Missing data are a problem in geophysical surveys, and interpolation and reconstruction of missing data is part of the data processing and interpretation. Based on the sparseness of the geophysical data or the transfo...Missing data are a problem in geophysical surveys, and interpolation and reconstruction of missing data is part of the data processing and interpretation. Based on the sparseness of the geophysical data or the transform domain, we can improve the accuracy and stability of the reconstruction by transforming it to a sparse optimization problem. In this paper, we propose a mathematical model for the sparse reconstruction of data based on the LO-norm minimization. Furthermore, we discuss two types of the approximation algorithm for the LO- norm minimization according to the size and characteristics of the geophysical data： namely, the iteratively reweighted least-squares algorithm and the fast iterative hard thresholding algorithm. Theoretical and numerical analysis showed that applying the iteratively reweighted least-squares algorithm to the reconstruction of potential field data exploits its fast convergence rate, short calculation time, and high precision, whereas the fast iterative hard thresholding algorithm is more suitable for processing seismic data, moreover, its computational efficiency is better than that of the traditional iterative hard thresholding algorithm.展开更多
The process to achieve time synchronization and ranging for a network of mobile nodes is raising a concern among researchers, and hence a variety of joint time synchronization and ranging algorithms have been proposed...The process to achieve time synchronization and ranging for a network of mobile nodes is raising a concern among researchers, and hence a variety of joint time synchronization and ranging algorithms have been proposed in recent years. However, few of them handle the case of all-node motion under unknown positions and velocities. This study addresses the problem of determining ranging and time synchronization for a group of nodes moving within a local area. First, we examined several models of clock discrepancy and synchronous two-way ranging. Based upon these models, we present a solution for time synchronization with known positions and velocities. Next, we propose a functional model that jointly estimates the clock skew, clock offset, and time of flight in the absence of a priori knowledge for a pair of mobile nodes. Then, we extend this model to a network-wide time synchronization scheme by way of a global least square estimator. We also discuss the advantages and disadvantages of our model compared to the existing algorithms, and we provide some applicable scenarios as well. Finally, we show that the simulation results verify the validity of our analysis.展开更多
基金supported by the National Natural Science Foundation of China (Grant No.41074133)
文摘Missing data are a problem in geophysical surveys, and interpolation and reconstruction of missing data is part of the data processing and interpretation. Based on the sparseness of the geophysical data or the transform domain, we can improve the accuracy and stability of the reconstruction by transforming it to a sparse optimization problem. In this paper, we propose a mathematical model for the sparse reconstruction of data based on the LO-norm minimization. Furthermore, we discuss two types of the approximation algorithm for the LO- norm minimization according to the size and characteristics of the geophysical data： namely, the iteratively reweighted least-squares algorithm and the fast iterative hard thresholding algorithm. Theoretical and numerical analysis showed that applying the iteratively reweighted least-squares algorithm to the reconstruction of potential field data exploits its fast convergence rate, short calculation time, and high precision, whereas the fast iterative hard thresholding algorithm is more suitable for processing seismic data, moreover, its computational efficiency is better than that of the traditional iterative hard thresholding algorithm.
基金supported by the National Natural Science Foundation of China(Grant No.61471021)
文摘The process to achieve time synchronization and ranging for a network of mobile nodes is raising a concern among researchers, and hence a variety of joint time synchronization and ranging algorithms have been proposed in recent years. However, few of them handle the case of all-node motion under unknown positions and velocities. This study addresses the problem of determining ranging and time synchronization for a group of nodes moving within a local area. First, we examined several models of clock discrepancy and synchronous two-way ranging. Based upon these models, we present a solution for time synchronization with known positions and velocities. Next, we propose a functional model that jointly estimates the clock skew, clock offset, and time of flight in the absence of a priori knowledge for a pair of mobile nodes. Then, we extend this model to a network-wide time synchronization scheme by way of a global least square estimator. We also discuss the advantages and disadvantages of our model compared to the existing algorithms, and we provide some applicable scenarios as well. Finally, we show that the simulation results verify the validity of our analysis.
