Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery
Since higher-order tensors are naturally suitable for representing multi-dimensional data in real-world, e.g., color images and videos, low-rank tensor representation has become one of the emerging areas in machine learning and computer vision. However, classical low-rank tensor representations can only represent data on finite meshgrid due to their intrinsical discrete nature, which hinders their potential applicability in many scenarios beyond meshgrid. To break this barrier, we propose a low-rank tensor function representation (LRTFR), which can continuously represent data beyond meshgrid with infinite resolution. Specifically, the suggested tensor function, which maps an arbitrary coordinate to the corresponding value, can continuously represent data in an infinite real space. Parallel to discrete tensors, we develop two fundamental concepts for tensor functions, i.e., the tensor function rank and low-rank tensor function factorization. We theoretically justify that both low-rank and smooth regularizations are harmoniously unified in the LRTFR, which leads to high effectiveness and efficiency for data continuous representation. Extensive multi-dimensional data recovery applications arising from image processing (image inpainting and denoising), machine learning (hyperparameter optimization), and computer graphics (point cloud upsampling) substantiate the superiority and versatility of our method as compared with state-of-the-art methods. Especially, the experiments beyond the original meshgrid resolution (hyperparameter optimization) or even beyond meshgrid (point cloud upsampling) validate the favorable performances of our method for continuous representation.
Code (0)
등록된 구현이 없습니다.
Tasks
DenoisingHyperparameter OptimizationImage Inpaintingpoint cloud upsamplingMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Tensor and Matrix Low-Rank Value-Function Approximation in Reinforcement Learning
Value-function (VF) approximation is a central problem in Reinforcement Learning (RL). Classical non-parametric VF estimation suffers from the curse of dimensionality. As a result, parsimonious parametric models have bee…
reinforcement-learningReinforcement Learning (RL)An Iterative Reweighted Method for Tucker Decomposition of Incomplete Multiway Tensors
We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applic…
Image InpaintingRecommendation SystemsTensor-Efficient High-Dimensional Q-learning
High-dimensional reinforcement learning(RL) faces challenges with complex calculations and low sample efficiency in large state-action spaces. Q-learning algorithms struggle particularly with the curse of dimensionality,…
Reinforcement LearningHLRTF: Hierarchical Low-Rank Tensor Factorization for Inverse Problems in Multi-Dimensional Imaging
Inverse problems in multi-dimensional imaging, e.g., completion, denoising, and compressive sensing, are challenging owing to the big volume of the data and the inherent ill-posedness. To tackle these issues, this wo…
Compressive SensingDenoisingWhen Bayesian Tensor Completion Meets Multioutput Gaussian Processes: Functional Universality and Rank Learning
Functional tensor decomposition can analyze multi-dimensional data with real-valued indices, paving the path for applications in machine learning and signal processing. A limitation of existing approaches is the assumpti…
Gaussian Processes