Resolvability of MUSIC algorithm in solving multiple dipole biomagnetic localization from spatio-temporal MCG data

The MUSIC (MUltiple SIgnal Classification) algorithm is a recently proposed method in solving multiple dipole localization problem from spatio-temporal magnetocardiograph (MCG) data. There are many factors that may effect the resolvability of MUSIC method in solving MCG inverse problem. For example, the number and space arrangement of sensors, the signal-noise ratio (SNR) of measurement data, the relative position of dipole to the sensors, the direction of dipole. In the case of multiple dipoles are assumed, the distance and time correlation between the dipoles may take a great effect on the solution accuracy. We need a quantitative method to evaluate the resolvability of MUSIC algorithm. In this paper spherically symmetric conductor model is applied as the forward model. The statistical performance of the MUSIC algorithm is discussed by using the MUSIC error covariance matrix. The Cramer-Rao Lower Bound (CRLB) on localization errors for MCG current source dipole models is presented. The performance of MUSIC algorithm is compared with the ultimate performance corresponding to the CRLB. The numerical studies with simulated MCG data are presented in two cases: one dipole is assumed and two dipoles are assumed, From our analysis and simulations, we can conclude that, for uncorrelated dipole signals, the MUSIC algorithm has an excellent performance. For correlated dipole signals, however, the MUSIC cannot achieve the CRLB. Our numerical analysis also demonstrate the degradation of the MUSIC efficiency when the time correlation between two dipoles increases even for high values of the number of sensors and SNR. We also see that localization error is not simply a function of the relative distance between the two dipoles, but rather a complex function of absolute dipole position and orientation.