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.

Compete Matching Pursuits Algorithm

Matching pursuits algorithm (MP), as an adaptive signal representation upon overcomplete fundamental waveforms, is a powerful tool in many applications. However, MP suffers from distinguishing a doublet structure. In this paper, the authors proposed an algorithm called compete matching pursuits (CMP), which can overcome this shortcoming and performance very well.

The W transform and its improved methods for time-frequency analysis of seismic data

The conventional linear time-frequency analysis method cannot achieve high resolution and energy focusing in the time and frequency dimensions at the same time,especially in the low frequency region.In order to improve the resolution of the linear time-frequency analysis method in the low-frequency region,we have proposed a W transform method,in which the instantaneous frequency is introduced as a parameter into the linear transformation,and the analysis time window is constructed which matches the instantaneous frequency of the seismic data.In this paper,the W transform method is compared with the Wigner-Ville distribution(WVD),a typical nonlinear time-frequency analysis method.The WVD method that shows the energy distribution in the time-frequency domain clearly indicates the gravitational center of time and the gravitational center of frequency of a wavelet,while the time-frequency spectrum of the W transform also has a clear gravitational center of energy focusing,because the instantaneous frequency corresponding to any time position is introduced as the transformation parameter.Therefore,the W transform can be benchmarked directly by the WVD method.We summarize the development of the W transform and three improved methods in recent years,and elaborate on the evolution of the standard W transform,the chirp-modulated W transform,the fractional-order W transform,and the linear canonical W transform.Through three application examples of W transform in fluvial sand body identification and reservoir prediction,it is verified that W transform can improve the resolution and energy focusing of time-frequency spectra.

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.

Single-trial evoked brain responses modeled by multichannel matching pursuit

A multichannel matching pursuit（MMP）algorithm is proposed to decompose the one-dimensional multichannel non-stationary magnetoencephalography（MEG）signal at a single-trial level.The single-channel matching pursuit（MP）linearly decomposes the signal into a set of Gabor atoms,which are adaptively chosen from an overcomplete dictionary with good time-frequency characters.The MMP is the extension of the MP,which represents multichannel signals using linear combination of Gabor atoms with the same occurrence,frequency,phase,and time width,but varying amplitude in all channels.The results demonstrate that the MMP can optimally reconstruct the original signal and automatically remove artifact noises.Moreover,the coherence between the 3D source reconstruction and the prior knowledge of psychology further suggests that the MMP is effective in MEG single-trial processing.

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.

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.

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.

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.

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.

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.

Single-Frequency Matching Pursuits Based Time-of-Flight Measurement in Viscoacoustic Medium

Broadband ultrasound signals will produce distortion in viscoacoustic medium, which may influence the accuracy of time-of-flight (TOF) measurement. Under the condition of single-frequency acoustic source, the wave propagation process in viscoacoustic medium was analyzed and an approximate solution of the wave propagation was given. Instances of broadband ultrasound were analyzed and simulated based on the single-frequency results. A single-frequency matching pursuits (SFMP) algorithm was then introduced to solve the waveform distortion problem. Time-frequency decomposition was applied to extracting the single-frequency compositions from broadband ultrasound signals, and then these compositions were sent to the matching pursuits (MP) algorithm for calculating the TOF parameters. Compared with the broadband signals, the shapes of extracted single-frequency signals change more slightly as distance and attenuation coefficient increase. The residuals of SFMP were far less than those of MP algorithm. Experimental results show that the SFMP algorithm is able to eliminate waveform distortion of broadband ultrasound in viscoacoustic medium, which helps improve the accuracy of TOF measurement.

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.

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.

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.

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.