Objective. Electrical recordings of neural activity from brain surface have been widely employed in basic neuroscience research and clinical practice for investigations of neural circuit functions, brain-computer interfaces, and treatments for neurological disorders. Traditionally, these surface potentials have been believed to mainly reflect local neural activity. It is not known how informative the locally recorded surface potentials are for the neural activities across multiple cortical regions.Approach. To investigate that, we perform simultaneous local electrical recording and wide-field calcium imaging in awake head-fixed mice. Using a recurrent neural network model, we try to decode the calcium fluorescence activity of multiple cortical regions from local electrical recordings.Main results. The mean activity of different cortical regions could be decoded from locally recorded surface potentials. Also, each frequency band of surface potentials differentially encodes activities from multiple cortical regions so that including all the frequency bands in the decoding model gives the highest decoding performance. Despite the close spacing between recording channels, surface potentials from different channels provide complementary information about the large-scale cortical activity and the decoding performance continues to improve as more channels are included. Finally, we demonstrate the successful decoding of whole dorsal cortex activity at pixel-level using locally recorded surface potentials.Significance. These results show that the locally recorded surface potentials indeed contain rich information of the large-scale neural activities, which could be further demixed to recover the neural activity across individual cortical regions. In the future, our cross-modality inference approach could be adapted to virtually reconstruct cortex-wide brain activity, greatly expanding the spatial reach of surface electrical recordings without increasing invasiveness. Furthermore, it could be used to facilitate imaging neural activity across the whole cortex in freely moving animals, without requirement of head-fixed microscopy configurations.