A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, ...A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3（iii）] with extra information about the bounds.展开更多
In this paper,using Parseval frames we generalize Sun’s results to g-frames in Hilbert C^(*)-modules.Moreover,for g-frames in Hilbert spaces,we present some characterizations in terms of a family of frames,not only f...In this paper,using Parseval frames we generalize Sun’s results to g-frames in Hilbert C^(*)-modules.Moreover,for g-frames in Hilbert spaces,we present some characterizations in terms of a family of frames,not only for orthonormal bases.Also,we have a note about a comment and a relation in the proof of Proposition 5.3 in[D.Li et al.,On weaving g-frames for Hilbert spaces,Complex Analysis and Operator Theory,2020].Finally,we have some results for g-Riesz bases,woven and P-woven g-frames.展开更多
Fusion-Riesz frame (Riesz frame of subspace) whose all subsets are fusion frame sequences with the same bounds is a special fusion frame. It is also considered a generalization of Riesz frame since it shares some impo...Fusion-Riesz frame (Riesz frame of subspace) whose all subsets are fusion frame sequences with the same bounds is a special fusion frame. It is also considered a generalization of Riesz frame since it shares some important properties of Riesz frame. In this paper, we show a part of these properties of fusion-Riesz frame and the new results about the stabilities of fusion-Riesz frames under operator perturbation (simple named operator perturbation of fusion-Riesz frames). Moreover, we also compare the operator perturbation of fusion-Riesz frame with that of fusion frame, fusion-Riesz basis (also called Riesz decomposition or Riesz fusion basis) and exact fusion frame.展开更多
Target signal acquisition and detection based on sonar images is a challenging task due to the complex underwater environment.In order to solve the problem that some semantic information in sonar images is lost and mo...Target signal acquisition and detection based on sonar images is a challenging task due to the complex underwater environment.In order to solve the problem that some semantic information in sonar images is lost and model detection performance is degraded due to the complex imaging environment,we proposed a more effective and robust target detection framework based on deep learning,which can make full use of the acoustic shadow information in the forward-looking sonar images to assist underwater target detection.Firstly,the weighted box fusion method is adopted to generate a fusion box by weighted fusion of prediction boxes with high confidence,so as to obtain accurate acoustic shadow boxes.Further,the acoustic shadow box is cut down to get the feature map containing the acoustic shadow information,and then the acoustic shadow feature map and the target information feature map are adaptively fused to make full use of the acoustic shadow feature information.In addition,we introduce a threshold processing module to improve the attention of the model to important feature information.Through the underwater sonar dataset provided by Pengcheng Laboratory,the proposed method improved the average accuracy by 3.14%at the IoU threshold of 0.7,which is better than the current traditional target detection model.展开更多
文摘A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3（iii）] with extra information about the bounds.
文摘In this paper,using Parseval frames we generalize Sun’s results to g-frames in Hilbert C^(*)-modules.Moreover,for g-frames in Hilbert spaces,we present some characterizations in terms of a family of frames,not only for orthonormal bases.Also,we have a note about a comment and a relation in the proof of Proposition 5.3 in[D.Li et al.,On weaving g-frames for Hilbert spaces,Complex Analysis and Operator Theory,2020].Finally,we have some results for g-Riesz bases,woven and P-woven g-frames.
基金Supported by the National Natural Science Foundation of China(11071152)the Natural Science Foundation of Guangdong Province(S2015A030313443)
文摘Fusion-Riesz frame (Riesz frame of subspace) whose all subsets are fusion frame sequences with the same bounds is a special fusion frame. It is also considered a generalization of Riesz frame since it shares some important properties of Riesz frame. In this paper, we show a part of these properties of fusion-Riesz frame and the new results about the stabilities of fusion-Riesz frames under operator perturbation (simple named operator perturbation of fusion-Riesz frames). Moreover, we also compare the operator perturbation of fusion-Riesz frame with that of fusion frame, fusion-Riesz basis (also called Riesz decomposition or Riesz fusion basis) and exact fusion frame.
基金This work is supported by National Natural Science Foundation of China(Grant:62272109).
文摘Target signal acquisition and detection based on sonar images is a challenging task due to the complex underwater environment.In order to solve the problem that some semantic information in sonar images is lost and model detection performance is degraded due to the complex imaging environment,we proposed a more effective and robust target detection framework based on deep learning,which can make full use of the acoustic shadow information in the forward-looking sonar images to assist underwater target detection.Firstly,the weighted box fusion method is adopted to generate a fusion box by weighted fusion of prediction boxes with high confidence,so as to obtain accurate acoustic shadow boxes.Further,the acoustic shadow box is cut down to get the feature map containing the acoustic shadow information,and then the acoustic shadow feature map and the target information feature map are adaptively fused to make full use of the acoustic shadow feature information.In addition,we introduce a threshold processing module to improve the attention of the model to important feature information.Through the underwater sonar dataset provided by Pengcheng Laboratory,the proposed method improved the average accuracy by 3.14%at the IoU threshold of 0.7,which is better than the current traditional target detection model.
