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.

Ultrasonic Nondestructive Signals Processing Based on Matching Pursuit with Gabor Dictionary

The success of ultrasonic nondestructive testing technology depends not only on the generation and measurement of the desired waveform, but also on the signal processing of the measured waves. The traditional time-domain methods have been partly successful in identifying small cracks, but not so successful in estimating crack size, especially in strong backscattering noise. Sparse signal representation can provide sparse information that represents the signal time-frequency signature, which can also be used in processing ultrasonic nondestructive signals. A novel ultrasonic nondestructive signal processing algorithm based on signal sparse representation is proposed. In order to suppress noise, matching pursuit algorithm with Gabor dictionary is selected as the signal decomposition method. Precise echoes information, such as crack location and size, can be estimated by quantitative analysis with Gabor atom. To verify the performance, the proposed algorithm is applied to computer simulation signal and experimental ultrasonic signals which represent multiple backscattered echoes from a thin metal plate with artificial holes. The results show that this algorithm not only has an excellent performance even when dealing with signals in the presence of strong noise, but also is successful in estimating crack location and size. Moreover, the algorithm can be applied to data compression of ultrasonic nondestructive signal.

Noise amplitude modulation jamming signal suppression based on weighted-matching pursuit

To suppress noise amplitude modulation jamming in a single-antenna radar system, a new method based on weighted-matching pursuit （WMP） algorithm is proposed, which can achieve underdetermined blind sources separation of the jamming and the target echo from the jammed mixture in the single channel of the receiver. Firstly, the presented method utilizes a prior information about the differences between the jamming component and the radar transmitted signal to construct two signal-adapted sub-dictionaries and to determine the weights. Then the WMP algorithm is applied to remove the jamming component from the mixture. Experimental results verify the validity of the presented method. By comparison of the pulse compression performance, the simulation results shows that the presented method is superior to the method of frequency domain cancellation （FDC） when the jamming-to-signal ratio （JSR） is lower than 15 dB.

MATCHING PURSUITS AMONG SHIFTED CAUCHY KERNELS IN HIGHER-DIMENSIONAL SPACES

Appealing to the Clifford analysis and matching pursuits, we study the adaptive decompositions of functions of several variables of finite energy under the dictionaries consisting of shifted Cauchy kernels. This is a realization of matching pursuits among shifted Cauchy kernels in higher-dimensional spaces. It offers a method to process signals in arbitrary dimensions.

An application of matching pursuit time-frequency decomposition method using multi-wavelet dictionaries

In the time-frequency analysis of seismic signals, the matching pursuit algorithm is an effective tool for non-stationary signals, and has high time-frequency resolution and a transient structure with local self-adaption. We expand the time-frequency dictionary library with Ricker, Morlet, and mixed phase seismic wavelets, to make the method more suitable for seismic signal time-frequency decomposition. In this paper, we demonstrated the algorithm theory using synthetic seismic data, and tested the method using synthetic data with 25% noise. We compared the matching pursuit results of the time-frequency dictionaries. The results indicated that the dictionary which matched the signal characteristics better would obtain better results, and can reflect the information of seismic data effectively.

Fast M-fold matching pursuit algorithm for image approximation

A simple and effective greedy algorithm for image approximation is proposed. Based on the matching pursuit approach, it is characterized by a reduced computational complexity benefiting from two major modifications. First, it iteratively finds an approximation by selecting M atoms instead of one at a time. Second, the inner product computations are confined within only a fraction of dictionary atoms at each iteration. The modifications are implemented very efficiently due to the spatial incoherence of the dictionary. Experimental results show that compared with full search matching pursuit, the proposed algorithm achieves a speed-up gain of 14.4-36.7 times while maintaining the approximation quality.

Fast matching pursuit for traffic images using differential evolution

To obtain the sparse decomposition and flexible representation of traffic images,this paper proposes a fast matching pursuit for traffic images using differential evolution. According to the structural features of traffic images,the introduced algorithm selects the image atoms in a fast and flexible way from an over-complete image dictionary to adaptively match the local structures of traffic images and therefore to implement the sparse decomposition. As compared with the traditional method and a genetic algorithm of matching pursuit by using extensive experiments,the differential evolution achieves much higher quality of traffic images with much less computational time,which indicates the effectiveness of the proposed algorithm.

