This paper models signals and noise for extracellular neural recording. Although recorded data approximately follow Gaussian distribution, there are slight deviations that are critical for signal detection: a statistical examination of neural data in Hilbert space shows that noise forms an exponential term while signals form a polynomial term. These two terms can be used to estimate a spiking probability map that indicates spike presence. Both synthesized data and animal data are used for the detection performance evaluation and comparison against other popular detectors. Experimental results suggest that the predicted spiking probability map is consistent with the benchmark and work robustly with different recording preparations.
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