Tikhonov regularization is a powerful tool for solving linear discrete ill-posed problems.However,effective methods for dealing with large-scale ill-posed problems are still lacking.The Kaczmarz method is an effective...Tikhonov regularization is a powerful tool for solving linear discrete ill-posed problems.However,effective methods for dealing with large-scale ill-posed problems are still lacking.The Kaczmarz method is an effective iterative projection algorithm for solving large linear equations due to its simplicity.We propose a regularized randomized extended Kaczmarz(RREK)algorithm for solving large discrete ill-posed problems via combining the Tikhonov regularization and the randomized Kaczmarz method.The convergence of the algorithm is proved.Numerical experiments illustrate that the proposed algorithm has higher accuracy and better image restoration quality compared with the existing randomized extended Kaczmarz(REK)method.展开更多
Based on the global land cover data at 30 m resolution(Globe Land30) in the year 2000 and 2010, the urban expansion process of 320 cities in China was analyzed using lognormal regression, and the expansion model were ...Based on the global land cover data at 30 m resolution(Globe Land30) in the year 2000 and 2010, the urban expansion process of 320 cities in China was analyzed using lognormal regression, and the expansion model were established. Three metrics were presented for the models, including the peak position, the full width at half maximum, and the skewness. It was found that the three metrics could reveal different patterns of the urban expansion process of cities with different sizes. Specifically, cities with larger size tend to expand outward strongly, and their expansion intensity and influence are likely to be higher. Moreover, most cities' expansion occurs around the urban core with spatially limited influence. In addition, it was also found that the city's expansion intensity is related to the city size. These results showed that the lognormal regression model could describe the distribution of urban expansion with effectiveness and robustness.展开更多
When solving the problem of simultaneous localization and mapping(SLAM) ,a standard extended Kalman filter(EKF) is subject to linearization errors and causes optimistic estimation.This paper proposes a submap algorith...When solving the problem of simultaneous localization and mapping(SLAM) ,a standard extended Kalman filter(EKF) is subject to linearization errors and causes optimistic estimation.This paper proposes a submap algorithm,which builds a weighted least squares(WLS) constraint between two adjacent submaps according to the different estimations of the common features and the relationship between the vehicle poses in the corresponding submaps.By establishing the constraint equation after loop closing,re-linearization is implemented and each submap's reference frame tends to its equilibrium position quickly.Experimental results demonstrate that the algorithm could get a globally consistent map and linearization errors are limited in local regions.展开更多
基金supported by the National Natural Science Foundations of China(Nos.11571171,62073161,and 61473148)。
文摘Tikhonov regularization is a powerful tool for solving linear discrete ill-posed problems.However,effective methods for dealing with large-scale ill-posed problems are still lacking.The Kaczmarz method is an effective iterative projection algorithm for solving large linear equations due to its simplicity.We propose a regularized randomized extended Kaczmarz(RREK)algorithm for solving large discrete ill-posed problems via combining the Tikhonov regularization and the randomized Kaczmarz method.The convergence of the algorithm is proved.Numerical experiments illustrate that the proposed algorithm has higher accuracy and better image restoration quality compared with the existing randomized extended Kaczmarz(REK)method.
基金supported by the National High-Tech Research Program of China (Grant No. 2013AA122802)
文摘Based on the global land cover data at 30 m resolution(Globe Land30) in the year 2000 and 2010, the urban expansion process of 320 cities in China was analyzed using lognormal regression, and the expansion model were established. Three metrics were presented for the models, including the peak position, the full width at half maximum, and the skewness. It was found that the three metrics could reveal different patterns of the urban expansion process of cities with different sizes. Specifically, cities with larger size tend to expand outward strongly, and their expansion intensity and influence are likely to be higher. Moreover, most cities' expansion occurs around the urban core with spatially limited influence. In addition, it was also found that the city's expansion intensity is related to the city size. These results showed that the lognormal regression model could describe the distribution of urban expansion with effectiveness and robustness.
基金the Knowledge Innovation Program of Shanghai Science and Technology Committee (No.08510708300)the Ph.D.Programs Foundation of Ministry of Education of China (No.20070248097)
文摘When solving the problem of simultaneous localization and mapping(SLAM) ,a standard extended Kalman filter(EKF) is subject to linearization errors and causes optimistic estimation.This paper proposes a submap algorithm,which builds a weighted least squares(WLS) constraint between two adjacent submaps according to the different estimations of the common features and the relationship between the vehicle poses in the corresponding submaps.By establishing the constraint equation after loop closing,re-linearization is implemented and each submap's reference frame tends to its equilibrium position quickly.Experimental results demonstrate that the algorithm could get a globally consistent map and linearization errors are limited in local regions.
