This paper aims to provide a method for using magnetic resonance electrical impedance tomography (MREIT) to visualize local conductivity changes associated with evoked neuronal activities in the brain. MREIT is an MRI-based technique for conductivity mapping by probing the magnetic flux density induced by an externally injected current through surface electrodes. Since local conductivity changes resulting from evoked neural activities are very small (less than a few %), a major challenge is to acquire exogenous magnetic flux density data exceeding a certain noise level. Noting that the signal-to-noise ratio is proportional to the square root of the number of averages, it is important to reduce the data acquisition time to get more averages within a given total data collection time. The proposed method uses a sub-sampled k-space data set in the phase-encoding direction to significantly reduce the data acquisition time. Since the sub-sampled data violates the Nyquist criteria, we only get a nonlinearly wrapped version of the exogenous magnetic flux density data, which is insufficient for conductivity imaging. Taking advantage of the sparseness of the conductivity change, the proposed method detects local conductivity changes by estimating the time-change of the Laplacian of the nonlinearly wrapped data.