Matching pursuit and atomic signal models based on recursive filterbanks

The matching pursuit algorithm can be used to derive signal decompositions in terms of the elements of a dictionary of time-frequency atoms. Using a structured overcomplete dictionary yields a signal model that is both parametric and signal adaptive. In this paper, we apply matching pursuit to the derivation of signal expansions based on damped sinusoids. It is shown that expansions in terms of complex damped sinusoids can be efficiently derived using simple recursive filter banks. We discuss a subspace extension of the pursuit algorithm that provides a framework for deriving real-valued expansions of real signals based on such complex atoms. Furthermore, we consider symmetric and asymmetric two-sided atoms constructed from underlying one-sided damped sinusoids. The primary concern is the application of this approach to the modeling of signals with transient behavior such as music; it is shown that time-frequency atoms based on damped sinusoids are more suitable for representing transients than symmetric Gabor atoms. The resulting atomic models are useful for signal coding and analysis modification synthesis     

Stochastic time-frequency dictionaries for matching pursuit

Analyzing large amounts of sleep electroencephalogram (EEG) data by means of the matching pursuit (MP) algorithm, we encountered a statistical bias of the decomposition, resulting from the structure of the applied dictionary. As a solution, we propose stochastic dictionaries, where the parameters of the dictionary's waveforms are randomized before each decomposition. The MP algorithm was modified for this purpose and tuned for maximum time-frequency resolution. Examples of applications of the new method include parameterization of EEG structures and time-frequency representation of signals with changing frequency     

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。     

Sparse approximation using M-term pursuit and application in image and video coding

This paper introduces a novel algorithm for sparse approximation in redundant dictionaries called the M-term pursuit (MTP). This algorithm decomposes a signal into a linear combination of atoms that are selected in order to represent the main signal components. The MTP algorithm provides an adaptive representation for signals in any complete dictionary. The basic idea behind the MTP is to partition the dictionary into L quasi-disjoint subdictionaries. A k-term signal approximation is then iteratively computed, where each iteration leads to the selection of M ≤ L atoms based on thresholding. The MTP algorithm is shown to achieve competitive performance with the matching pursuit (MP) algorithm that greedily selects atoms one by one. This is due to efficient partitioning of the dictionary. At the same time, the computational complexity is dramatically reduced compared to MP due to the batch selection of atoms. We finally illustrate the performance of MTP in image and video compression applications, where we show that the suboptimal atom selection of MTP is largely compensated by the reduction in complexity compared with MP.     

Harmonic decomposition of audio signals with matching pursuit

We introduce a dictionary of elementary waveforms, called harmonic atoms, that extends the Gabor dictionary and fits well the natural harmonic structures of audio signals. By modifying the "standard" matching pursuit, we define a new pursuit along with a fast algorithm, namely, the fast harmonic matching pursuit, to approximate N-dimensional audio signals with a linear combination of M harmonic atoms. Our algorithm has a computational complexity of O(MKN), where K is the number of partials in a given harmonic atom. The decomposition method is demonstrated on musical recordings, and we describe a simple note detection algorithm that shows how one could use a harmonic matching pursuit to detect notes even in difficult situations, e.g., very different note durations, lots of reverberation, and overlapping notes.     

A fast refinement for adaptive Gaussian chirplet decomposition

The chirp function is one of the most fundamental functions in nature. Many natural events, for example, most signals encountered in seismology and the signals in radar systems, can be modeled as the superposition of short-lived chirp functions. Hence, the chirp-based signal representation, such as the Gaussian chirplet decomposition, has been an active research area in the field of signal processing. A main challenge of the Gaussian chirplet decomposition is that Gaussian chirplets do not form an orthogonal basis. A promising solution is to employ adaptive type signal decomposition schemes, such as the matching pursuit. The general underlying theory of the matching pursuit method has been well accepted, but the numerical implementation, in terms of computational speed and accuracy, of the adaptive Gaussian chirplet decomposition remains an open research topic. We present a fast refinement algorithm to search for optimal Gaussian chirplets. With a coarse dictionary, the resulting adaptive Gaussian chirplet decomposition is not only fast but is also more accurate than other known adaptive schemes. The effectiveness of the algorithm introduced is demonstrated by numerical simulations     

基于先验估计的自适应Chirplet信号展开

该文提出一种新的时频表示方法--自适应线性调频小波(Chirplet)信号展开算法。算法基于信号本征空间,融参数的初值估计和精确估计于一体,利用匹配追踪算法将信号自适应地展开在高斯线性调频小波基函数集上。通过展开系数和基函数参数获得信号的时频分布,其时频聚集性、抗噪性和时频分辨率不仅优于一般的时频分布而且优于已有的自适应时频分布,可以更好地刻画信号的本质。应用数值仿真检验了算法的有效性和时频分布的优良性能。     

