Tensor completion is important to many areas such as computer vision, data analysis, and signal processing. Enforcing low-rank structures on completed tensors, a category of methods known as low-rank tensor completion has recently been studied extensively. While such methods attained great success, none considered exploiting numerical priors of tensor elements. Ignoring numerical priors causes loss of important information regarding the data, and therefore prevents the algorithms from reaching optimal accuracy. This work attempts to construct a new methodological framework called GCDTC (Generalized CP Decomposition Tensor Completion) for leveraging numerical priors and achieving higher accuracy in tensor completion. In this newly introduced framework, a generalized form of 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 instantiation of the GCDTC framework. A series of experiments on real-world data indicated that SPTC could produce results superior in completion accuracy to current state-of-the-arts.

翻译：张量补全在计算机视觉、数据分析和信号处理等多个领域具有重要意义。近年来，一类名为低秩张量补全的方法被广泛研究，其核心在于对补全后的张量施加低秩结构约束。尽管此类方法取得了巨大成功，但均未考虑利用张量元素的数值先验信息。忽略数值先验会导致丢失与数据相关的重要信息，从而阻碍算法达到最优精度。本文旨在构建一种名为GCDTC（广义CP分解张量补全）的新方法框架，以利用数值先验实现更高精度的张量补全。在该新框架中，广义形式的CP分解被应用于低秩张量补全。此外，本文还提出了一种名为SPTC（平滑泊松张量补全）的算法，作为GCDTC框架的一个实例，用于非负整数张量补全。一系列基于真实数据的实验表明，SPTC在补全精度上能够超越当前最先进的方法。