In order to provide larger capacity of the hidden secret data while maintaining a good visual quality of stego-image, in accordance with the visual property that human eyes are less sensitive to strong texture, a nove...In order to provide larger capacity of the hidden secret data while maintaining a good visual quality of stego-image, in accordance with the visual property that human eyes are less sensitive to strong texture, a novel steganographic method based on wavelet and modulus function is presented. First, an image is divided into blocks of prescribed size, and every block is decomposed into one-level wavelet. Then, the capacity of the hidden secret data is decided with the number of wavelet coefficients of larger magnitude. Finally, secret information is embedded by steganography based on modulus function. From the experimental results, the proposed method hides much more information and maintains a good visual quality of stego-image. Besides, the embedded data can be extracted from the stego-image without referencing the original image.展开更多
The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wave...The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wavelet, and research the local extreme point and extrema of the wavelet transform on periodic function for the collection of signal＇ s instantaneous amplitude and period.展开更多
Some properties of the wavelet transform of trigonometric Junction, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spect...Some properties of the wavelet transform of trigonometric Junction, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spectrum of a periodic function are in proportion to its period. At the same time, a new equation, which can truly reconstruct a trigonometric function with only one scale wavelet coefficient, is presented. The reconstructed wave shape of a periodic function with the equation is better than any term of its Fourier series. And the reconstructed wave shape of a class of nonstationary periodic function with this equation agrees well with the function.展开更多
A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver func-tion is expanded to different scales with different resolution by wavelet transformation. After an initi...A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver func-tion is expanded to different scales with different resolution by wavelet transformation. After an initial model be-ing taken, a generalized least-squares inversion procedure is gradually carried out for receiver function from low to high scale, with the inversion result for low order receiver function as the initial model for high order. A neighborhood containing the global minimum is firstly searched from low scale receiver function, and will gradu-ally focus at the global minimum by introducing high scale information of receiver function. With the gradual ad-dition of high wave-number to smooth background velocity structure, wavelet transformation can keep the inver-sion result converge to the global minimum, reduce to certain extent the dependence of inversion result on the initial model, overcome the nonuniqueness of generalized least-squares inversion, and obtain reliable crustal and upper mantle velocity with high resolution.展开更多
In order to solve the problems of local maximum modulus extraction and threshold selection in the edge detection of finite resolution digital images, a new wavelet transform based adaptive dual threshold edge detec...In order to solve the problems of local maximum modulus extraction and threshold selection in the edge detection of finite resolution digital images, a new wavelet transform based adaptive dual threshold edge detection algorithm is proposed. The local maximum modulus is extracted by linear interpolation in wavelet domain. With the analysis on histogram, the image is filtered with an adaptive dual threshold method, which effectively detects the contours of small structures as well as the boundaries of large objects. A wavelet domain's propagation function is used to further select weak edges. Experimental results have shown the self adaptivity of the threshold to images having the same kind of histogram, and the efficiency even in noise tampered images.展开更多
The development of accurate prediction models continues to be highly beneficial in myriad disciplines. Deep learning models have performed well in stock price prediction and give high accuracy. However, these models a...The development of accurate prediction models continues to be highly beneficial in myriad disciplines. Deep learning models have performed well in stock price prediction and give high accuracy. However, these models are largely affected by the vanishing gradient problem escalated by some activation functions. This study proposes the use of the Vanishing Gradient Resilient Optimized Gated Recurrent Unit (OGRU) model with a scaled mean Approximation Coefficient (AC) time lag which should counter slow convergence, vanishing gradient and large error metrics. This study employed the Rectified Linear Unit (ReLU), Hyperbolic Tangent (Tanh), Sigmoid and Exponential Linear Unit (ELU) activation functions. Real-life datasets including the daily Apple and 5-minute Netflix closing stock prices were used, and they were decomposed using the Stationary Wavelet Transform (SWT). The decomposed series formed a decomposed data model which was compared to an undecomposed data model with similar hyperparameters and different default lags. The Apple daily dataset performed well with a Default_1 lag, using an undecomposed data model and the ReLU, attaining 0.01312, 0.00854 and 3.67 minutes for RMSE, MAE and runtime. The Netflix data performed best with the MeanAC_42 lag, using decomposed data model and the ELU achieving 0.00620, 0.00487 and 3.01 minutes for the same metrics.展开更多
