基于Chirplet原子的雷达辐射源信号特征提取

特征提取是新体制雷达辐射源信号分选识别的关键技术.本文提出一种全新的雷达辐射源信号时频原子特征提取方法.在过完备多尺度Chirplet原子库基础上,采用匹配追踪(MP)方法对信号进行时频原子分解,并通过改进量子遗传算法(IQGA)降低MP搜索过程的时间复杂性,得到表示雷达辐射源信号特征信息的本征Chirplet原子.实验结果表明使用更少量的Chirplet原子可以得到比Gabor原子分解更准确的特征信息,证实了本文方法的可行性和有效性.     

Analysis-synthesis of the phonocardiogram based on the matchingpursuit method

The matching pursuit method of Mallat and Zhang (1993) is applied to the analysis and synthesis of phonocardiograms (PCGs). The method is based on a classical Gabor wavelet or time-frequency atom which is the product of a sinusoid and a Gaussian window function, it decomposes a signal into a series of time-frequency atoms by an iterative process based on selecting the largest inner product of the signal (and the subsequent residues) with atoms from a redundant dictionary. The Gaussian window controls the envelope duration and time position of each atom; and the sinusoid represents the frequency. The method was applied to two sets of PCGs: one with very low-noise level and the other with 10% noise energy. Each database includes 11 PCGs representing the normal and the pathological conditions of the heart. The normalized root-mean-square error (NRMSE) was computed between the original and the reconstructed signals. The results show that the matching pursuit method is very suitable to the transient and complex properties of the PCGs, as it yielded excellent NRMSEs around 2.2% for the two sets of 11 PCGs tested     

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     

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.     

基于迭代自适应的字典校正空时自适应处理算法

本文针对稀疏恢复空时自适应处理(Space-Time Adaptive Processing, STAP)由于字典设置不合适引起的离网效应，提出了一种基于迭代自适应(Iterative Adaptive Approach, IAA)的字典校正STAP算法。首先在IAA的每次迭代中，找到原始空时导向字典中每个量化空间频率最大功率对应的原子，围绕选定的原子，将其附近的多普勒频率均匀离散成一个集合，然后通过最大化联合似然函数在局域中搜索最优原子，并将选定的原子替换为最优原子，最后通过IAA的全局迭代，选择与杂波脊匹配的原子形成新的空时导向字典。实验证明，该方法可以有效地减轻离网效应引起的杂波脊扩展，杂波抑制性能优于现有的空时导向字典均匀离散化的IAA-STAP方法。      

Matching pursuits with time-frequency dictionaries

The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions. These waveforms are chosen in order to best match the signal structures. Matching pursuits are general procedures to compute adaptive signal representations. With a dictionary of Gabor functions a matching pursuit defines an adaptive time-frequency transform. They derive a signal energy distribution in the time-frequency plane, which does not include interference terms, unlike Wigner and Cohen class distributions. A matching pursuit isolates the signal structures that are coherent with respect to a given dictionary. An application to pattern extraction from noisy signals is described. They compare a matching pursuit decomposition with a signal expansion over an optimized wavepacket orthonormal basis, selected with the algorithm of Coifman and Wickerhauser see (IEEE Trans. Informat. Theory, vol. 38, Mar. 1992)     

Dictionary with tree structure for matching pursuit video coding

Matching pursuit video coding has many advantages. However, this method involves an extremely high computational cost. A new dictionary with a tree structure is proposed as a replacement for the Gabor dictionary. Equal video quality is achieved with both dictionaries but the computational cost is significantly reduced when using the proposed method     

基于子空间的三阶多项式相位信号快速稀疏分解算法

针对稀疏分解冗余字典中原子数量庞大的缺点,该文提出一种三阶多项式相位信号的快速稀疏分解算法。该算法根据三阶多项式相位信号的特点,把原有信号变换成两个子空间信号,并根据这两个子空间信号构建相应的冗余字典,然后采用正交匹配追踪法来完成其稀疏分解,最后利用稀疏分解原理完成原有信号的稀疏分解。该算法把原有信号变换成两个不同子空间信号,构建了两个不同的冗余字典,对比采用一个冗余字典库,这种采用两个冗余字典的算法大大减少了原子数量,并且通过快速傅里叶变换,在一个冗余字典进行稀疏分解时,同时找到另一个冗余字典中的最匹配的原子。因此该算法通过减少原子数量和采用快速傅里叶变换大大加快了稀疏分解速度。实验结果表明,相比于采用Gabor原子构建的冗余字典,采用匹配追踪算法与遗传算法及最近提出的基于调制相关划分的快速稀疏分解,它的稀疏分解速度更快,并且具有更好的收敛性。     

The adaptive chirplet transform and visual evoked potentials

We propose a new approach based upon the adaptive chirplet transform (ACT) to characterize the time-dependent behavior of the visual evoked potential (VEP) from its initial transient portion (tVEP) to the steady-state portion (ssVEP). This approach employs a matching pursuit (MP) algorithm to estimate the chirplets and then a maximum-likelihood estimation (MLE) algorithm to refine the results. The ACT decomposes signals into Gaussian chirplet basis functions with four adjustable parameters, i.e., time-spread, chirp rate, time-center and frequency-center. In this paper, we show how these four parameters can be used to distinguish between the transient and the steady-state phase of the response. We also show that as few as three chirplets are required to represent a VEP response. Compared to decomposition with Gabor logons, a more compact representation can be achieved by using Gaussian chirplets. Finally, we argue that the adaptive chirplet spectrogram gives a superior visualization of VEP signals' time-frequency structures when compared to the conventional spectrogram.     

