An iterative thresholding-based algorithm for brain–computer interface (BCI) application

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The EEG signals are recorded using surgical (invasive) or non-surgical (non-invasive) BCI neuroimaging modalities. Basically, we are dealing with a huge amount of data and long signal recordings.The classic solution to deal with the huge amount of data has been data compression, where the data is first collected in its original large format and then converted to a compressed format of smaller size for storage or transmission. This has become a traditional solution to the problem of handling the massive volume of data.Compressive sensing is a novel technique that senses the signal in a compressed format using a sub-Nyquist–Shannon sampling rate and reconstructs it when the data from the compressed sensed signal is required.In the context of applying CS, the first issue is how to construct the linear measurement matrix to ensure that compressive sensing meets the requirements of the application. The second issue depends on the way in which the sparse signal can be obtained from a small sample of observations. In this paper, nuclear norm minimization is proposed to enforce sparsity and low-rank structures in the reconstructed multi-channel EEG signals. To compute the optimization, we propose two new algorithms which we call: a weighted thresholding algorithm and a weighted thresholding orthogonal matching pursuit algorithm based on compressive sensing. We perform the experiments on the insomnia EEG dataset. Computer simulations provide and show the good behavior of these algorithms and the NNM norm, compared to others in the literature.