Linear Diophantine equation (LDE) decoder: A training‐free decoding algorithm for multifrequency SSVEP with reduced computation cost

Abstract

AbstractMultifrequency steady‐state visual evoked potentials (SSVEPs) have been developed to extend the capability of SSVEP‐based brain‐machine interfaces (BMIs) to complex applications that have large numbers of targets. Even though various multifrequency stimulation methods have been introduced, the decoding algorithms for multifrequency SSVEP are still in early development. The recently developed multifrequency canonical correlation analysis (MFCCA) was shown to be a feasible training‐free option to use in decoding multifrequency SSVEPs. However, the time complexity of MFCCA is shown to be , which will lead to long computation time as grows, where represents the input size in decoding. In this paper, a novel decoding algorithm is proposed with the aim to reduce the time complexity. This algorithm is based on linear Diophantine equation solvers and has a reduced computation cost while remaining training‐free. Our simulation results demonstrated that linear Diophantine equation (LDE) decoder run time is only one fifth of MFCCA run time under respective optimal settings on 5‐s single‐channel data. This reduced computation cost makes it easier to implement multifrequency SSVEP in real‐time systems. The effectiveness of this new decoding algorithm is validated with nine healthy participants when using dry electrode scalp electroencephalography (EEG).