The brief theories of wavelet analysis and Hilbert-Huang transform (HHT) are introduced firstly in the present paper. Then several signal data were analyzed by using wavelet and HHT methods, respectively. The comparis...The brief theories of wavelet analysis and Hilbert-Huang transform (HHT) are introduced firstly in the present paper. Then several signal data were analyzed by using wavelet and HHT methods, respectively. The comparison shows that HHT is not only an effective method for analyzing non-stationary data, but also is a useful tool for examining detailed characters of time history signal.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
The discrete time wavelet transform has been used to develop software that detects seismic P and S-phases. The detection algorithm is based on the enhanced amplitude and polarization information provided by the wavele...The discrete time wavelet transform has been used to develop software that detects seismic P and S-phases. The detection algorithm is based on the enhanced amplitude and polarization information provided by the wavelet transform coefficients of the raw seismic data. The algorithm detects phases, determines arrival times and indicates the seismic event direction from three component seismic data that represents the ground displacement in three orthogonal directions. The essential concept is that strong features of the seismic signal are present in the wavelet coefficients across several scales of time and direction. The P-phase is detected by generating a function using polarization information while S-phase is detected by generating a function based on the transverse to radial amplitude ratio. These functions are shown to be very effective metrics in detecting P and S-phases and for determining their arrival times for low signal-to-noise arrivals. Results are compared with arrival times obtained by a human analyst as well as with a standard STA/LTA algorithm from local and regional earthquakes and found to be consistent.展开更多
Continuous wavelet transform is employed to detect singularities in 2-D signals by tracking modulus maxima along maxima lines and particularly applied to microcalcification detection in mammograms. The microcalcificat...Continuous wavelet transform is employed to detect singularities in 2-D signals by tracking modulus maxima along maxima lines and particularly applied to microcalcification detection in mammograms. The microcalcifications are modeled as smoothed positive impulse functions. Other target property detection can be performed by adjusting its mathematical model. In this application, the general modulus maximum and its scale of each singular point are detected and statistically analyzed locally in its neighborhood. The diagnosed microcalcification cluster results are compared with health tissue results, showing that general modulus maxima can serve as a suspicious spot detection tool with the detection performance no significantly sensitive to the breast tissue background properties. Performed fractal analysis of selected singularities supports the statistical findings. It is important to select the suitable computation parameters-thresholds of magnitude, argument and frequency range-in accordance to mathematical description of the target property as well as spatial and numerical resolution of the analyzed signal. The tests are performed on a set of images with empirically selected parameters for 200 μm/pixel spatial and 8 bits/pixel numerical resolution, appropriate for detection of the suspicious spots in a mammogram. The results show that the magnitude of a singularity general maximum can play a significant role in the detection of microcalcification, while zooming into a cluster in image finer spatial resolution both magnitude of general maximum and the spatial distribution of the selected set of singularities may lead to the breast abnormality characterization.展开更多
This paper presents a wavelet-based hybrid threshold method according to the soft- and hard-threshold functions proposed by Donoho. The wavelet-based hybrid threshold method may help doctors to know more details on th...This paper presents a wavelet-based hybrid threshold method according to the soft- and hard-threshold functions proposed by Donoho. The wavelet-based hybrid threshold method may help doctors to know more details on the liver disease through denoising the ultrasound image of the liver. First of all, an analytical expression for the hybrid threshold function is discussed. The wavelet-based hybrid threshold method is then investigated for ultrasound image of the liver. Finally, we test the influence of this parameter on the proposed method with the real ultrasound image corrupted by speckle noise with different variances. Moreover, we compare the proposed method under the varying parameters with the soft-threshold function and the hard-threshold function. Three metrics, which are correlation coefficient, edge preservation index and structural similarity index, are measured to quantify the denoised results of ultrasound liver image. Experimental results demonstrate the potential of the proposed method for ultrasound liver image denosing.展开更多