A four-parameter atomic decomposition of chirplets

A new four-parameter atomic decomposition of chirplets is developed for compact and precise representation of signals with chirp components. The four-parameter chirplet atom is obtained from the unit Gaussian function by successive applications of scaling, fractional Fourier transform (FRFT), and time-shift and frequency-shift operators. The application of the FRFT operator results in a rotation of the Wigner distribution of the Gaussian in the time-frequency plane by a specified angle. The decomposition is realized by using the matching pursuit algorithm. For this purpose, the four-parameter space is discretized to obtain a small but complete subset in the Hilbert space. A time-frequency distribution (TFD) is developed for clear and readable visualization of the signal components. It is observed that the chirplet decomposition and the related TFD provide more compact and precise representation of signal inner structures compared with the commonly used time-frequency representations     

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     

A Gabor atom network for signal classification with application inradar target recognition

A Gabor atom neural network approach is proposed for signal classification. The Gabor atom network uses a multilayer feedforward neural network structure, and its input layer constitutes the feature extraction part, whereas the hidden layer and the output layer constitute the signal classification part. From the physics point of view, it is shown that the time-shifted, frequency-modulated, and scaled Gaussian function is available for a basic model for the signal of high-resolution radar. Two experiment examples show that the Gabor atom network approach has a higher recognition rate in radar target recognition from range profiles as compared with several existing methods     

改进多尺度Chirplet路径追踪算法在非线性调频信号估计中的应用

针对在低信噪比下雷达非线性调频信号(Non-linear Frequency Modulation,NLFM)瞬时频率估计精度不足的问题,提出一种基于多尺度线调频小波路径追踪算法(Multi-scale Chirplet Path Pursuit,MCPP)的拟合方法估计信号的瞬时频率。首先,该方法将时频平面分成二进制动态时间支撑区并形成多尺度线调频(Chirp)原子函数库;然后在每一个时间支撑区选择一个投影系数最大的Chirp原子,按照连接原则进行最佳路径连接;最后按时间支撑区顺序提取每个Chirp原子的起始和终止频率,采用最小二乘法进行瞬时频率拟合。仿真表明该方法在低信噪比下可以提高信号瞬时频率估计的精度。      

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.     

Adaptive subspace detection of extended target in white Gaussian noise using sinc basis

For the high resolution radar (HRR), the problem of detecting the extended target is considered in this paper. Based on a single observation, a new two-step detection based on sparse representation (TSDSR) method is proposed to detect the extended target in the presence of Gaussian noise with unknown covariance. In the new method, the Sinc dictionary is introduced to sparsely represent the high resolution range profile (HRRP). Meanwhile, adaptive subspace pursuit (ASP) is presented to recover the HRRP embedded in the Gaussian noise and estimate the noise covariance matrix. Based on the Sinc dictionary and the estimated noise covariance matrix, one step subspace detector (OSSD) for the first-order Gaussian (FOG) model without secondary data is adopted to realise the extended target detection. Finally, the proposed TSDSR method is applied to raw HRR data. Experimental results demonstrate that HRRPs of different targets can be sparsely represented very well with the Sinc dictionary. Moreover, the new method can estimate the noise power with tiny errors and have a good detection performance.     

基于信号稀疏分解的毫米波主动探测

基于信号稀疏分解的Gabor时频原子库,将毫米波主动探测回波信号进行分解与重构,提取原子的时频参数作为其特征信息,并用改进的混合粒子群算法克服计算量过大难以实现的问题。实验表明,文章所提方法利用少数的原子就可以表示回波信号的主要特征,为目标回波信号的分类和识别提供了依据。     

基于树形原子字典的匹配跟踪算法

为了降低匹配跟踪视频编码算法的运算复杂度,提出了一种原子字典的树形组织方法,并相应地提出了一种改进的树形字典搜索策略。此算法通过在树中寻找最优路径来搜索最佳原子,并在第一级搜索中引入了一种改进的全搜索策略,进一步降低了计算量。为了有效地捕捉预测误差帧中的曲线特征,冗余原子字典通过对各向异性的生成函数进行真正二维意义上的几何变换来构造,并尽可能地去除了性能不佳的原于以减小字典尺寸。实验结果表明,本文算法具有较高的搜索正确性及较快的收敛速度,而其计算量明显降低。     

基于字典学习的毫米波大规模MIMO系统混合预编码

针对毫米波大规模多输入多输出(MIMO)系统混合预编码方案设计的难题,采用字典学习的思想,提出了一种高精度混合预编码方案.该方案首先对全数字预编码矩阵的各列采用稀疏表示;进而按列将字典原子从稀疏表示中分离出来,通过对误差矩阵采用奇异值分解(SVD)来更新对应的字典原子,直到所有字典原子更新,以形成新的字典矩阵;最后,利用更新后的字典矩阵稀疏重构全数字预编码矩阵,以得到模拟预编码矩阵和数字预编码矩阵.仿真结果表明,相较于基于正交匹配追踪(OMP)的混合预编码方案,所提方案在提升系统频谱效率和降低误码率方面具有明显的优势.