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
A muitisensor image fusion algorithm is described using 2-dimensional nonseparable wavelet frame （NWF） transform. The source muitisensor images are first decomposed by the NWF transform. Then, the NWF transform coef...A muitisensor image fusion algorithm is described using 2-dimensional nonseparable wavelet frame （NWF） transform. The source muitisensor images are first decomposed by the NWF transform. Then, the NWF transform coefficients of the source images are combined into the composite NWF transform coefficients. Inverse NWF transform is performed on the composite NWF transform coefficients in order to obtain the intermediate fused image. Finally, intensity adjustment is applied to the intermediate fused image in order to maintain the dynamic intensity range. Experiment resuits using real data show that the proposed algorithm works well in muitisensor image fusion.展开更多
A new framework of region-based dynamic image fusion is proposed. First, the technique of target detection is applied to dynamic images (image sequences) to segment images into different targets and background regions...A new framework of region-based dynamic image fusion is proposed. First, the technique of target detection is applied to dynamic images (image sequences) to segment images into different targets and background regions. Then different fusion rules are employed in different regions so that the target information is preserved as much as possible. In addition, steerable non-separable wavelet frame transform is used in the process of multi-resolution analysis, so the system achieves favorable characters of orientation and invariant shift. Compared with other image fusion methods, experimental results showed that the proposed method has better capabilities of target recognition and preserves clear background information.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
For refinable functiombased affine bi-frames, nonhomogeneous ones admit fast algorithms and have extension principles as homogeneous ones. But all extension principles are based on some restrictions on refinable funct...For refinable functiombased affine bi-frames, nonhomogeneous ones admit fast algorithms and have extension principles as homogeneous ones. But all extension principles are based on some restrictions on refinable functions. So it is natural to ask what are expected from general refinable functions. In this paper, we introduce the notion of weak nonhomogeneous affine bi-frame （WNABF）. Under the setting of reducing subspaces of L2（Rd）, we characterize WNABFs and obtain a mixed oblique extension principle for WNABFs based on general refinable functions.展开更多
Motivated by K-frames and fusion frames, we study K-fusion frames in Hilbert spaces. By the means of operator K, frame operators and quotient operators, several necessary and sufficient conditions for a sequence of cl...Motivated by K-frames and fusion frames, we study K-fusion frames in Hilbert spaces. By the means of operator K, frame operators and quotient operators, several necessary and sufficient conditions for a sequence of closed subspaces and weights to be a K-fusion frame are obtained, and operators preserving K-fusion frames are discussed. In particular, we are interested in the K-fusion frames with the structure of unitary systems. Given a unitary system which has a complete wandering subspace, we give a necessary and sufficient condition for a closed subspace to be a K-fusion frame generator.展开更多
针对视觉背景提取(visual background extractor,ViBe)算法在运动目标检测过程中容易受到噪声干扰的问题,将两帧差分法融入ViBe的前景检测阶段,提出一种融合两帧差分信息的改进ViBe算法(ViBe with two-frame differencing,ViBe-TD)。首...针对视觉背景提取(visual background extractor,ViBe)算法在运动目标检测过程中容易受到噪声干扰的问题,将两帧差分法融入ViBe的前景检测阶段,提出一种融合两帧差分信息的改进ViBe算法(ViBe with two-frame differencing,ViBe-TD)。首先,设计单阈值形ViBe(single-threshold form of ViBe,S-ViBe)检测,为信息融合做准备;其次,基于逻辑斯蒂(logistic)回归模型,实现像素点上两帧差分和S-ViBe检测信息的融合;最后,综合两类检测信息完成前景像素点的判定。实验结果表明,ViBe-TD算法在4种不同场景视频上的检测效果达到了0.932的平均精确率,0.785的平均召回率以及0.842的平均F 1值。与原算法相比,ViBe-TD算法的各项指标平均有0.158的提高,具有良好的检测效果。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.
文摘A muitisensor image fusion algorithm is described using 2-dimensional nonseparable wavelet frame （NWF） transform. The source muitisensor images are first decomposed by the NWF transform. Then, the NWF transform coefficients of the source images are combined into the composite NWF transform coefficients. Inverse NWF transform is performed on the composite NWF transform coefficients in order to obtain the intermediate fused image. Finally, intensity adjustment is applied to the intermediate fused image in order to maintain the dynamic intensity range. Experiment resuits using real data show that the proposed algorithm works well in muitisensor image fusion.
基金Project (No. 2004CB719401) supported by the National Basic Research Program (973) of China
文摘A new framework of region-based dynamic image fusion is proposed. First, the technique of target detection is applied to dynamic images (image sequences) to segment images into different targets and background regions. Then different fusion rules are employed in different regions so that the target information is preserved as much as possible. In addition, steerable non-separable wavelet frame transform is used in the process of multi-resolution analysis, so the system achieves favorable characters of orientation and invariant shift. Compared with other image fusion methods, experimental results showed that the proposed method has better capabilities of target recognition and preserves clear background information.
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Supported by the National Natural Science Foundation of China(Grant No.11271037)
文摘For refinable functiombased affine bi-frames, nonhomogeneous ones admit fast algorithms and have extension principles as homogeneous ones. But all extension principles are based on some restrictions on refinable functions. So it is natural to ask what are expected from general refinable functions. In this paper, we introduce the notion of weak nonhomogeneous affine bi-frame （WNABF）. Under the setting of reducing subspaces of L2（Rd）, we characterize WNABFs and obtain a mixed oblique extension principle for WNABFs based on general refinable functions.
基金Supported by National Natural Science Foundation of China(Grant Nos.11671201 and 11571247)
文摘Motivated by K-frames and fusion frames, we study K-fusion frames in Hilbert spaces. By the means of operator K, frame operators and quotient operators, several necessary and sufficient conditions for a sequence of closed subspaces and weights to be a K-fusion frame are obtained, and operators preserving K-fusion frames are discussed. In particular, we are interested in the K-fusion frames with the structure of unitary systems. Given a unitary system which has a complete wandering subspace, we give a necessary and sufficient condition for a closed subspace to be a K-fusion frame generator.
文摘针对视觉背景提取(visual background extractor,ViBe)算法在运动目标检测过程中容易受到噪声干扰的问题,将两帧差分法融入ViBe的前景检测阶段,提出一种融合两帧差分信息的改进ViBe算法(ViBe with two-frame differencing,ViBe-TD)。首先,设计单阈值形ViBe(single-threshold form of ViBe,S-ViBe)检测,为信息融合做准备;其次,基于逻辑斯蒂(logistic)回归模型,实现像素点上两帧差分和S-ViBe检测信息的融合;最后,综合两类检测信息完成前景像素点的判定。实验结果表明,ViBe-TD算法在4种不同场景视频上的检测效果达到了0.932的平均精确率,0.785的平均召回率以及0.842的平均F 1值。与原算法相比,ViBe-TD算法的各项指标平均有0.158的提高,具有良好的检测效果。