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.

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.

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.

Improving the reconstruction efficiency of sparsity adaptive matching pursuit based on the Wilkinson matrix

Sparsity adaptive matching pursuit(SAMP)is a greedy reconstruction algorithm for compressive sensing signals.SAMP reconstructs signals without prior information of sparsity and presents better reconstruction performance for noisy signals compared to other greedy algorithms.However,SAMP still suffers from relatively poor reconstruction quality especially at high compression ratios.In the proposed research,the Wilkinson matrix is used as a sensing matrix to improve the reconstruction quality and to increase the compression ratio of the SAMP technique.Furthermore,the idea of block compressive sensing(BCS)is combined with the SAMP technique to improve the performance of the SAMP technique.Numerous simulations have been conducted to evaluate the proposed BCS-SAMP technique and to compare its results with those of several compressed sensing techniques.Simulation results show that the proposed BCS-SAMP technique improves the reconstruction quality by up to six decibels(d B)relative to the conventional SAMP technique.In addition,the reconstruction quality of the proposed BCS-SAMP is highly comparable to that of iterative techniques.Moreover,the computation time of the proposed BCS-SAMP is less than that of the iterative techniques,especially at lower measurement fractions.

Decomposition and compression for ECG and EEG signals with sequence index coding method based on matching pursuit

An efficient compression method is proposed by encoding the sequence index of atoms based on matching pursuit （MP） algorithm with over-complete Gabor dictionary, which has the merit to adjust the compression ratio （CR） according to the practical request with low distortion. It is also combined with genetic algorithm （GA） to reduce the computation complexity Then, the validity of this method is verified by applying it in the compression of electrocardiography （ECG） and Electroencephalography （EEG） signals. The simulation results show that the CR can be achieved at 18：1 with only 1.06% and 2.15% reconstruction errors on ECG and EEG signals respectively. It has higher CR and less reconstruction errors compared to that of the traditional methods, and noise suppression effect is also presented.

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.

Application of Dopplerlet matching pursuit to estimate the range and speed of a moving vessel

This paper presents a new method to estimate the range and the speed of a moving vessel by the features of line spectrum. Dopplerlet matching pursuit are used to estimate range and speed. The line spectrums of moving vessel radiated-noises show some time-frequency features. The features of line spectrum reflect the variation of moving state of the vessel. The computer simulation shows the method is practicable and effective. Moreover, the method is applied to estimate the range and the speed of a real underwater signal and the results agree with the data of the experiment on the sea.

Research on Damage Localization of Plate-like Structure Using Mode Acoustic Emission and Matching Pursuit

Based on mode acoustic emission theory,the paper analyses the acoustic emission analog signal of thin steel plate using matching pursuit,then obtains the characteristics interpretation of the different frequency signal energy concentration degree; Combined with four-point arc positioning method,the papers researches the damage localization of the plate-like structure. Simulation experiment shows that this method can accurately detect and locate the damage. This can provide data support for further imaging research based on time reverse theory.

A Practical Approach for Missing Wireless Sensor Networks Data Recovery

In wireless sensor networks(WSNs),the performance of related applications is highly dependent on the quality of data collected.Unfortunately,missing data is almost inevitable in the process of data acquisition and transmission.Existing methods often rely on prior information such as low-rank characteristics or spatiotemporal correlation when recovering missing WSNs data.However,in realistic application scenarios,it is very difficult to obtain these prior information from incomplete data sets.Therefore,we aim to recover the missing WSNs data effectively while getting rid of the perplexity of prior information.By designing the corresponding measurement matrix that can capture the position of missing data and sparse representation matrix,a compressive sensing(CS)based missing data recovery model is established.Then,we design a comparison standard to select the best sparse representation basis and introduce average cross-correlation to examine the rationality of the established model.Furthermore,an improved fast matching pursuit algorithm is proposed to solve the model.Simulation results show that the proposed method can effectively recover the missing WSNs data.

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.

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.