Real-Valued Discrete Gabor Transform of Linear Time-Varying Systems: Exact Representation and Approximation

An efficient algorithm for the representation and approximation of linear time-varying systems is presented via the fast real-valued discrete Gabor transform. Compared with the existing algorithm based on the traditional complex-valued discrete Gabor transform, the proposed algorithm runs faster, can more easily be implemented in software or hardware, and leads to a more compact representation. Simulation results are given for demonstration.

Effects of Gabor transform parameters on signa time-frequency resolution

窗函数的衰减系数和采样间隔究竟对地球物理信号时频分辨率造成多大的影响,如何才能更好地消除这种影响,是该文的主要出发点。提高分辨率是信号时频分析处理的关键,在地球物理数据处理和属性参数提取等方面具有重要作用和广泛应用。该文研究了Gabor变换窗函数衰减系数选择正确与否和采样间隔对信号分辨率的影响。参数选择不当,不仅降低信号时频谱的分辨率,甚至要丢失信号。在用Gabor变换作时频分析时,通过模拟计算预先给出最佳窗函数和最佳参数范围是十分必要的。文中还给出了常规地震信号最佳采样间隔的范围和选择、处理方法。

Compressive sampling and reconstruction in shift-invariant spaces associated with the fractional Gabor transform

In this paper,we propose a compressive sampling and reconstruction system based on the shift-invariant space associated with the fractional Gabor transform.With this system,we aim to achieve the subNyquist sampling and accurate reconstruction for chirp-like signals containing time-varying characteristics.Under the proposed scheme,we introduce the fractional Gabor transform to make a stable expansion for signals in the joint time-fractional-frequency domain.Then the compressive sampling and reconstruction system is constructed under the compressive sensing and shift-invariant space theory.We establish the reconstruction model and propose a block multiple response extension of sparse Bayesian learning algorithm to improve the reconstruction effect.The reconstruction error for the proposed system is analyzed.We show that,with considerations of noises and mismatches,the total error is bounded.The effectiveness of the proposed system is verified by numerical experiments.It is shown that our proposed system outperforms the other systems state-of-the-art.

Weinstein Gabor Transform and Applications

In this paper we consider Weinstein operator. We define and study the continuous Gabor transform associated with this operator. We prove a Plancherel formula, an inversion formula and a weak uncertainty principle for it. As applications, we obtain analogous of Heisenberg’s inequality for the generalized continuous Gabor transform. At the end we give the practical real inversion formula for the generalized continuous Gabor transform.

Spectrally Efficient Multi-Carrier Modulation Using Gabor Transform

Non Orthogonal Frequency Division Multiplexing (NOFDM) systems make use of a transmission signal set which is not restricted to orthonormal bases unlike previous OFDM systems. The usage of non-orthogonal bases generally results in a trade-off between Bit Error Rate (BER) and receiver complexity. This paper studies the use of Gabor based on designing a Spectrally Efficient Multi-Carrier Modulation Scheme. Using Gabor Transform with a specific Gaussian envelope;we derive the expected BER-SNR performance. The spectral usage of such a NOFDM system when affected by a channel that imparts Additive White Gaussian Noise (AWGN) is estimated. We compare the obtained results with an OFDM system and observe that with comparable BER performance, this system gives a better spectral usage. The effect of window length on spectral usage is also analyzed.

基于Gabor变换的电网调度自动化设备运行状态监控技术

提出基于Gabor变换的电网调度自动化设备运行状态监控技术。该方法从电网调度自动化设备的大规模数据库技术和自动化电网调度技术入手,分别采集2项技术在电网调度自动化设备运行中存储和调度的状态信息,并将状态信息与Gabor变换结合,消除状态信息携带的干扰噪声,通过将优化后的状态信息输入以模糊神经网络与电网调度自动化设备健康评估体系为基础建立的设备运行状态监控模型中,实现电网调度自动化设备运行状态监控。实验结果表明,所提方法能够迅速监控电网调度自动化设备运行故障状态,监控功率与实际功率一致,监控精确度高。

