Abstract. In many applications of signal processing, especially in communications and biomedicine, prepro- cessing is necessary to remove noise from data recorded by multiple sensors. Typically, each sensor or electrode measures the noisy mixture of original source signals. In this paper a noise reduction technique using independent component analysis (ICA) and subspace filtering is presented. In this approach we apply subspace filtering not to the observed raw data but to a demixed version of these data obtained by ICA. Finite impulse response filters are employed whose vectors are parameters estimated based on signal subspace extraction. ICA allows us to filter independent components. After the noise is removed we reconstruct the enhanced indepen- dent components to obtain clean original signals; i.e., we project the data to sensor level. Simulations as well as real application results for EEG-signal noise elimination are included to show the validity and effectiveness of the proposed approach. 1 Introduction and problem formulation In many real-world applications of signal processing, especially in communications and biomedicine, the problem of noise cancellation is important (Widrow and Walach 1996). Noise cancellation is a subject of wide interest in physical and communication systems. Several methods have been suggested in the literature for noise reduction. Signal processing techniques using for noise elimination include band-pass filtering, the fast Fourier transform, autocorrelation, autoregressive mod- eling, adaptive filtering, Kalman filtering, and singular value decomposition (SVD) (Akay 1996; Arnold et al. 1998; Sadasivan and Dutt 1996; Thakon 1987; Walter 1969; de Weerd and Martens 1978; Widrow and Walach 1996). Recently, the principal component analysis (PCA) (Callaerts et al. 1988; Laguna et al. 1999; Sadasivan and Dutt 1996) and independent component analysis (ICA) (Cichocki and Vorobyov 2000; Lee 1998) approaches have became very popular for the analysis of biomedical data e.g., EEG and MEG). One of the main advantages of these approaches relates to their applicability to multisensory observations of mixed signals. In this paper we consider the following linear mixture model for measured signals xðtÞ¼ AsðtÞþ vðtÞ ; ð1Þ where t ¼ 0; 1; 2; ... is discrete time; xðtÞ¼½x 1 ðtÞ; x 2 ðtÞ; ... ; x n ðtÞ T is an n-dimensional vector of observed noisy sensor signals; A is an n  m unknown full-rank mixing matrix; sðtÞ¼½s 1 ðtÞ; s 2 ðtÞ; ... ; s m ðtÞ T is an m-dimensional unknown vector of primary sources; and vðtÞ is n-dimensional also unknown vector of additive white (generally, could be colored) Gaussian noise represented measurement and environmental noise. Furthermore, we assume that the vector sðtÞ contains a subset of useful or ‘‘interesting’’ sources with temporal structure, and ‘‘uninteresting’’ interferences or ‘‘inner’’ noises. Our objective is to reduce the influence of additive noise vðtÞ and eliminate ‘‘inner’’ noise. In other words, our task is to obtain corrected or ‘‘cleaned’’ sensor sig- nals which contain only useful or ‘‘interesting’’ sources with temporal structure. By useful or ‘‘interesting’’ sig- nals we mean short-duration (sparse) signals with temporal structure such as the evoked potential/event- related potential (EP/ERP) in biomedical signal analysis applications (Goldstein and Alrich 1999; Niedermeyer and de Silva 1999). If these signals are statistically independent, our second objective is to estimate the corresponding sources. We apply model (1) to EEG signal analysis, by de- scribing all variables in model (1) as follows. Sources are original sparse signals generated by the brain. Some of sources can be noise sources. A noisy instantaneous mixture of original sources is available for measurement. Correspondence to: S. Vorobyov (Fax: +1-905-5212922, e-mail: svor@mail.ece.mcmaster.ca) * Department of Electrical and Computer Engineering, McMaster University, 1280 Main St.W., Hamilton, Ontario L8S 4K1, Canada * Warsaw University of Technology Poland Biol. Cybern. 86, 293–303 (2002) DOI 10.1007/s00422-001-0298-6 Ó Springer-Verlag 2002 Blind noise reduction for multisensory signals using ICA and subspace filtering, with application to EEG analysis Sergiy Vorobyov  , Andrzej Cichocki ** Laboratory for Advanced Brain Signal Processing, Brain Science Institute, RIKEN, 2-1 Hirosawa, Wako-shi, Saitama, 351-0198, Japan Received: 6 November 2000 / Accepted in revised form: 12 November 2001