论文标题
张量卷积稀疏用低级激活的编码，用于脑电图分析的应用
Tensor Convolutional Sparse Coding with Low-Rank activations, an application to EEG analysis
论文作者
论文摘要
最近，人们对脑电图（EEG）的频谱图的分析越来越兴趣，特别是研究全身麻醉期间（UN） - 意识的神经相关性（GA）。实际上，已经表明，订单三个张量（通道x频率x次）是这些信号的自然且有用的表示。但是，这种编码需要很大的困难，尤其是对于卷积稀疏编码（CSC），因为现有方法没有利用张量表示的特殊性，例如排名结构，并且容易受到医疗行为期间EEG固有的高噪声和扰动的影响。为了解决这个问题，在本文中，我们介绍了一种名为Kruskal CSC（K-CSC）的新CSC模型，该模型使用激活张量的Kruskal分解来利用这些表示形式的内在低级性质，以提取相关和可解释的编码。我们的主要贡献TC-FISTA使用多种工具来有效地解决了由此产生的优化问题，尽管张量表示的复杂性增加了增加。然后，我们在GA期间记录的合成数据集和实际脑电图上评估TC-FISTA。结果表明，TC-Fista对噪声和扰动具有鲁棒性，从而导致信号的准确，稀疏和可解释的编码。
Recently, there has been growing interest in the analysis of spectrograms of ElectroEncephaloGram (EEG), particularly to study the neural correlates of (un)-consciousness during General Anesthesia (GA). Indeed, it has been shown that order three tensors (channels x frequencies x times) are a natural and useful representation of these signals. However this encoding entails significant difficulties, especially for convolutional sparse coding (CSC) as existing methods do not take advantage of the particularities of tensor representation, such as rank structures, and are vulnerable to the high level of noise and perturbations that are inherent to EEG during medical acts. To address this issue, in this paper we introduce a new CSC model, named Kruskal CSC (K-CSC), that uses the Kruskal decomposition of the activation tensors to leverage the intrinsic low rank nature of these representations in order to extract relevant and interpretable encodings. Our main contribution, TC-FISTA, uses multiple tools to efficiently solve the resulting optimization problem despite the increasing complexity induced by the tensor representation. We then evaluate TC-FISTA on both synthetic dataset and real EEG recorded during GA. The results show that TC-FISTA is robust to noise and perturbations, resulting in accurate, sparse and interpretable encoding of the signals.
