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

Abstract

Multifrequency 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).

Sequential fusion estimation for multisensor multirate systems with measurement outliers

“…• Develop a local filter (11) such that the filtering error covariance p l (h k ) has an upper bound Γ l (h k ); • At each sampling moment, the desired filter gain k l (h k ) can be obtained by minimizing the upper bound Γ l (h k ); • The obtained local estimation values are fused by resorting to the sequential fusion method at each sampling moment.…”

“…Most of the literature on estimation issues is based on the assumption that the system devices and sensors have a uniform sampling rate. However, in a complex and practical system, the assumption of uniform sampling is frequently unreasonable due to various kinds of physical restrictions (equipment specification, energy, and cost) on system components [11][12][13]. Combined with the practical requirements, using diverse sampling rates to collect different signals for different efforts has clear engineering insights [14][15][16].…”

Dataset Evaluation Method and Application for Performance Testing of SSVEP-BCI Decoding Algorithm

“…However, the majority of current algorithmic research utilizes one or two datasets to verify their performance [ 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ], which did not make full use of public data resources, and the results were limited by the distribution of data samples in individual datasets, so it was not conducive to judge the application effect of the algorithm in the actual scene through the result. This issue has two underlying causes.…”