Analysis of frequency shifting in seismic signals using Gabor-Wigner transform

A hybrid time-frequency method known as Gabor-Wigner transform (GWT) is introduced in this paper for examining the time-frequency patterns of earthquake damaged buildings. GWT is developed by combining the Gabor transform (GT) and Wigner-Ville distribution (WVD). GT and WVD have been used separately on synthetic and recorded earthquake data to identify frequency shifting due to earthquake damages, but GT is prone to windowing effect and WVD involves ambiguity function. Hence to obtain better clarity and to remove the cross terms (frequency interference), GT and WVD are judiciously combined and the resultant GWT used to identify frequency shifting. Synthetic seismic response of an instrumented building and real-time earthquake data recorded on the building were investigated using GWT. It is found that GWT offers good accuracy for even slow variations in frequency, good time-frequency resolution, and localized response. Presented results confirm the efficacy of GWT when compared with GT and WVD used separately. Simulation results were quantified by the Renyi entropy measures and GWT shown to be an adequate technique in identifying localized response for structural damage detection.

基于多尺度多方向Gabor变换的Tsallis熵阈值分割方法

为了能在统一框架内处理无模态、单模态、双模态或者多模态直方图情形下的自动阈值选取问题,该文提出一种基于多尺度多方向Gabor变换的Tsallis熵阈值分割方法(MGTE)。该方法先通过Gabor变换得到多尺度乘积图像,然后利用内外轮廓图像从多尺度乘积图像中重构1维直方图,并在重构1维直方图上采用Tsallis熵计算模型来选取4个方向Tsallis熵取最大值时对应的阈值,最后对4个方向的阈值进行加权求和作为最终分割阈值。将提出的方法和5个分割方法在4幅合成图像和40幅真实世界图像上进行了实验。结果表明提出的方法虽然计算效率不占优势,但它的分割适应性和分割精度有明显的提高。

考虑Gabor小波特征的LBFI识别仿真

识别局部模糊人脸图像时,若不能增强模糊部分的信息,会降低图像识别精度,为提升模糊人脸图像的识别效果,提出基于Gabor小波特征的局部模糊人脸图像识别方法。使用均值滤波方法对图像噪声实施剔除,并根据剔除结果利用直方图均衡化算法对局部模糊实施信息增强处理;以上述图像处理结果为基础,使用Gabor小波变换方法提取图像显著、不显著特征向量,根据决策融合方法对提取的特征实施融合处理;通过LDA分类器对融合特征实施分类处理,基于分类结果实现人脸图像的精准识别。实验结果表明,使用上述方法开展人脸识别时,识别率较高、识别效果好。

SAR target detection based on the optimal fractional Gabor spectrum feature

In this paper,an algorithm based on a fractional time-frequency spectrum feature is proposed to improve the accuracy of synthetic aperture radar(SAR)target detection.By extending the fractional Gabor transform(FrGT)into two dimensions,the fractional time-frequency spectrum feature of an image can be obtained.In the achievement process,we search for the optimal order and design the optimal window function to accomplish the two-dimensional optimal FrGT.Finally,the energy attenuation gradient(EAG)feature of the optimal time-frequency spectrum is extracted for high-frequency detection.The simulation results show the proposed algorithm has a good performance in SAR target detection and lays the foundation for recognition.