The spectral analysis of stationary random processes is studied by using wavelet transform method. On the basis of wavelet transform, the conception of time-frequency power spectral density of random processes and tim...The spectral analysis of stationary random processes is studied by using wavelet transform method. On the basis of wavelet transform, the conception of time-frequency power spectral density of random processes and time-frequency cross-spectral density of jointly stationary random processes are presented. The characters of the time-frequency power spectral density and its relationship with traditional power spectral density are also studied in details.展开更多
We consider the problem of approximating two, possibly unrelated probability distributions from a single complex-valued function and its Fourier transform. We show that this problem always has a solution within a spec...We consider the problem of approximating two, possibly unrelated probability distributions from a single complex-valued function and its Fourier transform. We show that this problem always has a solution within a specified degree of accuracy, provided the distributions satisfy the necessary regularity conditions. We describe the algorithm and construction of and provide examples of approximating several pairs of distributions using the algorithm.展开更多
The present study conducted a multi-scale dynamic functional connectivity analysis to evaluate dynamic behavior of acupuncture at Taichong （LR3） and sham acupoints surrounding Taichong Results showed differences in ...The present study conducted a multi-scale dynamic functional connectivity analysis to evaluate dynamic behavior of acupuncture at Taichong （LR3） and sham acupoints surrounding Taichong Results showed differences in wavelet transform coherence characteristic curves in the declive, precuneus, postcentral gyrus, supramarginal gyrus, and occipital lobe between acupuncture at Taichong and acupuncture at sham acupoints. The differences in characteristic curves revealed that the specific effect of acupuncture existed during the post-acupuncture rest state and lasted for 5 minutes.展开更多
In this paper, the notion of p-wavelet packets on the positive half-line P＋ is introduced. A new method for constructing non-orthogonal wavelet packets related to Walsh functions is developed by splitting the wavelet...In this paper, the notion of p-wavelet packets on the positive half-line P＋ is introduced. A new method for constructing non-orthogonal wavelet packets related to Walsh functions is developed by splitting the wavelet subspaces directly instead of using the lowpass and high-pass filters associated with the multiresolution analysis as used in the classical theory of wavelet packets. Further, the method overcomes the difficulty of constructing non-orthogonal wavelet packets of the dilation factor p 〉 2.展开更多
基金the National Natural Science Foundation of China (50677014)Hunan Provincial Natural Science Foundation of China (06JJ50114).
文摘In order to provide larger capacity of the hidden secret data while maintaining a good visual quality of stego-image, in accordance with the visual property that human eyes are less sensitive to strong texture, a novel steganographic method based on wavelet and modulus function is presented. First, an image is divided into blocks of prescribed size, and every block is decomposed into one-level wavelet. Then, the capacity of the hidden secret data is decided with the number of wavelet coefficients of larger magnitude. Finally, secret information is embedded by steganography based on modulus function. From the experimental results, the proposed method hides much more information and maintains a good visual quality of stego-image. Besides, the embedded data can be extracted from the stego-image without referencing the original image.
基金Supported by the National Natural Science Founda-tion of China (49771060)
文摘The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wavelet, and research the local extreme point and extrema of the wavelet transform on periodic function for the collection of signal＇ s instantaneous amplitude and period.
基金Foundation items:the National Development Programming of Key Fundamental Researches of China(G1999022103)Planed Item for Distinguished Teacher Invested by Minisny of Education PRC
文摘Some properties of the wavelet transform of trigonometric Junction, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spectrum of a periodic function are in proportion to its period. At the same time, a new equation, which can truly reconstruct a trigonometric function with only one scale wavelet coefficient, is presented. The reconstructed wave shape of a periodic function with the equation is better than any term of its Fourier series. And the reconstructed wave shape of a class of nonstationary periodic function with this equation agrees well with the function.
