Fast wavelet transform algorithms for Toeplitz matrices are proposed in this paper. Distinctive from the well known discrete trigonometric transforms, such as the discrete cosine transform （DCT） and the discrete Fou...Fast wavelet transform algorithms for Toeplitz matrices are proposed in this paper. Distinctive from the well known discrete trigonometric transforms, such as the discrete cosine transform （DCT） and the discrete Fourier transform （DFT） for Toeplitz matrices, the new algorithms are achieved by compactly supported wavelet that preserve the character of a Toeplitz matrix after transform, which is quite useful in many applications involving a Toeplitz matrix. Results of numerical experiments show that the proposed method has good compression performance similar to using wavelet in the digital image coding. Since the proposed algorithms turn a dense Toeplitz matrix into a band-limited form, the arithmetic operations required by the new algorithms are O（N） that are reduced greatly compared with O（N log N） by the classical trigonometric transforms.展开更多
This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic d...This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic data obtained from the Tano Basin in West Africa, Ghana. The research focuses on a comparative analysis of image clarity in seismic attribute analysis to facilitate the identification of reservoir features within the subsurface structures. The findings of the study indicate that CWT has a significant advantage over FFT in terms of image quality and identifying subsurface structures. The results demonstrate the superior performance of CWT in providing a better representation, making it more effective for seismic attribute analysis. The study highlights the importance of choosing the appropriate image enhancement technique based on the specific application needs and the broader context of the study. While CWT provides high-quality images and superior performance in identifying subsurface structures, the selection between these methods should be made judiciously, taking into account the objectives of the study and the characteristics of the signals being analyzed. The research provides valuable insights into the decision-making process for selecting image enhancement techniques in seismic data analysis, helping researchers and practitioners make informed choices that cater to the unique requirements of their studies. Ultimately, this study contributes to the advancement of the field of subsurface imaging and geological feature identification.展开更多
The recently developed theory of wavelet applied in the Method of Moments (MoM) to solve the electromagnetic field integral equation is presented in this paper. For one dimension problem, we briefly discuss the follow...The recently developed theory of wavelet applied in the Method of Moments (MoM) to solve the electromagnetic field integral equation is presented in this paper. For one dimension problem, we briefly discuss the following aspects: Firstly, two different methods, which are same in essence: the method of the unknown induction current expansion and the method of the integral operator expansion are used to solve the EFIE, Secondly, how to choose the wavelet basis function in wavelet MoM. For two dimension problem, the wavelet MoM is employed and compared with the conventional MoM in CPU time, computational precision and matrix spareness etc. Here, the fast wavelet transform (FWT) is used to compute the matrix elements rapidly and efficiently. Typical numerical results are presented to illustrate the concepts.展开更多
A fast encoding algorithm based on the mean square error （MSE） distortion for vector quantization is introduced. The vector, which is effectively constructed with wavelet transform （WT） coefficients of images, can...A fast encoding algorithm based on the mean square error （MSE） distortion for vector quantization is introduced. The vector, which is effectively constructed with wavelet transform （WT） coefficients of images, can simplify the realization of the non-linear interpolated vector quantization （NLIVQ） technique and make the partial distance search （PDS） algorithm more efficient. Utilizing the relationship of vector L2-norm and its Euclidean distance, some conditions of eliminating unnecessary codewords are obtained. Further, using inequality constructed by the subvector L2-norm, more unnecessary codewords are eliminated. During the search process for code, mostly unlikely codewords can be rejected by the proposed algorithm combined with the non-linear interpolated vector quantization technique and the partial distance search technique. The experimental results show that the reduction of computation is outstanding in the encoding time and complexity against the full search method.展开更多
Fourier transform （FF） is a commonly used method in spectral analysis of ocean wave and offshore structure responses, but it is not suitable for records of short length. In this paper another method, wavelet transfo...Fourier transform （FF） is a commonly used method in spectral analysis of ocean wave and offshore structure responses, but it is not suitable for records of short length. In this paper another method, wavelet transform （WT）, is applied to ＇analyze the data of short length. The Morlet wavelet is employed to calculate the spectra density functions for wave records and simulated Floating Production Storage and Offloading （FPSO） vessels＇ responses. Computed wave data include simulated wave data based on JONSWAP spectrum and the recorded data of Storm 149 from North Alwyn. Wavelet method is validated by comparing the statistical characteristics by WF method and those by fast Fourier transform （FFT） method with those of target spectra. The spectral density fnnctions＇ shapes calculated by WT are less malformed and have less error of statistical characteristics compared with those by FT especially when the record lengths decrease.展开更多
