposed TS.

An underwater acoustic data compression method based on compressed sensing

The use of underwater acoustic data has rapidly expanded with the application of multichannel, large-aperture underwater detection arrays. This study presents an underwater acoustic data compression method that is based on compressed sensing. Underwater acoustic signals are transformed into the sparse domain for data storage at a receiving terminal, and the improved orthogonal matching pursuit(IOMP) algorithm is used to reconstruct the original underwater acoustic signals at a data processing terminal. When an increase in sidelobe level occasionally causes a direction of arrival estimation error, the proposed compression method can achieve a 10 times stronger compression for narrowband signals and a 5 times stronger compression for wideband signals than the orthogonal matching pursuit(OMP) algorithm. The IOMP algorithm also reduces the computing time by about 20% more than the original OMP algorithm. The simulation and experimental results are discussed.

AN ADAPTIVE MEASUREMENT SCHEME BASED ON COMPRESSED SENSING FOR WIDEBAND SPECTRUM DETECTION IN COGNITIVE WSN

An Adaptive Measurement Scheme (AMS) is investigated with Compressed Sensing (CS) theory in Cognitive Wireless Sensor Network (C-WSN). Local sensing information is collected via energy detection with Analog-to-Information Converter (AIC) at massive cognitive sensors, and sparse representation is considered with the exploration of spatial temporal correlation structure of detected signals. Adaptive measurement matrix is designed in AMS, which is based on maximum energy subset selection. Energy subset is calculated with sparse transformation of sensing information, and maximum energy subset is selected as the row vector of adaptive measurement matrix. In addition, the measurement matrix is constructed by orthogonalization of those selected row vectors, which also satisfies the Restricted Isometry Property (RIP) in CS theory. Orthogonal Matching Pursuit (OMP) reconstruction algorithm is implemented at sink node to recover original information. Simulation results are performed with the comparison of Random Measurement Scheme (RMS). It is revealed that, signal reconstruction effect based on AMS is superior to conventional RMS Gaussian measurement. Moreover, AMS has better detection performance than RMS at lower compression rate region, and it is suitable for large-scale C-WSN wideband spectrum sensing.