Wavelet, a powerful tool for signal processing, can be used to approximate the target func-tion. For enhancing the sparse property of wavelet approximation, a new algorithm was proposed by using wavelet kernel Support...Wavelet, a powerful tool for signal processing, can be used to approximate the target func-tion. For enhancing the sparse property of wavelet approximation, a new algorithm was proposed by using wavelet kernel Support Vector Machines (SVM), which can converge to minimum error with bet-ter sparsity. Here, wavelet functions would be firstly used to construct the admitted kernel for SVM according to Mercy theory; then new SVM with this kernel can be used to approximate the target fun-citon with better sparsity than wavelet approxiamtion itself. The results obtained by our simulation ex-periment show the feasibility and validity of wavelet kernel support vector machines.展开更多
By combining the wavelet decomposition with kernel method, a practical approach of universal multiscale wavelet kernels constructed in reproducing kernel Hilbert space （RKHS） is discussed, and an identification sche...By combining the wavelet decomposition with kernel method, a practical approach of universal multiscale wavelet kernels constructed in reproducing kernel Hilbert space （RKHS） is discussed, and an identification scheme using wavelet support vector machines （WSVM） estimator is proposed for nordinear dynamic systems. The good approximating properties of wavelet kernel function enhance the generalization ability of the proposed method, and the comparison of some numerical experimental results between the novel approach and some existing methods is encouraging.展开更多
Structured illumination microscopy(SIM)is a popular and powerful super-resolution(SR)technique in biomedical research.However,the conventional reconstruction algorithm for SIM heavily relies on the accurate prior know...Structured illumination microscopy(SIM)is a popular and powerful super-resolution(SR)technique in biomedical research.However,the conventional reconstruction algorithm for SIM heavily relies on the accurate prior knowledge of illumination patterns and signal-to-noise ratio(SNR)of raw images.To obtain high-quality SR images,several raw images need to be captured under high fluorescence level,which further restricts SIM’s temporal resolution and its applications.Deep learning(DL)is a data-driven technology that has been used to expand the limits of optical microscopy.In this study,we propose a deep neural network based on multi-level wavelet and attention mechanism(MWAM)for SIM.Our results show that the MWAM network can extract high-frequency information contained in SIM raw images and accurately integrate it into the output image,resulting in superior SR images compared to those generated using wide-field images as input data.We also demonstrate that the number of SIM raw images can be reduced to three,with one image in each illumination orientation,to achieve the optimal tradeoff between temporal and spatial resolution.Furthermore,our MWAM network exhibits superior reconstruction ability on low-SNR images compared to conventional SIM algorithms.We have also analyzed the adaptability of this network on other biological samples and successfully applied the pretrained model to other SIM systems.展开更多
The relationship among Mercer kernel, reproducing kernel and positive definite kernel in support vector machine （SVM） is proved and their roles in SVM are discussed. The quadratic form of the kernel matrix is used t...The relationship among Mercer kernel, reproducing kernel and positive definite kernel in support vector machine （SVM） is proved and their roles in SVM are discussed. The quadratic form of the kernel matrix is used to confirm the positive definiteness and their construction. Based on the Bochner theorem, some translation invariant kernels are checked in their Fourier domain. Some rotation invariant radial kernels are inspected according to the Schoenberg theorem. Finally, the construction of discrete scaling and wavelet kernels, the kernel selection and the kernel parameter learning are discussed.展开更多
A new filtering method for SAR data de-noising using wavelet support vector regression （WSVR） is developed. On the basis of the grey scale distribution character of SAR imagery, the logarithmic SAR image as a noise ...A new filtering method for SAR data de-noising using wavelet support vector regression （WSVR） is developed. On the basis of the grey scale distribution character of SAR imagery, the logarithmic SAR image as a noise polluted signal is taken and the noise model assumption in logarithmic domain with Gaussian noise and impact noise is proposed. Based on the better per- formance of support vector regression （SVR） for complex signal approximation and the wavelet for signal detail expression, the wavelet kernel function is chosen as support vector kernel func- tion. Then the logarithmic SAR image is regressed with WSVR. Furthermore the regression distance is used as a judgment index of the noise type. According to the judgment of noise type every pixel can be adaptively de-noised with different filters. Through an approximation experiment for a one-dimensional complex signal, the feasibility of SAR data regression based on WSVR is con- firmed. Afterward the SAR image is treated as a two-dimensional continuous signal and filtered by an SVR with wavelet kernel function. The results show that the method proposed here reduces the radar speckle noise effectively while maintaining edge features and details well.展开更多
