Eigenspace Minimum L1-Norm Beamformer Reconstruction of Functional Magnetic Resonance Inverse Imaging of Visuomotor Processing

INTRODUCTION Dynamic magnetic resonance (MR) inverse imaging (InI) can improve the temporal resolution of blood oxygen level dependent (BOLD) contrasts fMRI to the order of milliseconds [1]. In InI, the spatial resolution and the source localization accuracy both critically rely on the signal-to-noise ratio (SNR) of the measurements [1]. The localization of the functional activity in ill-posed InI measurements with improved SNR can be done by employing beamformers. Many beamformers are mainly derived from minimizing the output variance of spatial filters quantified by the L2 norm. And the results are usually spatially blurred. Previously, source localizations based on the L1 norm minimization has been proposed to give spatially focal estimates of neuronal currents measured by the magnetocephalography (MEG) [2][3]. Mathematically, the minimization of the L1 norm has always been applied to the current distribution itself. To our knowledge, there has no studies incorporating the minimization of the L1 norm in the design of spatial filter for functional brain imaging analysis yet. Here we propose a beamformer approach combining the eigenspace of the measured data and the L1 norm minimization of the spatial filters’ output noise amplitudes. The method was found capable of reconstructing hemodynamic signals in both spatial and temporal fashion and providing less blurry functional images than LCMV beamformer in our visuomotor experiments. METHODS The noise-whitened InI measurement for one pixel in the accelerated projection image within the FOV is denoted as Yw, which can be expressed as w w w n X A Y + ⋅ = ,