匹配追踪算法及其在MI-EEG的应用

介绍了采用随机时频函数词典的匹配追踪法（Matching Pursuit，MP）的基本原理，及其在运动想象脑电（Motor Imagination EEG，MI—EEG）分析中的应用。该算法可将信号分解成一系列时频原子函数的线性组合，并在每次分解前自适应地初始化时频原子的参数，它具有较高时-频分辨率和信号微观结构的参数化表示的优点。模拟信号分析表明MP算法可在强噪声背景下表达信号的基本时-频特征。在MI—EEG应用中，MP算法分析出脑电特定频率成分（如α波、β波）的一些规律，它们符合运动相关的mu节律的结论，且发生了事件相关EEG现象。     

Size of the dictionary in matching pursuit algorithm

The matching pursuit algorithm has been successfully applied in many areas such as data compression and pattern recognition. The performance of matching pursuit is closely related to the selection of the dictionary. In this paper, we propose an algorithm to estimate the optimal dictionary distribution ratio and discuss the decay of the norm of residual signal in matching pursuit when the coefficients are quantized by a uniform scalar quantizer. It is proposed that if the approximation error E and the dimension of the space N are given, the optimal size of the dictionary and the optimal quantizer step should be obtained by minimizing the number of bits required to store the matching pursuit representation of any signal in the space to satisfy the error bound.     

Single-Trial Evoked Brain Responses Modeled by Multivariate Matching Pursuit

We present a new approach to the analysis of brain evoked electromagnetic potentials and fields. Multivariate version of the matching pursuit algorithm (MMP) performs an iterative, exhaustive search for waveforms, which optimally fit to signal structures, persistent in all the responses (trials) with the same time of occurrence, frequency, phase, and time width, but varying amplitude. The search is performed in a highly redundant time--frequency dictionary of Gabor functions, i.e., sines modulated by Gaussians. We present the feasibility of such a single-trial MMP analysis of the auditory M100 response, using an illustrative dataset acquired in a magnetoencephalographic (MEG) measurement with auditory stimulation with sinusoidal 1-kHz tones. We find that the morphology of the M100 estimate obtained from simple averaging of single trials can be very well explained by the average reconstruction with a few Gabor functions that parametrize those single trials. The M100 peak amplitude of single-trial reconstructions is observed to decrease with repetitions, which indicates habituation to the stimulus. This finding suggests that certain waveforms fitted by MMP could possibly be related to physiologically distinct components of evoked magnetic fields, which would allow tracing their dynamics on a single-trial level.      

Matching pursuit algorithm for RCL decomposition with antennas dictionary

We develop robust algorithms (such as ‘matching pursuit’, ‘orthogonal matching pursuit’ which are methods of computing adaptive signal representations with respect to a nonorthogonal dictionary of basic building blocks) in order to decompose thercl signal of a 2D scatterer (an infinite perfectly conducting cylinder of triangular section) as a combination of elementary atoms from a redundant dictionary. Such a decomposition theoretically provides some antenna pattern arrangements that could be used for the minimization of thisrcl.     

基于OMP算法的风轮机杂波滤除研究

针对雷达在探测目标过程中风电场杂波的抑制问题,提出了一种基于正交匹配追踪(OMP)的杂波抑制算法。首先,建立风轮机的回波模型,分析了回波时频域特征;然后,推导了多径回波模型下的风轮机回波,介绍了风电场回波的特点;最后,给出了OMP算法的理论基础和实现步骤。该算法中,通过建立一个回波字典矩阵,寻找矩阵中最匹配原子,从目标信号中减去最匹配原子,并通过循环操作滤除杂波。实验结果表明:该方法能够有效滤除风轮机杂波。     

基于迭代自适应稀疏分解的雷达信号去噪

稀疏分解能有效分离信号和噪声,因此适用于信号去噪.文中构造了雷达回波稀疏表示的冗余字典,字典原子与目标回波波形匹配,基于该字典的雷达回波信号稀疏度就是目标数.针对稀疏度自适应匹配追踪算法进行低信噪比信号稀疏分解时的不足,提出了一种迭代自适应匹配追踪算法,采用规范化的残差之差作为迭代终止条件,使得稀疏分解过程能依据噪声水平自适应终止,以逐次逼近方式估计信号稀疏度,改善了稀疏分解的精度.仿真实验结果表明,该算法在低信噪比以及稀疏度未知的条件下,实现了雷达回波信号的准确稀疏分解,极大地提高了信噪比.     