基于Gabor滤波的软包电池表面缺陷检测

针对当前锂锰软包电池表面在生产过程中容易出现凸点、凹点等缺陷的问题,提出了一种基于光度立体法与频域Gabor滤波相结合的电池表面缺陷检测方法。首先,采用3个光源采集图片,然后进行图像融合,生成电池样本的反照率图片,可以使缺陷更加明显;然后对反照率图片进行快速傅里叶变换,在频域状态下使用Gabor滤波器进行处理,处理的结果再用逆傅里叶变换转换到时域,对于去除拍摄反光引起的图片噪声,采用中值滤波去除,将缺陷部分根据灰度值的大小用一个矩形掩膜进行增强;然后采用全局自适应阈值分割提取缺陷区域;最后利用形态学操作细化缺陷,凹坑准确率在98%,凸点准确率在96.7%,能够达到实际工业应用要求。

基于Gabor纹理学习的地震数据重建算法

地震数据重建技术主要用于解决地震数据采集过程中出现的地震道缺失或空间采样不足等问题。针对支持向量回归(SVR)地震数据重建方法未充分利用地震数据物理信息的不足,引入可提取不同尺度和方向纹理特征的Gabor变换,旨在充分挖掘地震数据的物理信息,并基于SVR算法框架重建缺失的地震数据。即首先利用Gabor滤波器提取地震数据的纹理特征,并与原始数据特征相结合,构建新的特征向量数据库;然后通过SVR算法学习回归模型,用于重建缺失的地震数据。通过大量合成地震数据与实际地震数据重建实例,表明由Gabor变换提取的纹理特征能有效提高SVR算法的重建精度,并获得更高信噪比。

基于可调因子Gabor小波变换的地震高分辨处理方法

时频分析是利用地震资料识别薄层的重要方法之一,常规的时频分析方法受到固定时窗、窗函数等因素影响。为此,采用一种基于可调因子Gabor小波(Tunable Factor Gabor Wavelet,TFGW)的连续小波变换(Continuous Wavelet Transform,CWT)(简称TFGW-CWT)的时频分析方法对地震资料进行处理。该方法采用具有可调因子的Gabor小波进行变换,然后使用最小绝对值投影方法组合每个可调因子的连续小波系数,降低邻近频率的交叉干扰,提高局部时频分辨率。进一步采用非负矩阵分解(Non-negative Matrix Factorization,NMF)对时频数据体降维,得到一个低秩的特征数据结构关系体,减少了高维空间的数据冗余,凸显了高频信息,达到提高地震资料分辨率的目的。模拟记录和实际资料处理结果证实了该方法的有效性,可为薄层检测提供一种新的技术手段。

Global motion estimation with Gabor wavelet transform

A novel algorithm of global motion estimation is proposed. First, through Gabor wavelet transform （GWT）, a kind of energy distribution of image is obtained and checkpoints are selected according to a probability decision approach proposed. Then, the initialized motion vectors are obtained via a hierarcbal block-matching based on these checkpoints. Finally, by employing a 3-parameter motion model, precise parameters of global motion are found. From the experiment, the algorithm is reliable and robust.

应用组稀疏正则化反演的高分辨率自适应Gabor时频分析方法

地震信号频率成分随时间的变化规律(时频特性)对油气检测具有重要意义,且Gabor变换作为最简便的时频分析技术在地震资料解释中得到了广泛应用。然而常规Gabor变换所得时频谱的时间分辨率低,相邻反射子波频谱信息混叠严重,不利于开展高分辨率地震资料解释。为了提高Gabor时频谱的时间分辨率,首先基于Gabor反变换的定义将Gabor时频谱的计算归结为求解反演问题;然后以相同时刻频谱分入同一组的策略加入组稀疏正则化约束项;最终利用投影快速软阈值迭代算法实现上述目标函数求解并获得Gabor时频谱。同时,还给出一种利用地震信号瞬时质心频率自适应地构造Gabor时频分析所需高斯窗函数的方法。理论信号实验及实际数据应用表明,该方法可在时间方向上对Gabor时频谱的能量团进行显著压缩,低频端和高频端的时间分辨率获得同步提高,进而在低频和高频剖面上同时清晰揭示薄储层顶、底界面,便于精细对比解释。

