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.

一种基于Matching pursuits时频分解算法的语音降噪方法

提出一种基于时频分解算法的语音降噪方法,利用Matchingpursuits时频分解算法对含噪语音信号进行分解,把分解后的各个分量的魏格纳分布之和作为整个信号的魏格纳分布,这样便使得信号和噪声在时频平面上有了较直观的分布,利用这个特点对信号进行降噪。仿真结果表明,该方法能在保证可听懂度的情况下,有效地去除含噪语音信号中的宽带噪声。

Matching Pursuits方法综述

Matching Pursuits(匹配逼近)算法是在一个确定的函数集合中自适应地选择一些函数来表示一个信号的计算过程,函数集合中的每个函数都称为原子.多样化的信号特征决定了可以精确刻画信号特征的原子的类型,而重复迭代逼近的贪婪算法又确定了运算效率是MP算法的存在和发展的问题核心.本文围绕MP算法中原子库的生成,原子参数的搜索索引方式和迭代逼近过程中的快速算法等方面,阐述了MP算法发展变化过程.

基于FFT-Matching Pursuit的心电身份识别算法研究

研究了心电信号在身份识别中的应用,提出了基于快速傅里叶变换的匹配追踪心电特征提取算法。在预处理阶段,对心电信号进行消噪、标准化和质量检测等预处理,有效去除了心电信号中的噪声和心率变异所带来的干扰。特征提取阶段,对心电模板进行基于快速傅里叶变换的匹配追踪稀疏分解,原子的时频参数和投影值作为特征参数,然后构建支持向量机分类器,实现了身份识别。最后利用MIT-BIH的ST Change、PTB、QT等数据库测试了算法性能,获得了较高的识别率。

Matching Pursuits视频编码中原子匹配块搜索中的权值设计

基于 Matching Pursuits的误差图像编码算法因其基函数的灵活性 ,是一种在低码率视频编码应用中较为理想的算法 ,块能量搜索算法被用于减少该算法的编码复杂度 .针对固定权值加权块搜索算法的不足之处 ,提出了一种自适应加权块搜索算法 ,在不增加算法复杂度的情况下 ,对不同的被编码序列采用不同的权值表完成加权块能量算法 ;在各种情况下均得到了较理想的编码效果 .

基于Matching Pursuits时频分解算法的传声器阵语音增强

根据在时频域中对含噪语音信号进行的时频分析研究,提出1种基于MatchingPursuits时频分解算法的语音降噪方法。利用MatchingPursuits算法对含噪语音信号进行分解,将分解后各分量的魏格纳分布之和作为整个信号的魏格纳分布,使信号在时频平面上有较直观的分布,并利用此特点对信号进行降噪。仿真结果表明:此方法能在保证可懂度的情况下,有效去除含噪语音信号中的宽带噪声。

基于Matching Pursuit算法的阵列信号降噪方法

提出了一种基于Matching Pursuit算法的阵列信号降噪方法,有效改进了DOA估计的性能。该算法首先依据信号模型构建过完备原子库,然后通过梯度跟踪的稀疏分解方法找到最优原子。利用最优原子重构的信号在有效消除噪声的同时保留了信号的全部空间方位特征。计算机仿真证明,新方法与传统的DOA估计方法相结合有效地提高了阵列信号DOA估计的精度和准确度。

Acoustic sound speed profile inversion based on orthogonal matching pursuit

The estimation of ocean sound speed profiles(SSPs)requires the inversion of an acoustic field using limited observations.Such inverse problems are underdetermined,and require regularization to ensure physically realistic solutions.The empirical orthonormal function(EOF)is capable of a very large compression of the data set.In this paper,the non-linear response of the sound pressure to SSP is linearized using a first order Taylor expansion,and the pressure is expanded in a sparse domain using EOFs.Since the parameters of the inverse model are sparse,compressive sensing(CS)can help solve such underdetermined problems accurately,efficiently,and with enhanced resolution.Here,the orthogonal matching pursuit(OMP)is used to estimate range-independent acoustic SSPs using the simulated acoustic field.The superior resolution of OMP is demonstrated with the SSP data from the South China Sea experiment.By shortening the duration of the training set,the temporal correlation between EOF and test sets is enhanced,and the accuracy of sound velocity inversion is improved.The SSP estimation error versus depth is calculated,and the 99%confidence interval of error is within±0.6 m/s.The 82%of mean absolute error(MAE)is less than 1 m/s.It is shown that SSPs can be well estimated using OMP.

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.

基于Matching Pursuit的音像信号的分析

利用声音和视频数据的相关性可以检测出该音像信号中的发声源.传统的方法,对视频序列的表示是基于像素的方法,而对声音的表示运用的则是类似Fourier变换的方法,这些考虑的仅仅是边缘效应.本文提出了基于Matching Pursuit(MP)框架下表示音像信号的方法,利用冗余的字典能更好的表示信号结构中比较突出变化的部分,有效地减少了引入的信号的时变变量,利用Pearson系数,对测试序列进行了音像熔合分析,仿真结果表明能定位视频序列中声源的位置.

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.

Guided Waves Mode Discrimination in Pipes NDT Based on the Matching Pursuit Method

Ultrasonic guided wave have the multi-modes and dispersive characteristics, and its modes are easy to be converted at boundary or when running into defects in pipes, which makes the discrimination of different guided waves modes of the reflection signals in pipes NDT very hard. In this work, firstly, the experiments are carried out to test two kinds of stainless steel pipes by applying guided waves NDT, one is integrated pipe and another is non-integrated pipe with a small hole defect, and the detected guided waves echo signals are respectively obtained. Secondly, the measured signals are processed by matching pursuit method and the Chirplet matching atom parameters are calculated. By calculating the time-frequency distributions spectrum of detected guided waves echo signals, torsional, flexural and longitudinal guided waves modes are identified from the intact pipe, and the two wave-packets with torsional and flexural guided waves modes are also identified from the pipe with hole defect. The results showed that the matching pursuit method has a tremendous advantage to identify different guided waves modes in pipes nondestructive testing.

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.

DOPPLERLET BASED TIME-FREQUENCY REPRESENTATION VIA MATCHING PURSUITS

A new time-frequency representation called Dopplerlet transform, which uses the dilated, translated and modulated windowed Doppler signals as its basis functions, is proposed, and the Fourier transform, short-time Fourier transform (including Gabor transform), wavelet transform, and chirplet transform are formulated in one framework of Dopplerlet transform accordingly.It is proved that the matching pursuits based on Dopplerlet basis functions are convergent, and that the energy of residual signals yielded in the decomposition process decays exponentially. Simulation results show that the matching pursuits with Dopplerlet basis functions can characterize compactly a nonstationary signal.

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.