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.

基于Gabor卷积和Transformer的课堂表情识别研究

为了针对复杂环境变化无法精准识别学生表情问题,本文设计了一个基于Gabor卷积和Transformer的表情识别模型Gabor-Vision-Transformer(GVT).将Gabor卷积和Transformer的思想相结合,设计了一个特征提取块GVT-Block.首先通过Gabor卷积提取富含丰富纹理和边缘信息的面部局部特征,再通过Transformer提取全局数据之间的长距离信息,从而更好地学习面部关键特征,显著提高模型的分类效果.GVT模型在RAF-DB和FER2013Plus数据集上的准确率分别为88.56%和87.38%,并与多个模型进行对比实验和分析,验证了本模型效果的优越性.

The optimal fractional Gabor transform based on the adaptive window function and its application

We designed the window function of the optimal Gabor transform based on the time-frequency rotation property of the fractional Fourier transform. Thus, we obtained the adaptive optimal Gabor transform in the fractional domain and improved the time-frequency concentration of the Gabor transform. The algorithm first searches for the optimal rotation factor, then performs the p-th FrFT of the signal and, finally, performs time and frequency analysis of the FrFT result. Finally, the algorithm rotates the plane in the fractional domain back to the normal time-frequency plane. This promotes the application of FrFT in the field of high-resolution reservoir prediction. Additionally, we proposed an adaptive search method for the optimal rotation factor using the Parseval principle in the fractional domain, which simplifies the algorithm. We carried out spectrum decomposition of the seismic signal, which showed that the instantaneous frequency slices obtained by the proposed algorithm are superior to the ones obtained by the traditional Gabor transform. The adaptive time frequency analysis is of great significance to seismic signal processing.

Effects of Gabor transform parameters on signa time-frequency resolution

In this paper, it is described that the time-frequency resolution of geophysical signals is affected by the time window function attenuation coefficient and sampling interval and how such effects are eliminated effectively. Improving the signal resolution is the key to signal time-frequency analysis processing and has wide use in geophysical data processing and extraction of attribute parameters. In this paper, authors research the effects of the attenuation coefficient choice of the Gabor transform window function and sampling interval on signal resolution. Unsuitable parameters not only decrease the signal resolution on the frequency spectrum but also miss the signals. It is essential to first give the optimum window and range of parameters through time-frequency analysis simulation using the Gabor transform. In the paper, the suggestions about the range and choice of the optimum sampling interval and processing methods of general seismic signals are given.

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.

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.

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.

Properties of an improved Gabor wavelet transform and its applications to seismic signal processing and interpretation

This paper presents an analytical study of the complete transform of improved Gabor wavelets （IGWs）, and discusses its application to the processing and interpretation of seismic signals. The complete Gabor wavelet transform has the following properties. First, unlike the conventional transform, the improved Gabor wavelet transform （IGWT） maps time domain signals to the time-frequency domain instead of the time-scale domain. Second, the IGW＇s dominant frequency is fixed, so the transform can perform signal frequency division, where the dominant frequency components of the extracted sub-band signal carry essentially the same information as the corresponding components of the original signal, and the sub- band signal bandwidth can be regulated effectively by the transform＇s resolution factor. Third, a time-frequency filter consisting of an IGWT and its inverse transform can accurately locate target areas in the time-frequency field and perform filtering in a given time-frequency range. The complete IGW transform＇s properties are investigated using simulation experiments and test cases, showing positive results for seismic signal processing and interpretation, such as enhancing seismic signal resolution, permitting signal frequency division, and allowing small faults to be identified.

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.

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.

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。

基于Gabor时频滤波的电磁超声螺栓轴力测量

高强度螺栓轴向预紧力(轴力)的测量在工程应用中具有重要意义。使用电磁超声波对螺栓轴力检测时对超声回波声时测量精度要求较高,传统互相关估计法对超声回波声时估计易因噪声干扰发生估计错误,无法满足轴力测量精度要求。针对互相关法对电磁超声测量信号声时估计存在不准确的问题,提出了Gabor时频滤波法。通过螺栓轴力测量实验采集测量信号,对测量信号进行Gabor变换,在时频域中进行滤波,再对去噪后的信号进行互相关估计测得信号的声时,进而计算出螺栓轴力。实验表明:Gabor时频滤波法能有效地滤除电磁超声信号中的噪声,改善互相关估计的稳定性,提高螺栓轴力测量的准确率。

基于Gabor变换的TDLAS检测信号的降噪研究

可调谐二极管激光吸收光谱（TDLAS）技术结合波长调制光谱（WMS）技术是用于痕量气体检测的重要技术手段。通过锁相放大器进行谐波检测,对解调得到的二次谐波信号进行分析可获得气体吸收的信息。但由于二次谐波信号受到噪声的影响,降低了检测系统的精度和稳定性。为了提高 TDLAS检测系统的信噪比（SNR）,提出了一种基于 Gabor变换对二次谐波信号进行数字滤波降噪的方法。以 CH4在1653.72 nm处的吸收光谱为例,通过仿真和实验对该降噪方法的有效性进行了验证。仿真结果表明,通过 Gabor 变换对信噪比为0dB的二次谐波信号进行处理后,系统的信噪比可提高15.73 dB。实验结果表明,基于Gabor变换进行降噪处理后,CH4浓度在0.001%-0.02%区间内与二次谐波峰值的线性相关系数r达到了0.99659,且系统的检测精度和稳定性明显提高。

