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 fractiona...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.展开更多
Sparse representation has been highly successful in various tasks related to image processing and computer vision.For ancient mural image inpainting,traditional group sparse representation models usually lead to struc...Sparse representation has been highly successful in various tasks related to image processing and computer vision.For ancient mural image inpainting,traditional group sparse representation models usually lead to structure blur and line discontinuity due to the construction of similarity group solely based on the Euclidean distance and the randomness of dictionary initialization.To address the aforementioned issues,an improved curvature Gabor transform and group sparse representation(CGabor-GSR)model for ancient Dunhuang mural inpainting is proposed.To begin with,mutual information is introduced to weight the Euclidean distance,and then the weighted Euclidean distance acts as a new standard of similarity group.Subsequently,to mitigate the randomness of dictionary initialization,a curvature Gabor wavelet transform is proposed to extract the features and initialize the feature dictionary with dimension reduction based on principal component analysis(PCA).Ultimately,singular value decomposition(SVD)and split Bregman iteration(SBI)can be used to resolve the CGabor-GSR model to reconstruct the mural images.Experimental results on Dunhuang mural inpainting demonstrate tha the proposed CGabor-GSR achieves a better performance than compared algorithms in both objective and visual evaluation.展开更多
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 effect...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.展开更多
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 traditio...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.展开更多
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 an...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.展开更多
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 ...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.展开更多
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 general...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.展开更多
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 trans...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.展开更多
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 dec...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.展开更多
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 ...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.展开更多
Collaborative representation-based classification(CRC) is a distance based method, and it obtains the original contributions from all samples to solve the sparse representation coefficient. We find out that it helps t...Collaborative representation-based classification(CRC) is a distance based method, and it obtains the original contributions from all samples to solve the sparse representation coefficient. We find out that it helps to enhance the discrimination in classification by integrating other distance based features and/or adding signal preprocessing to the original samples. In this paper, we propose an improved version of the CRC method which uses the Gabor wavelet transformation to preprocess the samples and also adapts the nearest neighbor(NN)features, and hence we call it GNN-CRC. Firstly, Gabor wavelet transformation is applied to minimize the effects from the background in face images and build Gabor features into the input data. Secondly, the distances solved by NN and CRC are fused together to obtain a more discriminative classification. Extensive experiments are conducted to evaluate the proposed method for face recognition with different instantiations. The experimental results illustrate that our method outperforms the naive CRC as well as some other state-of-the-art algorithms.展开更多
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 dimens...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.展开更多
基金supported by national natural science foundation of China(No.41274127,41301460,40874066,and 40839905)
文摘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.
基金supported by National Natural Science Foundation of China(No.61963023)Humanities and Social Sciences Youth Foundation of Ministry of Education(No.19YJC760012)Lanzhou Jiaotong University Basic Top-Notch Personnel Project(No.2022JC36).
文摘Sparse representation has been highly successful in various tasks related to image processing and computer vision.For ancient mural image inpainting,traditional group sparse representation models usually lead to structure blur and line discontinuity due to the construction of similarity group solely based on the Euclidean distance and the randomness of dictionary initialization.To address the aforementioned issues,an improved curvature Gabor transform and group sparse representation(CGabor-GSR)model for ancient Dunhuang mural inpainting is proposed.To begin with,mutual information is introduced to weight the Euclidean distance,and then the weighted Euclidean distance acts as a new standard of similarity group.Subsequently,to mitigate the randomness of dictionary initialization,a curvature Gabor wavelet transform is proposed to extract the features and initialize the feature dictionary with dimension reduction based on principal component analysis(PCA).Ultimately,singular value decomposition(SVD)and split Bregman iteration(SBI)can be used to resolve the CGabor-GSR model to reconstruct the mural images.Experimental results on Dunhuang mural inpainting demonstrate tha the proposed CGabor-GSR achieves a better performance than compared algorithms in both objective and visual evaluation.
基金This work was funded by National Natural Science Foundation of China-（No. 40474044）.
文摘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.
基金Supported by the Excellent Young Teachers Program of the Ministry of Education, P. R. China (No. 2001-1739 and No. 2003-145)
文摘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.
基金supported by National Natural Science Foundation of China(Grant No.61501493)。
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
基金supported by the Innovation Fund for Small and Medium Technology-based Enterprise of China(No.12C26216106562)Shaanxi Province Education Department Science and Technology Research Plan(No.11JK0777)
文摘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.
基金the National Natural Science Foundation of China(No.61502208)the Natural Science Foundation of Jiangsu Province of China(No.BK20150522)+1 种基金the Scientific and Technical Program of City of Huizhou(Nos.2016X0422037 and 2017C0405021)the Natural Science Foundation of Huizhou University(Nos.hzux1201606 and hzu201701)
文摘Collaborative representation-based classification(CRC) is a distance based method, and it obtains the original contributions from all samples to solve the sparse representation coefficient. We find out that it helps to enhance the discrimination in classification by integrating other distance based features and/or adding signal preprocessing to the original samples. In this paper, we propose an improved version of the CRC method which uses the Gabor wavelet transformation to preprocess the samples and also adapts the nearest neighbor(NN)features, and hence we call it GNN-CRC. Firstly, Gabor wavelet transformation is applied to minimize the effects from the background in face images and build Gabor features into the input data. Secondly, the distances solved by NN and CRC are fused together to obtain a more discriminative classification. Extensive experiments are conducted to evaluate the proposed method for face recognition with different instantiations. The experimental results illustrate that our method outperforms the naive CRC as well as some other state-of-the-art algorithms.
文摘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.
