In this paper we develope a theory of new generalized functions by using Nonstandard Analysis which is closely relevant to that of Colombeau's new generalized functions.
In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the gen...In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the generalized resolvent operator technique associated with the (A,η,m)-monotone operators, the approximation solvability of the operator equation problems and the convergence of iterative sequences generated by the algorithm are discussed. Our results improve and generalize the corresponding results in the literature.展开更多
It is well known that the Two-step Weighted Least-Squares(TWLS) is a widely used method for source localization and sensor position refinement. For this reason, we propose a unified framework of the TWLS method for jo...It is well known that the Two-step Weighted Least-Squares(TWLS) is a widely used method for source localization and sensor position refinement. For this reason, we propose a unified framework of the TWLS method for joint estimation of multiple disjoint sources and sensor locations in this paper. Unlike some existing works, the presented method is based on more general measurement model, and therefore it can be applied to many different localization scenarios.Besides, it does not have the initialization and local convergence problem. The closed-form expression for the covariance matrix of the proposed TWLS estimator is also derived by exploiting the first-order perturbation analysis. Moreover, the estimation accuracy of the TWLS method is shown analytically to achieve the Cramér-Rao Bound(CRB) before the threshold effect takes place. The theoretical analysis is also performed in a common mathematical framework, rather than aiming at some specific signal metrics. Finally, two numerical experiments are performed to support the theoretical development in this paper.展开更多
Deep learning is capable of greatly promoting the progress of super-resolution imaging technology in terms of imaging and reconstruction speed,imaging resolution,and imagingflux.This paper proposes a deep neural netwo...Deep learning is capable of greatly promoting the progress of super-resolution imaging technology in terms of imaging and reconstruction speed,imaging resolution,and imagingflux.This paper proposes a deep neural network based on a generative adversarial network(GAN).The generator employs a U-Net-based network,which integrates Dense Net for the downsampling component.The proposed method has excellent properties,for example,the network model is trained with several different datasets of biological structures;the trained model can improve the imaging resolution of different microscopy imaging modalities such as confocal imaging and wide-field imaging;and the model demonstrates a generalized ability to improve the resolution of different biological structures even out of the datasets.In addition,experimental results showed that the method improved the resolution of caveolin-coated pits(CCPs)structures from 264 nm to 138 nm,a 1.91-fold increase,and nearly doubled the resolution of DNA molecules imaged while being transported through microfluidic channels.展开更多
文摘In this paper we develope a theory of new generalized functions by using Nonstandard Analysis which is closely relevant to that of Colombeau's new generalized functions.
文摘In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the generalized resolvent operator technique associated with the (A,η,m)-monotone operators, the approximation solvability of the operator equation problems and the convergence of iterative sequences generated by the algorithm are discussed. Our results improve and generalize the corresponding results in the literature.
基金co-supported by the National Natural Science Foundation of China (Nos. 61201381, 61401513 and 61772548)the China Postdoctoral Science Foundation (No. 2016M592989)+1 种基金the Self-Topic Foundation of Information Engineering University, China (No. 2016600701)the Outstanding Youth Foundation of Information Engineering University, China (No. 2016603201)
文摘It is well known that the Two-step Weighted Least-Squares(TWLS) is a widely used method for source localization and sensor position refinement. For this reason, we propose a unified framework of the TWLS method for joint estimation of multiple disjoint sources and sensor locations in this paper. Unlike some existing works, the presented method is based on more general measurement model, and therefore it can be applied to many different localization scenarios.Besides, it does not have the initialization and local convergence problem. The closed-form expression for the covariance matrix of the proposed TWLS estimator is also derived by exploiting the first-order perturbation analysis. Moreover, the estimation accuracy of the TWLS method is shown analytically to achieve the Cramér-Rao Bound(CRB) before the threshold effect takes place. The theoretical analysis is also performed in a common mathematical framework, rather than aiming at some specific signal metrics. Finally, two numerical experiments are performed to support the theoretical development in this paper.
基金Subjects funded by the National Natural Science Foundation of China(Nos.62275216 and 61775181)the Natural Science Basic Research Programme of Shaanxi Province-Major Basic Research Special Project(Nos.S2018-ZC-TD-0061 and TZ0393)the Special Project for the Development of National Key Scientific Instruments and Equipment No.(51927804).
文摘Deep learning is capable of greatly promoting the progress of super-resolution imaging technology in terms of imaging and reconstruction speed,imaging resolution,and imagingflux.This paper proposes a deep neural network based on a generative adversarial network(GAN).The generator employs a U-Net-based network,which integrates Dense Net for the downsampling component.The proposed method has excellent properties,for example,the network model is trained with several different datasets of biological structures;the trained model can improve the imaging resolution of different microscopy imaging modalities such as confocal imaging and wide-field imaging;and the model demonstrates a generalized ability to improve the resolution of different biological structures even out of the datasets.In addition,experimental results showed that the method improved the resolution of caveolin-coated pits(CCPs)structures from 264 nm to 138 nm,a 1.91-fold increase,and nearly doubled the resolution of DNA molecules imaged while being transported through microfluidic channels.