We present wavelet bases made of piecewise (low degree) polynomial functions with an (arbitrary) assigned number of vanishing moments. We study some of the properties of these wavelet bases;in particular we consider t...We present wavelet bases made of piecewise (low degree) polynomial functions with an (arbitrary) assigned number of vanishing moments. We study some of the properties of these wavelet bases;in particular we consider their use in the approximation of functions and in numerical quadrature. We focus on two applications: integral kernel sparsification and digital image compression and reconstruction. In these application areas the use of these wavelet bases gives very satisfactory results.展开更多
In this article, we consider a fast algorithm for first generation Calderon-Zygmund operators. First, we estimate the convergence speed of the relative approximation algorithm. Then, we establish the continuity on Bes...In this article, we consider a fast algorithm for first generation Calderon-Zygmund operators. First, we estimate the convergence speed of the relative approximation algorithm. Then, we establish the continuity on Besov spaces and Triebel-Lizorkin spaces for the oper- ators with rough kernel.展开更多
The vector sampling theorem has been investigated and widely used by multi-channel deconvolution, multi-source separation and multi-input multi-output （MIh40） systems. Commonly, for most of the results on MIMO syste...The vector sampling theorem has been investigated and widely used by multi-channel deconvolution, multi-source separation and multi-input multi-output （MIh40） systems. Commonly, for most of the results on MIMO systems, the input signals are supposed to be band-limited. In this paper, we study the vector sampling theorem for the wavelet subspaces with reproducing kernel. The case of uniform sampling is discussed, and the necessary and sufficient conditions for reconstruction are given. Examples axe also presented.展开更多
There has been a lot of research has been performed regarding diagnosing rolling element bearing faults using wavelet analysis, but almost all methods are not ideal for picking up fault signal characteristics under st...There has been a lot of research has been performed regarding diagnosing rolling element bearing faults using wavelet analysis, but almost all methods are not ideal for picking up fault signal characteristics under strong noise. Therefore, this paper proposes auto-correlation, cross-correlation and weighted average fault diagnosis methods based on wavelet transform (WT) de-noising which combine correlation analysis with WT for the first time. These three methods compute the auto-correlation, the cross-correlation and the weighted average of the measured vibration signals, then de-noise by thresholding and computing the auto-correlation of de-noised coefficients of WT and FFT of energy sequence. The simulation results indicate that all methods enhance the capabilities of fault diagnosis of rolling bearings and pick up the fault characteristics effectively.展开更多
Robust watermarking requires finding invariant features under multiple attacks to ensure correct extraction.Deep learning has extremely powerful in extracting features,and watermarking algorithms based on deep learnin...Robust watermarking requires finding invariant features under multiple attacks to ensure correct extraction.Deep learning has extremely powerful in extracting features,and watermarking algorithms based on deep learning have attracted widespread attention.Most existing methods use 3×3 small kernel convolution to extract image features and embed the watermarking.However,the effective perception fields for small kernel convolution are extremely confined,so the pixels that each watermarking can affect are restricted,thus limiting the performance of the watermarking.To address these problems,we propose a watermarking network based on large kernel convolution and adaptive weight assignment for loss functions.It uses large-kernel depth-wise convolution to extract features for learning large-scale image information and subsequently projects the watermarking into a highdimensional space by 1×1 convolution to achieve adaptability in the channel dimension.Subsequently,the modification of the embedded watermarking on the cover image is extended to more pixels.Because the magnitude and convergence rates of each loss function are different,an adaptive loss weight assignment strategy is proposed to make theweights participate in the network training together and adjust theweight dynamically.Further,a high-frequency wavelet loss is proposed,by which the watermarking is restricted to only the low-frequency wavelet sub-bands,thereby enhancing the robustness of watermarking against image compression.The experimental results show that the peak signal-to-noise ratio(PSNR)of the encoded image reaches 40.12,the structural similarity(SSIM)reaches 0.9721,and the watermarking has good robustness against various types of noise.展开更多
文摘Wavelet, a powerful tool for signal processing, can be used to approximate the target func-tion. For enhancing the sparse property of wavelet approximation, a new algorithm was proposed by using wavelet kernel Support Vector Machines (SVM), which can converge to minimum error with bet-ter sparsity. Here, wavelet functions would be firstly used to construct the admitted kernel for SVM according to Mercy theory; then new SVM with this kernel can be used to approximate the target fun-citon with better sparsity than wavelet approxiamtion itself. The results obtained by our simulation ex-periment show the feasibility and validity of wavelet kernel support vector machines.
