This paper studies the limit distributions for discretization error of irregular sam- pling approximations of stochastic integral. The irregular sampling approximation was first presented in Hayashi et al.[3], which w...This paper studies the limit distributions for discretization error of irregular sam- pling approximations of stochastic integral. The irregular sampling approximation was first presented in Hayashi et al.[3], which was more general than the sampling approximation in Lindberg and Rootzen [10]. As applications, we derive the asymptotic distribution of hedging error and the Euler scheme of stochastic differential equation respectively.展开更多
In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregu...In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.展开更多
Seismic data interpolation,especially irregularly sampled data interpolation,is a critical task for seismic processing and subsequent interpretation.Recently,with the development of machine learning and deep learning,...Seismic data interpolation,especially irregularly sampled data interpolation,is a critical task for seismic processing and subsequent interpretation.Recently,with the development of machine learning and deep learning,convolutional neural networks(CNNs)are applied for interpolating irregularly sampled seismic data.CNN based approaches can address the apparent defects of traditional interpolation methods,such as the low computational efficiency and the difficulty on parameters selection.However,current CNN based methods only consider the temporal and spatial features of irregularly sampled seismic data,which fail to consider the frequency features of seismic data,i.e.,the multi-scale features.To overcome these drawbacks,we propose a wavelet-based convolutional block attention deep learning(W-CBADL)network for irregularly sampled seismic data reconstruction.We firstly introduce the discrete wavelet transform(DWT)and the inverse wavelet transform(IWT)to the commonly used U-Net by considering the multi-scale features of irregularly sampled seismic data.Moreover,we propose to adopt the convolutional block attention module(CBAM)to precisely restore sampled seismic traces,which could apply the attention to both channel and spatial dimensions.Finally,we adopt the proposed W-CBADL model to synthetic and pre-stack field data to evaluate its validity and effectiveness.The results demonstrate that the proposed W-CBADL model could reconstruct irregularly sampled seismic data more effectively and more efficiently than the state-of-the-art contrastive CNN based models.展开更多
In this paper, we mainly pay attention to the weighted sampling and reconstruction algorithm in lattice-invariant signal spaces. We give the reconstruction formula in lattice-invariant signal spaces, which is a genera...In this paper, we mainly pay attention to the weighted sampling and reconstruction algorithm in lattice-invariant signal spaces. We give the reconstruction formula in lattice-invariant signal spaces, which is a generalization of former results in shift-invariant signal spaces. That is, we generalize and improve Aldroubi, Groechenig and Chen＇s results, respectively. So we obtain a general reconstruction algorithm in lattice-invariant signal spaces, which the signal spaces is sufficiently large to accommodate a large number of possible models. They are maybe useful for signal processing and communication theory.展开更多
As a special shift-invariant spaces, spline subspaces yield many advantages so that there are many practical applications for signal or image processing. In this paper, we pay attention to the sampling and reconstruct...As a special shift-invariant spaces, spline subspaces yield many advantages so that there are many practical applications for signal or image processing. In this paper, we pay attention to the sampling and reconstruction problem in spline subspaces. We improve lower bound of sampling set conditions in spline subspaces. Based on the improved explicit lower bound, a improved explicit convergence ratio of reconstruction algorithm is obtained. The improved convergence ratio occupies faster convergence rate than old one. At the end, some numerical examples are shown to validate our results.展开更多
A general A-P iterative algorithm in a shift-invariant space is presented. We use the algorithm to show reconstruction of signals from weighted samples and also show that the general improved algorithm has better conv...A general A-P iterative algorithm in a shift-invariant space is presented. We use the algorithm to show reconstruction of signals from weighted samples and also show that the general improved algorithm has better convergence rate than the existing one. An explicit estimate for a guaranteed rate of convergence is given.展开更多
基金Supported by the National Natural Science Foundation of China(11371317)
文摘This paper studies the limit distributions for discretization error of irregular sam- pling approximations of stochastic integral. The irregular sampling approximation was first presented in Hayashi et al.[3], which was more general than the sampling approximation in Lindberg and Rootzen [10]. As applications, we derive the asymptotic distribution of hedging error and the Euler scheme of stochastic differential equation respectively.
基金supported by National Natural Science Foundation of China (Grant No. 10671019)Research Fund for the Doctoral Program Higher Education (Grant No. 20050027007)Key Project of Technology Bureau of Sichuan Province (Grant No. 05JY029-138)
文摘In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.
基金Supported by the National Natural Science Foundation of China under Grant 42274144 and under Grant 41974137.
文摘Seismic data interpolation,especially irregularly sampled data interpolation,is a critical task for seismic processing and subsequent interpretation.Recently,with the development of machine learning and deep learning,convolutional neural networks(CNNs)are applied for interpolating irregularly sampled seismic data.CNN based approaches can address the apparent defects of traditional interpolation methods,such as the low computational efficiency and the difficulty on parameters selection.However,current CNN based methods only consider the temporal and spatial features of irregularly sampled seismic data,which fail to consider the frequency features of seismic data,i.e.,the multi-scale features.To overcome these drawbacks,we propose a wavelet-based convolutional block attention deep learning(W-CBADL)network for irregularly sampled seismic data reconstruction.We firstly introduce the discrete wavelet transform(DWT)and the inverse wavelet transform(IWT)to the commonly used U-Net by considering the multi-scale features of irregularly sampled seismic data.Moreover,we propose to adopt the convolutional block attention module(CBAM)to precisely restore sampled seismic traces,which could apply the attention to both channel and spatial dimensions.Finally,we adopt the proposed W-CBADL model to synthetic and pre-stack field data to evaluate its validity and effectiveness.The results demonstrate that the proposed W-CBADL model could reconstruct irregularly sampled seismic data more effectively and more efficiently than the state-of-the-art contrastive CNN based models.
文摘In this paper, we mainly pay attention to the weighted sampling and reconstruction algorithm in lattice-invariant signal spaces. We give the reconstruction formula in lattice-invariant signal spaces, which is a generalization of former results in shift-invariant signal spaces. That is, we generalize and improve Aldroubi, Groechenig and Chen＇s results, respectively. So we obtain a general reconstruction algorithm in lattice-invariant signal spaces, which the signal spaces is sufficiently large to accommodate a large number of possible models. They are maybe useful for signal processing and communication theory.
基金supported by the National Natural Science Foundation of China(11422102)the Fundamental Research Funds for the Central Universities(15lgzd07)+2 种基金the Guangdong Provincial Government of China through the Computational Science Innovative Research Team programthe Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen Universitysupported by the National Natural Science Foundation of China(11171299,91130009)
文摘As a special shift-invariant spaces, spline subspaces yield many advantages so that there are many practical applications for signal or image processing. In this paper, we pay attention to the sampling and reconstruction problem in spline subspaces. We improve lower bound of sampling set conditions in spline subspaces. Based on the improved explicit lower bound, a improved explicit convergence ratio of reconstruction algorithm is obtained. The improved convergence ratio occupies faster convergence rate than old one. At the end, some numerical examples are shown to validate our results.
基金This work is supported in part by the National Natural Science Foundation of China （10771190, 10801136）, the Mathematical Tianyuan Foundation of China NSF （10526036）, China Postdoctoral Science Foundation （20060391063）, Natural Science Foundation of Guangdong Province （07300434）
文摘A general A-P iterative algorithm in a shift-invariant space is presented. We use the algorithm to show reconstruction of signals from weighted samples and also show that the general improved algorithm has better convergence rate than the existing one. An explicit estimate for a guaranteed rate of convergence is given.
