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. Whilst 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 indicate that SPTC could produce results superior in completion accuracy to current state-of-the-art methods. Related code is available in the supplemental materials.

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，一类被称为低秩张量补全的方法通过强制完成后的张量具有低秩结构，得到了广泛研究。尽管此类方法取得了巨大成功，但尚未有研究考虑利用张量元素的数值先验信息。忽略数值先验会导致数据中的重要信息丢失，从而阻碍算法达到最优精度。本文尝试构建一种名为GCDTC（广义CP分解张量补全）的新方法论框架，以利用数值先验并在张量补全中实现更高精度。在该新引入的框架中，将广义形式的CP分解应用于低秩张量补全。本文还提出一种称为SPTC（平滑泊松张量补全）的算法用于非负整数张量补全，作为GCDTC框架的一个实例化。一系列真实数据上的实验表明，SPTC在补全精度上能够产生优于当前最先进方法的结果。相关代码可在补充材料中获取。