Exploring Tensor-Based Optimization for Missing EEG Signal Recovery: A Comparative Study of Optimization Methods Across Different Tensor Decomposition Frameworks

Electroencephalography (EEG) signals are frequently compromised by missing data due to electrode contact issues or subject movement. Tensor decomposition has emerged as a powerful technique for analyzing multidimensional EEG data. This study evaluates various tensor-based methods for reconstructing structured and unstructured missing EEG signals, including recovery methods based on canonical polyadic (CP) decomposition, tensor singular value decomposition (t-SVD), and tucker decomposition. Notably, this research represents the first application of t-SVD-based recovery to missing EEG data. To rigorously assess the efficacy of our proposed method, we implement a dual evaluation framework encompassing: a) signal recovery indices and b) classification performance metrics. In the most challenging structured missing data scenario (missing segments <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> = 80, duration <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> = 1.8<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i>), the t-SVD-based method demonstrate superior performance based on signal recovery indices, followed by the tucker-based method, while CP-based approaches exhibited inferior results. We further evaluate the impact of signal recovery on classification accuracy by comparing performance on complete, missing, and recovered data using six classifiers and five metrics. In the most severe structured-missing case, employing a Linear Discriminant Analysis classifier, the t-SVD method enhance accuracy from 46.36% (missing data) to 56.50%, surpassing the tucker-based method (54.29%) and both CP-based methods (48.21% and 49.07%), approaching the accuracy achieved with the original data (58.57%). These results demonstrate the superior capability of t-SVD-based recovery method in preserving discriminative features within EEG signals. This research offers promising solutions for enhancing EEG signals quality and subsequent analysis in challenging real-world scenarios.