基于Gabor函数的小波域指纹图像增强算法

针对指纹大规模采集库中存在的指纹图像局部区过干或过湿的问题,提出了一种基于Gabor函数的小波域指纹增强算法。该算法在小波域利用低频系数图估计指纹方向,从而抑制了指纹局部过干或过湿的影响,进而分别实现基于Gabor函数的小波域各子图增强,最终将各增强子图利用小波逆变换实现重构。通过对FVC2004的DB1指纹库中的部分低质量图像的增强结果比较,该算法对低质量指纹图像的增强效果明显,且处理速度明显快于现存的Gabor增强方法。

地震信号分数阶Gabor变换谱分解方法及应用

本文将分数阶Gabor变换(FrGT)引入到地震信号的分析与处理中,即利用新近兴起的分数域时频分析技术及其良好的局部时频能量聚集特性,进行地震信号的分数域谱分解及特征分析.论文在基本Gobor变换原理基础上推导了FrGT的公式及紧支撑时频带宽积下的最优阶次确定方法,建立了FrGT的一般流程,并进行了信号的数值仿真和性能分析.最后,将该方法应用于实际地震信号的时频分析,可获得最优阶下的各个高分辨率的单频剖面.解释结果表明,该方法具有潜在优势,可为地震储层预测,尤其是储层流体识别应用提供一条新的途径.

基于Gabor多方向特征融合与分块直方图的人脸表情识别方法

针对传统的Gabor特征表征全局特征能力弱以及特征数据存在冗余性的缺点,提出一种新颖的采用Gabor多方向特征融合与分块直方图统计相结合的方法来提取表情特征.为了提取局部方向信息并降低特征维数,首先采用Gabor滤波器提取人脸表情图像的多尺度和多方向特征,然后按照两个融合规则将相同尺度不同方向的特征融合到一起.为了能够有效地表征图像全局特征,将融合图像进一步划分为若干矩形不重叠且大小相等的子块,分别计算每个子块区域内融合特征的直方图分布,将其联合起来实现图像表征.实验结果表明,这种方法无论在计算量上还是识别性能上都比传统的Gabor滤波器组更具有优势.该方法的创新处在于提出了两个Gabor多方向特征融合规则,应用在JAFFE表情库上最高平均识别率达到98.24%,表明其适用于人脸表情图像的分析.

基于Gabor变换的微动目标微多普勒分析与仿真

由于目标微动特征信号具有非线性和非平稳的特点,为有效提取雷达目标的微动特征,为雷达目标的分类与识别提供依据,在单频信号体制下,以旋转散射点目标为例,基于时频分析的方法提取了旋转目标的微多普勒信息,通过仿真验证,得到了微动目标的微多普勒特征,比较了几种常见时频分析工具的变换结果及性能差异。仿真结果表明,Gabor变换方法在微动目标微多普勒提取方面是可行而稳健的,Gabor变换的巨大潜力将为微动目标特征识别提供新的途径。

基于三维Gabor变换的视频水印算法

水印技术是把版权信息隐藏于载体信号中达到版权认证的一种版权保护技术.利用Gabor基函数波形类似人视觉皮层简单细胞的感受野波形的特性,结合视觉通道中心频率具有对数频程关系的特点,从视觉系统时-空多通道模型角度出发,提出一种三维塔式Gabor变换视频水印算法.实验表明,该水印算法具有较好的鲁棒性和不可感知性.

基于Gabor低秩恢复稀疏表示分类的人脸图像识别方法

针对含光照、表情、姿态、遮挡等误差或被噪声污染的人脸图像的识别问题,本文提出一种基于Gabor低秩恢复稀疏表示分类的人脸图像识别方法.该方法首先用低秩矩阵恢复算法求得训练样本图像对应的误差图像;然后,对每一个训练样本图像及其对应的误差图像进行Gabor变换,得到相应的Gabor特征向量,并将这些Gabor特征向量组成一个Gabor特征字典;进而,计算测试样本图像Gabor特征向量在该Gabor特征字典下的稀疏表示系数,并用该稀疏表示系数和Gabor特征字典,对测试样本图像的Gabor特征向量进行类关联重构,同时计算相应的类关联重构误差.最后,根据测试样本图像Gabor特征向量的类关联重构误差,实现对测试样本图像的分类识别.在CMU PIE、Extended Yale B和AR数据库上的实验结果表明,本文提出的人脸图像识别方法具有较高的识别率和较强的抗干扰能力.