基于Gabor纹理特征和支持向量机的跳频调制识别

针对跳频信号调制方式识别问题,提出一种基于Gabor变换和支持向量机的调制识别方法,该方法将信号识别问题转化为图像识别问题。利用Choi-Williams分布获得6种跳频信号的时频图像;将Choi-Williams时频图像灰度化处理,应用Gabor变换提取单一尺度4个角度下的纹理特征,通过PCA降维处理形成特征参数;利用多分类支持向量机分类训练、识别。仿真结果表明,所提方法在信噪比-8 dB时,BFSK、BASK、BPSK、QPSK、MSK及16QAM共6种跳频信号调制识别率高达90.67%,相比于其他纹理特征方法,具有更高的识别率及抗噪性。

Face Representation Using Combined Method of Gabor Filters, Wavelet Transformation and DCV and Recognition Using RBF

An efficient face representation is a vital step for a successful face recognition system. Gabor features are known to be effective for face recognition. The Gabor features extracted by Gabor filters have large dimensionality. The feature of wavelet transformation is feature reduction. Hence, the large dimensional Gabor features are reduced by wavelet transformation. The discriminative common vectors are obtained using the within-class scatter matrix method to get a feature representation of face images with enhanced discrimination and are classified using radial basis function network. The proposed system is validated using three face databases such as ORL, The Japanese Female Facial Expression (JAFFE) and Essex Face database. Experimental results show that the proposed method reduces the number of features, minimizes the computational complexity and yielded the better recognition rates.

基于Gabor变换与克隆选择的高保真遥感影像阴影角度精确校正方法

面对遥感影像受到噪点影响无法有效补偿阴影角度,使得校正结果陷入局部最优而导致角度校正耗时长的问题,提出了基于Gabor变换与克隆选择的高保真遥感影像阴影角度精确校正方法。采用Gabor滤波函数提取影像纹理特征,根据局部化特点计算空间纵横比,将影像纹理集中在中频区域,推导出Gabor滤波中心频率。通过选择Gabor滤波参数,完成对遥感卫星信号噪声滤除处理。结合自适应全局阈值法分割遥感影像序列,获取前景和背景区域两组序列,计算两组序列方差,分割前景和背景区域。引入阴影色彩索引,计算索引梯度值,滤除噪点影像阴影区域,保持影像原有轮廓特征。构建阴影估计模型,对滤波处理影像阴影区域补偿,完成阴影区域角度校正。利用克隆选择算法的选择、克隆、变异操作,优化校正结果,避免陷入局部最优。由试验结果可知,该方法阴影区域无噪点,校正后影像与初始影像一致,且耗费最短时间为5 s,具有精确校正效果。

基于粒子群优化Gabor滤波器的钢板表面缺陷检测

为了解决钢板表面缺陷形态差别大、对比度低,无法准确检测的问题,提出一种基于粒子群优化(PSO)-Gabor滤波器的钢板表面缺陷检测方法。为了消除图像噪声,突显缺陷目标,首先,对缺陷图像进行自适应中值滤波和对数变换;然后,通过PSO算法对二维Gabor滤波器的频率、方向、尺度和滤波窗口进行参数寻优;并基于最优Gabor滤波器对图像进行滤波,获得缺陷能量图;最后,根据所得能量图进行缺陷分割,从而完成缺陷检测。实验结果表明:基于PSO-Gabor滤波器的缺陷检测方法对钢板表面4种缺陷检测准确率达93.75%,检测耗时为0.05 s,可实现对低对比度钢板表面缺陷图像快速、准确地检测,为钢板表面缺陷实时在线检测提供理论依据和技术支持。

基于Gabor小波变换和神经网络算法的人脸智能自动识别方法

常规人脸智能识别方法使用Fused-MBConv结构生成智能识别参数,易受输入图像的浅层特征影响,导致人脸识别准确率较低,为此提出基于Gabor小波变换和神经网络算法的人脸智能识别方法。为验证该方法的识别效果,将其与其他人脸智能自动识别方法进行对比。实验结果表明,该方法的识别率较高,具有一定的应用价值。