Electroencephalography (EEG) source imaging aims to reconstruct brain activity maps from the neuroelectric potential difference measured on the skull. To obtain the brain activity map, we need to solve an ill-posed and ill-conditioned inverse problem that requires regularization techniques to make the solution viable. When dealing with real-time applications, dimensionality reduction techniques can be used to reduce the computational load required to evaluate the numerical solution of the EEG inverse problem. To this end, in this paper we use the random dipole sampling method, in which a Monte Carlo technique is used to reduce the number of neural sources. This is equivalent to reducing the number of the unknowns in the inverse problem and can be seen as a first regularization step. Then, we solve the reduced EEG inverse problem with two popular inversion methods, the weighted Minimum Norm Estimate (wMNE) and the standardized LOw Resolution brain Electromagnetic TomogrAphy (sLORETA). The main result of this paper is the error estimates of the reconstructed activity map obtained with the randomized version of wMNE and sLORETA. Numerical experiments on synthetic EEG data demonstrate the effectiveness of the random dipole sampling method.

Abstract. Electroencephalography (EEG) source imaging aims to reconstruct brainactivity maps from the neuroelectric potential difference measured on the skull. Toobtain the brain activity map, we need to solve an ill-posed and ill-conditionedinverse problem that requires regularization techniques to make the solution viable.When dealing with real-time applications, dimensionality reduction techniques can beused to reduce the computational load required to evaluate the numerical solutionof the EEG inverse problem. To this end, in this paper we use the random dipolesampling method, in which a Monte Carlo technique is used to reduce the numberof neural sources. This is equivalent to reducing the number of the unknownsin the inverse problem and can be seen as a first regularization step. Then, wesolve the reduced EEG inverse problem with two popular inversion methods, theweighted Minimum Norm Estimate (wMNE) and the standardized LOw Resolutionbrain Electromagnetic TomogrAphy (sLORETA). The main result of this paper is theerror estimates of the reconstructed activity map obtained with the randomized versionof wMNE and sLORETA. Numerical experiments on synthetic EEG data demonstratethe effectiveness of the random dipole sampling method.