This paper describes the background noise estimation technique of the tensor product expansion with absolute error (TPE-AE) to estimate multiple sources. The electroencephalogram (EEG) signal produced by the saccadic eye movement is adopted to analyze relationship between a brain function and a human activity. The electrooculogram (EOG) generated by eye movements yields significant problems for the EEG analysis. The denoising of EOG artifacts is important task to perform an accurate analysis. In this paper, the two types of TPE-AE are proposed to estimates EOG and other components in EEG during eye movement. One technique estimates two outer products using median filter based TPE-AE. The another technique uses a reference signal to separate the two sources. We show that the proposed method is effective to estimate and separate two sources in EEG.

This paper proposes a background noise estimation method using an outer product expansion with non-linear filters for ELF (extremely low frequency) electromagnetic (EM) waves. We proposed a novel source separation technique that uses a tensor product expansion. This signal separation technique means that the background noise, which is observed in almost all input signals, can be estimated using a tensor product expansion (TPE) where the absolute error (AE) is used as the error function, which is thus known as TPE-AE. TPE-AE has two problems: the first is that the results of TPE-AE are strongly affected by Gaussian random noise, and the second is that the estimated signal varies widely because of the random search. To solve these problems, an outer product expansion based on a modified trimmed mean (MTM) is proposed in this paper. The results show that this novel technique separates the background noise from the signal more accurately than conventional methods.

This paper proposes a novel signal estimation method that uses a tensor product expansion. When a bivariable function, which is expressed by two-dimensional matrix, is subjected to conventional tensor product expansion, two single variable functions are calculated by minimizing the mean square error between the input vector and its outer product. A tensor product expansion is useful for feature extraction and signal compression, however, it is difficult to separate global noise from other signals. This paper shows that global noise, which is observed in almost all input signals, can be estimated by using a tensor product expansion where absolute error is used as the error function.