Back-Projection Cortical Potential Imaging Using a Multi-Resolution Optimization Algorithm

Over the last decade, electroencephalogram (EEG) has evolved to be a well-established brain activity imaging tool. This progress is mainly due to high-resolution (HR) EEG methods. These methods aim to reduce the smearing of the scalp potentials, which is the effect of the low-conductive skull. One type of these HR-EEG is the cortical potential imaging (CPI) that estimates the detailed cortical potential distribution from the measured scalp EEG potentials, known as the inverse problem. Even though some of these methods exhibit good performance, most of them hold inherent inaccuracies and limit out-coming from their principle of operation which is mostly based on a set of constraints on the solution. Some other CPI methods exhibit good results but are computational exhaustive. The back-projection CPI (BP-CPI) method has the advantages of being constraint free and computation inexpensive along with good estimation accuracy. However, better performance must be achieved. This study propose two improvements to the BP-CPI algorithm. Both improvements are successive stages to the BP-CPI and based on the multi-resolution optimization approach. The novel techniques differ in their clustering algorithm that have random and deterministic components, denoted as the rMR-CPI and dMR-CPI, respectively. A series of simulations were performed to examine the proposed improvements. The results have shown fast convergence to highly accurate cortical potential estimations, demonstrating accuracy of 96% (rMR-CPI) and 93% (dMR-CPI), relative to the BP-CPI which has shown accuracy of 85%. The MR-CPI methods were shown to be reliable CPI methods enabling researchers fast and robust high-resolution EEG.