正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)调制因其高效的频带利用率和良好的抗多径能力广泛用于合作与非合作通信系统中。合作通信场景下,通常接收机可以利用已知帧结构实现OFDM信号的检测。但在非合作场景下,...正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)调制因其高效的频带利用率和良好的抗多径能力广泛用于合作与非合作通信系统中。合作通信场景下,通常接收机可以利用已知帧结构实现OFDM信号的检测。但在非合作场景下,接收机没有足够的先验信息,导致帧检测难度加大。针对这一问题,提出了一种适合于非合作通信场景的OFDM数据帧的检测算法。所提算法利用快速小波变换将含噪OFDM信号的功率包络进行小波分解与重构,对重构得到的功率包络进行差分运算后,再通过与阈值比较实现OFDM信号的帧检测。相较于混合能量检测算法,所提算法计算预设参数少,复杂度低。仿真结果表明,所提算法在加性高斯白噪声信道和多径衰落信道下带内信噪比分别取-6 dB和3 dB时即可实现零漏报率,且零漏报率的阈值选取范围比混合能量检测算法扩大了约6 dB。展开更多
基金Supported by the National Natural Science Foundation under Grants （No.10171109）
文摘Fast wavelet transform algorithms for Toeplitz matrices are proposed in this paper. Distinctive from the well known discrete trigonometric transforms, such as the discrete cosine transform （DCT） and the discrete Fourier transform （DFT） for Toeplitz matrices, the new algorithms are achieved by compactly supported wavelet that preserve the character of a Toeplitz matrix after transform, which is quite useful in many applications involving a Toeplitz matrix. Results of numerical experiments show that the proposed method has good compression performance similar to using wavelet in the digital image coding. Since the proposed algorithms turn a dense Toeplitz matrix into a band-limited form, the arithmetic operations required by the new algorithms are O（N） that are reduced greatly compared with O（N log N） by the classical trigonometric transforms.
文摘This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic data obtained from the Tano Basin in West Africa, Ghana. The research focuses on a comparative analysis of image clarity in seismic attribute analysis to facilitate the identification of reservoir features within the subsurface structures. The findings of the study indicate that CWT has a significant advantage over FFT in terms of image quality and identifying subsurface structures. The results demonstrate the superior performance of CWT in providing a better representation, making it more effective for seismic attribute analysis. The study highlights the importance of choosing the appropriate image enhancement technique based on the specific application needs and the broader context of the study. While CWT provides high-quality images and superior performance in identifying subsurface structures, the selection between these methods should be made judiciously, taking into account the objectives of the study and the characteristics of the signals being analyzed. The research provides valuable insights into the decision-making process for selecting image enhancement techniques in seismic data analysis, helping researchers and practitioners make informed choices that cater to the unique requirements of their studies. Ultimately, this study contributes to the advancement of the field of subsurface imaging and geological feature identification.
文摘The recently developed theory of wavelet applied in the Method of Moments (MoM) to solve the electromagnetic field integral equation is presented in this paper. For one dimension problem, we briefly discuss the following aspects: Firstly, two different methods, which are same in essence: the method of the unknown induction current expansion and the method of the integral operator expansion are used to solve the EFIE, Secondly, how to choose the wavelet basis function in wavelet MoM. For two dimension problem, the wavelet MoM is employed and compared with the conventional MoM in CPU time, computational precision and matrix spareness etc. Here, the fast wavelet transform (FWT) is used to compute the matrix elements rapidly and efficiently. Typical numerical results are presented to illustrate the concepts.
基金the National Natural Science Foundation of China (60602057)the NaturalScience Foundation of Chongqing Science and Technology Commission (2006BB2373).
文摘A fast encoding algorithm based on the mean square error （MSE） distortion for vector quantization is introduced. The vector, which is effectively constructed with wavelet transform （WT） coefficients of images, can simplify the realization of the non-linear interpolated vector quantization （NLIVQ） technique and make the partial distance search （PDS） algorithm more efficient. Utilizing the relationship of vector L2-norm and its Euclidean distance, some conditions of eliminating unnecessary codewords are obtained. Further, using inequality constructed by the subvector L2-norm, more unnecessary codewords are eliminated. During the search process for code, mostly unlikely codewords can be rejected by the proposed algorithm combined with the non-linear interpolated vector quantization technique and the partial distance search technique. The experimental results show that the reduction of computation is outstanding in the encoding time and complexity against the full search method.
文摘Fourier transform （FF） is a commonly used method in spectral analysis of ocean wave and offshore structure responses, but it is not suitable for records of short length. In this paper another method, wavelet transform （WT）, is applied to ＇analyze the data of short length. The Morlet wavelet is employed to calculate the spectra density functions for wave records and simulated Floating Production Storage and Offloading （FPSO） vessels＇ responses. Computed wave data include simulated wave data based on JONSWAP spectrum and the recorded data of Storm 149 from North Alwyn. Wavelet method is validated by comparing the statistical characteristics by WF method and those by fast Fourier transform （FFT） method with those of target spectra. The spectral density fnnctions＇ shapes calculated by WT are less malformed and have less error of statistical characteristics compared with those by FT especially when the record lengths decrease.