基金National Nature Science Foundation of China (49974021).
文摘A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver func-tion is expanded to different scales with different resolution by wavelet transformation. After an initial model be-ing taken, a generalized least-squares inversion procedure is gradually carried out for receiver function from low to high scale, with the inversion result for low order receiver function as the initial model for high order. A neighborhood containing the global minimum is firstly searched from low scale receiver function, and will gradu-ally focus at the global minimum by introducing high scale information of receiver function. With the gradual ad-dition of high wave-number to smooth background velocity structure, wavelet transformation can keep the inver-sion result converge to the global minimum, reduce to certain extent the dependence of inversion result on the initial model, overcome the nonuniqueness of generalized least-squares inversion, and obtain reliable crustal and upper mantle velocity with high resolution.
文摘In order to solve the problems of local maximum modulus extraction and threshold selection in the edge detection of finite resolution digital images, a new wavelet transform based adaptive dual threshold edge detection algorithm is proposed. The local maximum modulus is extracted by linear interpolation in wavelet domain. With the analysis on histogram, the image is filtered with an adaptive dual threshold method, which effectively detects the contours of small structures as well as the boundaries of large objects. A wavelet domain's propagation function is used to further select weak edges. Experimental results have shown the self adaptivity of the threshold to images having the same kind of histogram, and the efficiency even in noise tampered images.
文摘The development of accurate prediction models continues to be highly beneficial in myriad disciplines. Deep learning models have performed well in stock price prediction and give high accuracy. However, these models are largely affected by the vanishing gradient problem escalated by some activation functions. This study proposes the use of the Vanishing Gradient Resilient Optimized Gated Recurrent Unit (OGRU) model with a scaled mean Approximation Coefficient (AC) time lag which should counter slow convergence, vanishing gradient and large error metrics. This study employed the Rectified Linear Unit (ReLU), Hyperbolic Tangent (Tanh), Sigmoid and Exponential Linear Unit (ELU) activation functions. Real-life datasets including the daily Apple and 5-minute Netflix closing stock prices were used, and they were decomposed using the Stationary Wavelet Transform (SWT). The decomposed series formed a decomposed data model which was compared to an undecomposed data model with similar hyperparameters and different default lags. The Apple daily dataset performed well with a Default_1 lag, using an undecomposed data model and the ReLU, attaining 0.01312, 0.00854 and 3.67 minutes for RMSE, MAE and runtime. The Netflix data performed best with the MeanAC_42 lag, using decomposed data model and the ELU achieving 0.00620, 0.00487 and 3.01 minutes for the same metrics.
基金State Natural Science Foundation of China (50178055).
文摘The brief theories of wavelet analysis and Hilbert-Huang transform (HHT) are introduced firstly in the present paper. Then several signal data were analyzed by using wavelet and HHT methods, respectively. The comparison shows that HHT is not only an effective method for analyzing non-stationary data, but also is a useful tool for examining detailed characters of time history signal.
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.
文摘The discrete time wavelet transform has been used to develop software that detects seismic P and S-phases. The detection algorithm is based on the enhanced amplitude and polarization information provided by the wavelet transform coefficients of the raw seismic data. The algorithm detects phases, determines arrival times and indicates the seismic event direction from three component seismic data that represents the ground displacement in three orthogonal directions. The essential concept is that strong features of the seismic signal are present in the wavelet coefficients across several scales of time and direction. The P-phase is detected by generating a function using polarization information while S-phase is detected by generating a function based on the transverse to radial amplitude ratio. These functions are shown to be very effective metrics in detecting P and S-phases and for determining their arrival times for low signal-to-noise arrivals. Results are compared with arrival times obtained by a human analyst as well as with a standard STA/LTA algorithm from local and regional earthquakes and found to be consistent.
