Signal Analysis Inc., Hachioji, Tokyo, Japan. Department of Advanced Technology in Medicine, Tokyo Medical and Dental University, 1-5-45 Yushima, Bunkyo-ku, Tokyo 113-8519, Japan.
J Neural Eng. 2017 Oct;14(5):051001. doi: 10.1088/1741-2552/aa7693. Epub 2017 Aug 18.
In biomagnetic signal processing, the theory of the signal subspace has been applied to removing interfering magnetic fields, and a representative algorithm is the signal space projection algorithm, in which the signal/interference subspace is defined in the spatial domain as the span of signal/interference-source lead field vectors. This paper extends the notion of this conventional (spatial domain) signal subspace by introducing a new definition of signal subspace in the time domain.
It defines the time-domain signal subspace as the span of row vectors that contain the source time course values. This definition leads to symmetric relationships between the time-domain and the conventional (spatial-domain) signal subspaces. As a review, this article shows that the notion of the time-domain signal subspace provides useful insights over existing interference removal methods from a unified perspective. Main results and significance. Using the time-domain signal subspace, it is possible to interpret a number of interference removal methods as the time domain signal space projection. Such methods include adaptive noise canceling, sensor noise suppression, the common temporal subspace projection, the spatio-temporal signal space separation, and the recently-proposed dual signal subspace projection. Our analysis using the notion of the time domain signal space projection reveals implicit assumptions these methods rely on, and shows that the difference between these methods results only from the manner of deriving the interference subspace. Numerical examples that illustrate the results of our arguments are provided.
在生物磁信号处理中，信号子空间理论已被应用于去除干扰磁场，其中一个有代表性的算法是信号空间投影算法，该算法将信号/干扰子空间定义为信号/干扰源导联向量的张成空间。本文通过引入一种新的时域信号子空间定义，扩展了传统（空域）信号子空间的概念。
它将时域信号子空间定义为包含源时程值的行向量的张成空间。该定义导致时域信号子空间与传统（空域）信号子空间之间存在对称关系。作为回顾，本文表明，从统一的角度来看，时域信号子空间的概念为现有的干扰消除方法提供了有用的见解。主要结果和意义：使用时域信号子空间，可以将许多干扰消除方法解释为时域信号空间投影。这些方法包括自适应噪声消除、传感器噪声抑制、公共时间子空间投影、时空信号空间分离以及最近提出的双信号子空间投影。我们使用时域信号空间投影的概念进行的分析揭示了这些方法所依赖的隐含假设，并表明这些方法之间的差异仅源于推导干扰子空间的方式。提供了说明我们论点结果的数值示例。