基金the National 973 Key Fundamental Research Project of China (Grant No.2002CB312200)
文摘By combining the wavelet decomposition with kernel method, a practical approach of universal multiscale wavelet kernels constructed in reproducing kernel Hilbert space （RKHS） is discussed, and an identification scheme using wavelet support vector machines （WSVM） estimator is proposed for nordinear dynamic systems. The good approximating properties of wavelet kernel function enhance the generalization ability of the proposed method, and the comparison of some numerical experimental results between the novel approach and some existing methods is encouraging.
基金supported by the National Natural Science Foundation of China(Grant Nos.62005307 and 61975228).
文摘Structured illumination microscopy(SIM)is a popular and powerful super-resolution(SR)technique in biomedical research.However,the conventional reconstruction algorithm for SIM heavily relies on the accurate prior knowledge of illumination patterns and signal-to-noise ratio(SNR)of raw images.To obtain high-quality SR images,several raw images need to be captured under high fluorescence level,which further restricts SIM’s temporal resolution and its applications.Deep learning(DL)is a data-driven technology that has been used to expand the limits of optical microscopy.In this study,we propose a deep neural network based on multi-level wavelet and attention mechanism(MWAM)for SIM.Our results show that the MWAM network can extract high-frequency information contained in SIM raw images and accurately integrate it into the output image,resulting in superior SR images compared to those generated using wide-field images as input data.We also demonstrate that the number of SIM raw images can be reduced to three,with one image in each illumination orientation,to achieve the optimal tradeoff between temporal and spatial resolution.Furthermore,our MWAM network exhibits superior reconstruction ability on low-SNR images compared to conventional SIM algorithms.We have also analyzed the adaptability of this network on other biological samples and successfully applied the pretrained model to other SIM systems.
基金Supported by the National Natural Science Foundation of China(60473035)~~
文摘The relationship among Mercer kernel, reproducing kernel and positive definite kernel in support vector machine （SVM） is proved and their roles in SVM are discussed. The quadratic form of the kernel matrix is used to confirm the positive definiteness and their construction. Based on the Bochner theorem, some translation invariant kernels are checked in their Fourier domain. Some rotation invariant radial kernels are inspected according to the Schoenberg theorem. Finally, the construction of discrete scaling and wavelet kernels, the kernel selection and the kernel parameter learning are discussed.
基金supported by Shanghai Science and Technology Commission Innovation Action Plan(08DZ1205708)
文摘A new filtering method for SAR data de-noising using wavelet support vector regression （WSVR） is developed. On the basis of the grey scale distribution character of SAR imagery, the logarithmic SAR image as a noise polluted signal is taken and the noise model assumption in logarithmic domain with Gaussian noise and impact noise is proposed. Based on the better per- formance of support vector regression （SVR） for complex signal approximation and the wavelet for signal detail expression, the wavelet kernel function is chosen as support vector kernel func- tion. Then the logarithmic SAR image is regressed with WSVR. Furthermore the regression distance is used as a judgment index of the noise type. According to the judgment of noise type every pixel can be adaptively de-noised with different filters. Through an approximation experiment for a one-dimensional complex signal, the feasibility of SAR data regression based on WSVR is con- firmed. Afterward the SAR image is treated as a two-dimensional continuous signal and filtered by an SVR with wavelet kernel function. The results show that the method proposed here reduces the radar speckle noise effectively while maintaining edge features and details well.