文摘Continuous wavelet transform is employed to detect singularities in 2-D signals by tracking modulus maxima along maxima lines and particularly applied to microcalcification detection in mammograms. The microcalcifications are modeled as smoothed positive impulse functions. Other target property detection can be performed by adjusting its mathematical model. In this application, the general modulus maximum and its scale of each singular point are detected and statistically analyzed locally in its neighborhood. The diagnosed microcalcification cluster results are compared with health tissue results, showing that general modulus maxima can serve as a suspicious spot detection tool with the detection performance no significantly sensitive to the breast tissue background properties. Performed fractal analysis of selected singularities supports the statistical findings. It is important to select the suitable computation parameters-thresholds of magnitude, argument and frequency range-in accordance to mathematical description of the target property as well as spatial and numerical resolution of the analyzed signal. The tests are performed on a set of images with empirically selected parameters for 200 μm/pixel spatial and 8 bits/pixel numerical resolution, appropriate for detection of the suspicious spots in a mammogram. The results show that the magnitude of a singularity general maximum can play a significant role in the detection of microcalcification, while zooming into a cluster in image finer spatial resolution both magnitude of general maximum and the spatial distribution of the selected set of singularities may lead to the breast abnormality characterization.
基金the Fundamental Research Funds for the Central Universities of China(No.YS1404)the Beijing University of Chemical Technology Interdisciplinary Funds for "Visual Media Computing"
文摘This paper presents a wavelet-based hybrid threshold method according to the soft- and hard-threshold functions proposed by Donoho. The wavelet-based hybrid threshold method may help doctors to know more details on the liver disease through denoising the ultrasound image of the liver. First of all, an analytical expression for the hybrid threshold function is discussed. The wavelet-based hybrid threshold method is then investigated for ultrasound image of the liver. Finally, we test the influence of this parameter on the proposed method with the real ultrasound image corrupted by speckle noise with different variances. Moreover, we compare the proposed method under the varying parameters with the soft-threshold function and the hard-threshold function. Three metrics, which are correlation coefficient, edge preservation index and structural similarity index, are measured to quantify the denoised results of ultrasound liver image. Experimental results demonstrate the potential of the proposed method for ultrasound liver image denosing.
文摘The spectral analysis of stationary random processes is studied by using wavelet transform method. On the basis of wavelet transform, the conception of time-frequency power spectral density of random processes and time-frequency cross-spectral density of jointly stationary random processes are presented. The characters of the time-frequency power spectral density and its relationship with traditional power spectral density are also studied in details.
文摘We consider the problem of approximating two, possibly unrelated probability distributions from a single complex-valued function and its Fourier transform. We show that this problem always has a solution within a specified degree of accuracy, provided the distributions satisfy the necessary regularity conditions. We describe the algorithm and construction of and provide examples of approximating several pairs of distributions using the algorithm.
基金sponsored by the National High-Technology Research and Development Program of China (863 Program), No. 2009AA012201
文摘The present study conducted a multi-scale dynamic functional connectivity analysis to evaluate dynamic behavior of acupuncture at Taichong （LR3） and sham acupoints surrounding Taichong Results showed differences in wavelet transform coherence characteristic curves in the declive, precuneus, postcentral gyrus, supramarginal gyrus, and occipital lobe between acupuncture at Taichong and acupuncture at sham acupoints. The differences in characteristic curves revealed that the specific effect of acupuncture existed during the post-acupuncture rest state and lasted for 5 minutes.
文摘In this paper, the notion of p-wavelet packets on the positive half-line P＋ is introduced. A new method for constructing non-orthogonal wavelet packets related to Walsh functions is developed by splitting the wavelet subspaces directly instead of using the lowpass and high-pass filters associated with the multiresolution analysis as used in the classical theory of wavelet packets. Further, the method overcomes the difficulty of constructing non-orthogonal wavelet packets of the dilation factor p 〉 2.