由时频分布引导的四参数子空间匹配追踪算法

为了克服四参数匹配追踪计算量巨大的缺点,本文提出了一种由时频分布引导的四参数子空间匹配追踪算法.该算法由引导时频分布确定chirp原子的时频中心,然后用模板匹配方法搜索原子的尺度和调频率(chirp rate).这样,一个高计算复杂度的四维搜索问题被转化为两个相对简单的二维搜索问题.为有效利用时频分布,每次搜索多个时频原子,这些原子不再相互正交.为此,我们利用最小二乘方法计算信号(或残差信号)在相应子空间上的正交投影.同快速脊追踪算法相比,四参数子空间匹配追踪需要更少的原子逼近信号,对实测语音信号的数值计算也证实了这点.     

Forward sequential algorithms for best basis selection

The problem of signal representation in terms of basis vectors from a large, over-complete, spanning dictionary has been the focus of much research. Achieving a succinct, or `sparse', representation is known as the problem of best basis representation. Methods are considered which seek to solve this problem by sequentially building up a basis set for the signal. Three distinct algorithm types have appeared in the literature which are here termed basic matching pursuit (BMP), order recursive matching pursuit (ORMP) and modified matching pursuit (MMP). The algorithms are first described and then their computation is closely examined. Modifications are made to each of the procedures which improve their computational efficiency. The complexity of each algorithm is considered in two contexts; one where the dictionary is variable (time-dependent) and the other where the dictionary is fixed (time-independent). Experimental results are presented which demonstrate that the ORMP method is the best procedure in terms of its ability to give the most compact signal representation, followed by MMP and then BMP which gives the poorest results. Finally, weighing the performance of each algorithm, its computational complexity and the type of dictionary available, recommendations are made as to which algorithm should be used for a given problem     

Time-varying techniques for multisensor signal detection

In source detection and localization, the presence of a common but unknown signal can be detected from several noisy sensor measurements using the generalized coherence (GC) estimate. We propose to improve the performance of the GC estimate for multisensor detection using noise-suppressed signal estimates obtained from time-varying techniques. If one of the sensors has a significantly higher signal-to-noise ratio (SNR) than the other sensors, then it could be preprocessed prior to the GC estimate to improve detection performance for the remaining, lower SNR sensors. We perform this processing by estimating time-varying signals of interest with nonlinear phase functions using two methods: a) a modified matching pursuit decomposition (MMPD) algorithm whose dictionary is similar, in time-frequency structure, to the signal and b) an instantaneous frequency (IF) estimation method using highly localized time-frequency representations. The MMPD can yield signal estimates with lower mean square errors than the IF estimation technique but at the expense of higher computational cost and memory requirements. Using simulations, we compare the performance of the GC estimate with the significantly improved performance of the GC estimate that employs the signal estimate from the high SNR sensor. For the two-sensor detection, the estimated signal is also used with a generalized likelihood ratio test statistic to further improve performance.     

基于稀疏分解的高分辨雷达信号特征提取

从含噪的目标波形中提取稳健的目标特征,是准确识别目标的关键.通过稀疏分解将高分辨雷达回波信号展开于一个超完备Gabor时频字典上,从具有局部化时频结构的信号中提取相关特征量,并采用改进的混合粒子群算法降低匹配追踪过大计算量的问题.实验表明,使用少数原子就可以表示原信号的主要特征信息,可作为目标识别的依据.     

Fast matching pursuit with a multiscale dictionary of Gaussianchirps

We introduce a modified matching pursuit algorithm, called fast ridge pursuit, to approximate N-dimensional signals with M Gaussian chirps at a computational cost O(MN) instead of the expected O(MN² logN). At each iteration of the pursuit, the best Gabor atom is first selected, and then, its scale and chirp rate are locally optimized so as to get a “good” chirp atom, i.e., one for which the correlation with the residual is locally maximized. A ridge theorem of the Gaussian chirp dictionary is proved, from which an estimate of the locally optimal scale and chirp is built. The procedure is restricted to a sub-dictionary of local maxima of the Gaussian Gabor dictionary to accelerate the pursuit further. The efficiency and speed of the method is demonstrated on a sound signal     

Compressed sensing based deconvolution algorithm for time-domain UWB channel modeling

Extracting the parameters of the multipath with high accuracy can be achieved by using high-resolution algorithm for time-domain ultra wideband (UWB) channel modeling.The CLEAN algorithm has been used ...     

基于自适应冗余字典的语音信号稀疏表示算法

基于冗余字典的信号稀疏表示是一种新的信号表示理论,当前的理论研究主要集中在字典构造算法和稀疏分解算法两方面。该文提出一种新的基于自适应冗余字典的语音信号稀疏表示算法,该算法针对自相关函数为指数衰减的平稳信号,从K-L展开出发,建立了匹配信号结构的冗余字典,进而提出一种高效的基于非线性逼近的信号稀疏表示算法。实验结果表明冗余字典中原子的自适应性和代数结构使短时平稳语音信号稀疏表示具有较高的稀疏度和较好的重构精度,并使稀疏表示算法较好地应用于语音压缩感知理论。