文摘We present wavelet bases made of piecewise (low degree) polynomial functions with an (arbitrary) assigned number of vanishing moments. We study some of the properties of these wavelet bases;in particular we consider their use in the approximation of functions and in numerical quadrature. We focus on two applications: integral kernel sparsification and digital image compression and reconstruction. In these application areas the use of these wavelet bases gives very satisfactory results.
基金Supported by NNSF of China(11271209,1137105,11571261)and SRFDP(20130003110003)
文摘In this article, we consider a fast algorithm for first generation Calderon-Zygmund operators. First, we estimate the convergence speed of the relative approximation algorithm. Then, we establish the continuity on Besov spaces and Triebel-Lizorkin spaces for the oper- ators with rough kernel.
基金supported by the National Natural Science Foundation of China (Grant No.60873130)the Shanghai Leading Academic Discipline Project (Grant No.J50104)
文摘The vector sampling theorem has been investigated and widely used by multi-channel deconvolution, multi-source separation and multi-input multi-output （MIh40） systems. Commonly, for most of the results on MIMO systems, the input signals are supposed to be band-limited. In this paper, we study the vector sampling theorem for the wavelet subspaces with reproducing kernel. The case of uniform sampling is discussed, and the necessary and sufficient conditions for reconstruction are given. Examples axe also presented.
文摘There has been a lot of research has been performed regarding diagnosing rolling element bearing faults using wavelet analysis, but almost all methods are not ideal for picking up fault signal characteristics under strong noise. Therefore, this paper proposes auto-correlation, cross-correlation and weighted average fault diagnosis methods based on wavelet transform (WT) de-noising which combine correlation analysis with WT for the first time. These three methods compute the auto-correlation, the cross-correlation and the weighted average of the measured vibration signals, then de-noise by thresholding and computing the auto-correlation of de-noised coefficients of WT and FFT of energy sequence. The simulation results indicate that all methods enhance the capabilities of fault diagnosis of rolling bearings and pick up the fault characteristics effectively.
基金supported,in part,by the National Nature Science Foundation of China under grant numbers 62272236in part,by the Natural Science Foundation of Jiangsu Province under grant numbers BK20201136,BK20191401in part,by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)fund.
文摘Robust watermarking requires finding invariant features under multiple attacks to ensure correct extraction.Deep learning has extremely powerful in extracting features,and watermarking algorithms based on deep learning have attracted widespread attention.Most existing methods use 3×3 small kernel convolution to extract image features and embed the watermarking.However,the effective perception fields for small kernel convolution are extremely confined,so the pixels that each watermarking can affect are restricted,thus limiting the performance of the watermarking.To address these problems,we propose a watermarking network based on large kernel convolution and adaptive weight assignment for loss functions.It uses large-kernel depth-wise convolution to extract features for learning large-scale image information and subsequently projects the watermarking into a highdimensional space by 1×1 convolution to achieve adaptability in the channel dimension.Subsequently,the modification of the embedded watermarking on the cover image is extended to more pixels.Because the magnitude and convergence rates of each loss function are different,an adaptive loss weight assignment strategy is proposed to make theweights participate in the network training together and adjust theweight dynamically.Further,a high-frequency wavelet loss is proposed,by which the watermarking is restricted to only the low-frequency wavelet sub-bands,thereby enhancing the robustness of watermarking against image compression.The experimental results show that the peak signal-to-noise ratio(PSNR)of the encoded image reaches 40.12,the structural similarity(SSIM)reaches 0.9721,and the watermarking has good robustness against various types of noise.
