Sparse reconstruction of correlated multichannel activity

Abstract

Parametric methods for modeling sinusoidal signals with line spectra have been studied for decades. In general, these methods start by representing each sinusoidal component by means of two complex exponential functions, thereby doubling the number of unknown parameters. Recently, a Hankel-plus-Toeplitz matrix pencil method was proposed which directly models sinusoidal signals with discrete spectral content. Compared to its counterpart, which uses a Hankel matrix pencil, it halves the required number of time-domain samples and reduces the size of the involved linear systems. The aim of this paper is twofold. Firstly, to show that this Hankel-plus-Toeplitz matrix pencil also applies to continuous spectra. Secondly, to explore its use in the reconstruction of real-life signals. Promising preliminary results in the recon- struction of correlated multichannel electroencephalographic (EEG) activity are presented. A principal component analysis preprocessing step is carried out to exploit the redundancy in the channel domain. Then the reduced signal representation is successfully reconstructed from fewer samples using the Hankel-plus-Toeplitz matrix pencil. The obtained results encourage the future development of this matrix pencil method along the lines of well-established spectral analysis methods.