A new data covariance matrix estimation for improving minimum variance brain source localization

Abstract

Data with finite samples results in accuracy and robustness reduction of data covariance matrix estimation, which in turn results in performance reduction of minimum variance beamformer (MVB) for brain source localization (BSL). General linear combination (GLC) and convex combination (CC) are methods of interest for data covariance matrix estimation and increasing its accuracy and robustness because their scalar coefficients are obtained automatically and adaptively. However, based on our best knowledge, the applicability of GLC and CC algorithms has not been investigated for BSL to inform us about their performance. In this paper, we have two goals: 1) Investigation of GLC and CC covariance matrices applications for BSL is carried out using various simulated MEG scenarios and real MEG and clinical epilepsy data; 2) Modified GLC and CC are developed for more accurate and robust estimation of data covariance matrix when data with finite samples is available. In the modified versions, the scalar coefficients are replaced by diagonal matrix form coefficients. These matrix form coefficients are computed using the Hadamard product and mean square error concept. The evaluations show that the CC and modified CC based MVBs are not robust for BSL due to very small values of coefficients. Based on the simulated, real, and clinical data results, it can be stated that the modified GLC is significantly superior to conventional GLC in terms of localization error, spatial resolution (all z < -2; all p-values < 0.001), and offering reliable results. Also, the proposed GLC offers fewer missed sources and less sensitivity to the depth biasing problem, particularly in a high signal-to-noise ratio. In conclusion, it can be said that the covariance matrix of modified GLC which is user-free and robust against the finite data samples can improve the MVB performance for BSL in terms of localization error and spatial resolution.