No abstract

No abstract

The efficient estimation of an approximate model order is very important for real applications with multi-dimensional data if the observed low-rank data is corrupted by additive noise. In this paper, we present a novel robust method for model order estimation of noise-corrupted multi-dimensional low-rank data based on the LineAr Regression of Global Eigenvalues (LaRGE). The LaRGE method uses the multi-linear singular values obtained from the HOSVD of the measurement tensor to construct global eigenvalues. In contrast to the Modified Exponential Test (EFT) that also exploits the approximate exponential profile of the noise eigenvalues, LaRGE does not require the calculation of the probability of false alarm. Moreover, LaRGE achieves a significantly improved performance in comparison with popular state-of-the-art methods. It is well suited for the analysis of biomedical data. The excellent performance of the LaRGE method is illustrated via simulations and results obtained from EEG recordings.Index Terms-eigenvalue, global eigenvalue, tensor, the rank of the tensor, the model order of multi-dimensional data I. INTRODUCTIONM ULTI-DIMENSIONAL MODELS are widespread in a variety of applications, for example, radar, sonar, channel modeling in wireless communications, image processing, the estimation of MIMO channels parameters, blind source separation and many more [1]. According to these models the measured signals or the data can be stacked into multi-dimensional arrays or tensors. Moreover, in biomedical data processing multi-dimensional models have been widely used recently. For example, biomedical signals like Electroencephalograms (EEG), Magnetoencephalograms (MEG) or Electrocardiograms (ECG) are recorded from many sensors simultaneously. Therefore, it is natural to use multi-dimensional models or tensors for representing these signals.Different types of tensor decompositions are used for the extraction of features from the data or to denoise recorded signals. However, in biomedical signal processing the most frequently used decompositions of multi-dimensional data Alexey A. Korobkov and Marina K. Diugurova are with the