基于凸化ℓ0-范数近似的离散感知张量补全
Discrete Aware Tensor Completion via Convexized $\ell_0$-Norm Approximation
AI总结：
本文提出了一种基于凸化ℓ0-范数近似的离散感知张量补全算法，通过引入离散正则化项提升低秩张量补全的性能。
摘要：
我们考虑了一种新的算法，用于补全部分观测的低秩张量，其中张量的每个条目可以从一个离散有限字母集中选择，例如在常见的图像处理问题中，条目代表RGB值。所提出的低秩张量补全（TC）方法基于传统的核范数（NN）最小化低秩TC范式，通过添加一个离散感知正则化项，该正则化项通过一个近似于连续可微函数的ℓ0-范数正则化项来强制问题的目标函数的离散性，该函数通过分数规划（FP）在近端梯度（PG）框架下进行归一化，以解决所提出的问题。仿真结果表明，新方法在归一化均方误差（NMSE）和收敛性方面均优于传统最先进的（SotA）技术，包括NN最小化方法，以及后者与矩阵分解方法的混合。
英文摘要：
We consider a novel algorithm, for the completion of partially observed low-rank tensors, where each entry of the tensor can be chosen from a discrete finite alphabet set, such as in common image processing problems, where the entries represent the RGB values. The proposed low-rank tensor completion (TC) method builds on the conventional nuclear norm (NN) minimization-based low-rank TC paradigm, through the addition of a discrete-aware regularizer, which enforces discreteness in the objective of the problem, by an $\ell_0$-norm regularizer that is approximated by a continuous and differentiable function normalized via fractional programming (FP) under a proximal gradient (PG) framework, in order to solve the proposed problem. Simulation results demonstrate the superior performance of the new method both in terms of normalized mean square error (NMSE) and convergence, compared to the conventional state of-the-art (SotA) techniques, including NN minimization approaches, as well as a mixture of the latter with a matrix factorization approach.
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