Tensor completion is important to many areas such as computer vision, data analysis, and signal processing. Previously, a category of methods known as low-rank tensor completion has been proposed and developed, involving the enforcement of low-rank structures on completed tensors. While such methods have been constantly improved, none considered exploiting the numerical properties of tensor elements. This work attempts to construct a new methodological framework called GCDTC (Generalized CP Decomposition Tensor Completion) based on numerical properties to achieve higher accuracy in tensor completion. In this newly introduced framework, a generalized form of the CP Decomposition is applied to low-rank tensor completion. This paper also proposes an algorithm known as SPTC (Smooth Poisson Tensor Completion) for nonnegative integer tensor completion as an application of the GCDTC framework. Through experimentation with real-life data, it is verified that this method could produce results superior in completion accuracy to current state-of-the-art methodologies.

翻译：张量补全在计算机视觉、数据分析及信号处理等多个领域具有重要意义。此前，一类被称为低秩张量补全的方法已被提出并发展，其核心在于对补全后的张量施加低秩约束。尽管这类方法不断得到改进，但均未考虑利用张量元素的数值特性。本研究尝试构建一种基于数值特性的新方法论框架——GCDTC（广义CP分解张量补全），以期在张量补全中实现更高精度。在该新框架中，将CP分解的广义形式应用于低秩张量补全。作为GCDTC框架的具体应用，本文还提出了一种名为SPTC（平滑泊松张量补全）的算法，用于非负整数张量补全。通过真实数据的实验验证，该方法在补全精度上优于当前最先进的技术方法。