Owing to the constraints of depth sensing technology,images acquired by depth cameras are inevitably mixed with various noises.For depth maps presented in gray values,this research proposes a novel denoising model,ter...Owing to the constraints of depth sensing technology,images acquired by depth cameras are inevitably mixed with various noises.For depth maps presented in gray values,this research proposes a novel denoising model,termed graph-based transform(GBT)and dual graph Laplacian regularization(DGLR)(DGLR-GBT).This model specifically aims to remove Gaussian white noise by capitalizing on the nonlocal self-similarity(NSS)and the piecewise smoothness properties intrinsic to depth maps.Within the group sparse coding(GSC)framework,a combination of GBT and DGLR is implemented.Firstly,within each group,the graph is constructed by using estimates of the true values of the averaged blocks instead of the observations.Secondly,the graph Laplacian regular terms are constructed based on rows and columns of similar block groups,respectively.Lastly,the solution is obtained effectively by combining the alternating direction multiplication method(ADMM)with the weighted thresholding method within the domain of GBT.展开更多
Non-negative Matrix Factorization (NMF) has been an ideal tool for machine learning. Non-negative Matrix Tri-Factorization (NMTF) is a generalization of NMF that incorporates a third non-negative factorization matrix,...Non-negative Matrix Factorization (NMF) has been an ideal tool for machine learning. Non-negative Matrix Tri-Factorization (NMTF) is a generalization of NMF that incorporates a third non-negative factorization matrix, and has shown impressive clustering performance by imposing simultaneous orthogonality constraints on both sample and feature spaces. However, the performance of NMTF dramatically degrades if the data are contaminated with noises and outliers. Furthermore, the high-order geometric information is rarely considered. In this paper, a Robust NMTF with Dual Hyper-graph regularization (namely RDHNMTF) is introduced. Firstly, to enhance the robustness of NMTF, an improvement is made by utilizing the l_(2,1)-norm to evaluate the reconstruction error. Secondly, a dual hyper-graph is established to uncover the higher-order inherent information within sample space and feature spaces for clustering. Furthermore, an alternating iteration algorithm is devised, and its convergence is thoroughly analyzed. Additionally, computational complexity is analyzed among comparison algorithms. The effectiveness of RDHNMTF is verified by benchmarking against ten cutting-edge algorithms across seven datasets corrupted with four types of noise.展开更多
We define the right regular dual of an object X in a monoidal category l, and give several results regarding the weak rigid monoidal category. Based on the definition of the right regular dual, we construct a weak Hop...We define the right regular dual of an object X in a monoidal category l, and give several results regarding the weak rigid monoidal category. Based on the definition of the right regular dual, we construct a weak Hopf algebra structure of H = End（F） whenever （F, J） is a fiber functor from category l to Vec and every X ∈ l has a right regular dual. To conclude, we give a weak reconstruction theorem for a kind of weak Hopf algebra.展开更多
基金National Natural Science Foundation of China(No.62372100)。
文摘Owing to the constraints of depth sensing technology,images acquired by depth cameras are inevitably mixed with various noises.For depth maps presented in gray values,this research proposes a novel denoising model,termed graph-based transform(GBT)and dual graph Laplacian regularization(DGLR)(DGLR-GBT).This model specifically aims to remove Gaussian white noise by capitalizing on the nonlocal self-similarity(NSS)and the piecewise smoothness properties intrinsic to depth maps.Within the group sparse coding(GSC)framework,a combination of GBT and DGLR is implemented.Firstly,within each group,the graph is constructed by using estimates of the true values of the averaged blocks instead of the observations.Secondly,the graph Laplacian regular terms are constructed based on rows and columns of similar block groups,respectively.Lastly,the solution is obtained effectively by combining the alternating direction multiplication method(ADMM)with the weighted thresholding method within the domain of GBT.
基金supported by the National Natural Science Foundation of China(No.62003281)the Natural Science Foundation of Chongqing,China(No.cstc2021jcyjmsxmX1169)the Science and Technology Research Program of Chongqing Municipal Education Commission(No.KJQN202200207).
文摘Non-negative Matrix Factorization (NMF) has been an ideal tool for machine learning. Non-negative Matrix Tri-Factorization (NMTF) is a generalization of NMF that incorporates a third non-negative factorization matrix, and has shown impressive clustering performance by imposing simultaneous orthogonality constraints on both sample and feature spaces. However, the performance of NMTF dramatically degrades if the data are contaminated with noises and outliers. Furthermore, the high-order geometric information is rarely considered. In this paper, a Robust NMTF with Dual Hyper-graph regularization (namely RDHNMTF) is introduced. Firstly, to enhance the robustness of NMTF, an improvement is made by utilizing the l_(2,1)-norm to evaluate the reconstruction error. Secondly, a dual hyper-graph is established to uncover the higher-order inherent information within sample space and feature spaces for clustering. Furthermore, an alternating iteration algorithm is devised, and its convergence is thoroughly analyzed. Additionally, computational complexity is analyzed among comparison algorithms. The effectiveness of RDHNMTF is verified by benchmarking against ten cutting-edge algorithms across seven datasets corrupted with four types of noise.
文摘We define the right regular dual of an object X in a monoidal category l, and give several results regarding the weak rigid monoidal category. Based on the definition of the right regular dual, we construct a weak Hopf algebra structure of H = End（F） whenever （F, J） is a fiber functor from category l to Vec and every X ∈ l has a right regular dual. To conclude, we give a weak reconstruction theorem for a kind of weak Hopf algebra.
