Results 11 to 20 of about 1,788,984 (247)

The Ideal of σ-Nuclear Operators and Its Associated Tensor Norm

Mathematics, 2020
We introduce a new tensor norm ( σ -tensor norm) and show that it is associated with the ideal of σ -nuclear operators. In this paper, we investigate the ideal of σ -nuclear operators and the σ -tensor norm.
Ju Myung Kim, Keun Young Lee
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Quaternion Nuclear Norm Minus Frobenius Norm Minimization for color image reconstruction [PDF]

Pattern Recognition
This paper was accepted by Pattern Recognition on September 5 ...
Yu Guo 0008, Guoqing Chen, Tieyong Zeng, Qiyu Jin, Michael Kwok-Po Ng   +4 more
openaire   +4 more sources

Tensor Completion Based on Triple Tubal Nuclear Norm

Algorithms, 2018
Many tasks in computer vision suffer from missing values in tensor data, i.e., multi-way data array. The recently proposed tensor tubal nuclear norm (TNN) has shown superiority in imputing missing values in 3D visual data, like color images and videos ...
Dongxu Wei, Andong Wang, Xiaoqin Feng, Boyu Wang, Bo Wang   +4 more
doaj   +2 more sources

Measures with relatively norm compact range and infinite-nuclear operators

Le Matematiche, 1995
We prove that measures with relatively norm compact range correspond to the infinite-nuclear operators and to a p-Bochner integrable function (resp. p-Pettis integrable function) correspond a p-nuclear operator (resp. a q-nuclear operator).
Dumitru Popa
doaj   +1 more source

Nuclear Norm Regularization for Deep Learning

Advances in Neural Information Processing Systems 37
Penalizing the nuclear norm of a function's Jacobian encourages it to locally behave like a low-rank linear map. Such functions vary locally along only a handful of directions, making the Jacobian nuclear norm a natural regularizer for machine learning problems.
Christopher Scarvelis, Justin Solomon 0001   +1 more
openaire   +4 more sources

Finding Approximately Rank-One Submatrices with the Nuclear Norm and $\ell_1$-Norm

SIAM Journal on Optimization, 2013
We propose a convex optimization formulation with the nuclear norm and $\ell_1$-norm to find a large approximately rank-one submatrix of a given nonnegative matrix. We develop optimality conditions for the formulation and characterize the properties of the optimal solutions.
Xuan Vinh Doan, Stephen A. Vavasis
openaire   +3 more sources

Norm-Attaining Tensors and Nuclear Operators [PDF]

Mediterranean Journal of Mathematics, 2022
25 pages.
Sheldon Dantas, Mingu Jung, Óscar Roldán, Abraham Rueda Zoca   +3 more
openaire   +5 more sources

Dynamic MRI Reconstruction Combining Tensor Nuclear Norm and Casorati Matrix Nuclear Norm [PDF]

, 2022
Low-rank tensor models have been applied in accelerating dynamic magnetic resonance imaging (dMRI). Recently, a new tensor nuclear norm based on t-SVD has been proposed and applied to tensor completion.
Hu, Yue, Lu, Xin, Zhang, Yinghao
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Impossibility of dimension reduction in the nuclear norm [PDF]

Discrete & Computational Geometry, 2018
Let $\mathsf{S}_1$ (the Schatten--von Neumann trace class) denote the Banach space of all compact linear operators $T:\ell_2\to \ell_2$ whose nuclear norm $\|T\|_{\mathsf{S}_1}=\sum_{j=1}^\inftyσ_j(T)$ is finite, where $\{σ_j(T)\}_{j=1}^\infty$ are the singular values of $T$. We prove that for arbitrarily large $n\in \mathbb{N}$ there exists a subset $\
Assaf Naor, Gilles Pisier, Gideon Schechtman   +2 more
openaire   +6 more sources

Proximal algorithms for nuclear norm system identification [PDF]

, 2022
In this thesis, we present four proximal algorithms for the solution of a nuclear norm optimization problem. Respect to other papers, we solve a more generic version of this problem.
Faccio, Chiara
core