Grid cell firing field detection using compressed sensing

The discovery of the striking tessellating firing fields of the grid cells has boosted research on brain circuits that dynamically represent self-location. The detection of such cells demands long-ran recordings, in order for the whole grid mosaic to be clearly revealed. The scope of this study is to present a methodology for unraveling the complete firing field of a grid cell even when it is poorly represented by the recorded spikes. The proposed approach is based on the fact that the recorded spikes of a grid cell during random navigation in the environment can be considered as a sampling process of the respective whole grid field (GF) seen as a binary image. In this work the Approximate Message Passing algorithm is used to reveal the whole GF image of a grid cell only by a few samples. The proposed approach was tested both in simulated and real data with promising results (mean squared error less than 0.15). The efficiency of the reconstruction process appeared to depend on the rat's route within the environment and on the respective probability of changing route direction in every step. The proposed approach pave the way for efficient methods to detect and identify grid cells. Nevertheless, experimentation with real rats' sample routes would further enhance the reconstruction efficiency. Overall, this paper tackles, for the first time, the problem of detecting grid cells' firing fields even if the corresponding recorded spikes do not represent their figure adequately and proposes respective signal processing methodology for its solution.