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Estimating single-trial evoked potentials (EPs) corrupted by the spontaneous electroencephalogram (EEG) can be regarded as signal denoising problem. Sparse coding has significant success in signal denoising and EPs have been proven to have strong sparsity over an appropriate dictionary. In sparse coding, the noise generally is considered to be a Gaussian random process. However, some studies have shown that the background noise in EPs may present an impulsive characteristic which is far from Gaussian but suitable to be modeled by the  α -stable distribution (1 < α ≤ 2). Consequently, the performances of general sparse coding will degrade or even fail. In view of this, we present a new sparse coding algorithm using  p -norm optimization in single-trial EPs estimating. The algorithm can track the underlying EPs corrupted by  α -stable distribution noise, trial-by-trial, without the need to estimate the  α  value. Simulations and experiments on human visual evoked potentials and event-related potentials are carried out to examine the performance of the proposed approach. Experimental results show that the proposed method is effective in estimating single-trial EPs under impulsive noise environment.

Single-Trial Evoked Potential Estimating Based on Sparse Coding under Impulsive Noise Environment