Multidimensional signals like multispectral images and color videos are becoming ubiquitous in modern times, constantly introducing challenges in data storage and transfer, and therefore demanding efficient compression strategies. Such high dimensional observations can be naturally encoded as tensors, exhibiting significant redundancies across dimensions. This property is exploited by tensor decomposition techniques that are being increasingly used for compactly encoding large multidimensional arrays. While efficient, these methods are incapable of utilizing prior information present in training data. In this paper, a novel tensor decomposition learning method is proposed for the compression of high dimensional signals. Specifically, instead of extracting independent bases for each example, our method learns an appropriate basis for each dimension from a set of training samples by solving a constrained optimization problem. As such, each sample is quantized and encoded into a reduced-size core tensor of coefficients that corresponds to the multilinear combination of the learned basis matrices. Furthermore, the proposed method employs a symbol encoding dictionary for binarizing the decomposition outputs. Experimental results on synthetic data and real satellite multispectral image sequences demonstrate the efficacy of our method, surpassing competing compression methods while offering the flexibility to handle arbitrary high dimensional data structures.

中文翻译：

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张量分解学习在多维信号压缩中的应用

诸如多光谱图像和彩色视频之类的多维信号在现代变得无处不在，不断地在数据存储和传输中引入挑战，因此需要有效的压缩策略。这样的高维观测值可以自然地编码为张量，在维数之间表现出显着的冗余。张量分解技术已利用此属性，而张量分解技术已越来越多地用于紧凑地编码大型多维数组。这些方法虽然有效，但无法利用训练数据中存在的先验信息。本文提出了一种新的张量分解学习方法，用于高维信号的压缩。具体来说，不是为每个示例提取独立的碱基，我们的方法通过解决约束优化问题，从一组训练样本中为每个维度学习合适的基础。这样，每个样本被量化并编码为与学习的基础矩阵的多线性组合相对应的系数的减小尺寸的核心张量。此外，所提出的方法采用符号编码字典来对分解输出进行二值化。在合成数据和真实卫星多光谱图像序列上的实验结果证明了我们方法的有效性，超越了竞争压缩方法，同时提供了处理任意高维数据结构的灵活性。每个样本都被量化并编码为与学习的基础矩阵的多线性组合相对应的缩小的核心核心张量。此外，所提出的方法采用符号编码字典来对分解输出进行二值化。在合成数据和真实卫星多光谱图像序列上的实验结果证明了我们方法的有效性，超越了竞争压缩方法，同时提供了处理任意高维数据结构的灵活性。每个样本都被量化并编码为与学习的基础矩阵的多线性组合相对应的缩小的核心核心张量。此外，所提出的方法采用符号编码字典来对分解输出进行二值化。在合成数据和真实卫星多光谱图像序列上的实验结果证明了我们方法的有效性，超越了竞争压缩方法，同时提供了处理任意高维数据结构的灵活性。