Massively parallel neural circuits for stereoscopic color vision: encoding, decoding and identification.

Past work demonstrated how monochromatic visual stimuli could be faithfully encoded and decoded under Nyquist-type rate conditions. Color visual stimuli were then traditionally encoded and decoded in multiple separate monochromatic channels. The brain, however, appears to mix information about color channels at the earliest stages of the visual system, including the retina itself. If information about color is mixed and encoded by a common pool of neurons, how can colors be demixed and perceived? We present Color Video Time Encoding Machines (Color Video TEMs) for encoding color visual stimuli that take into account a variety of color representations within a single neural circuit. We then derive a Color Video Time Decoding Machine (Color Video TDM) algorithm for color demixing and reconstruction of color visual scenes from spikes produced by a population of visual neurons. In addition, we formulate Color Video Channel Identification Machines (Color Video CIMs) for functionally identifying color visual processing performed by a spiking neural circuit. Furthermore, we derive a duality between TDMs and CIMs that unifies the two and leads to a general theory of neural information representation for stereoscopic color vision. We provide examples demonstrating that a massively parallel color visual neural circuit can be first identified with arbitrary precision and its spike trains can be subsequently used to reconstruct the encoded stimuli. We argue that evaluation of the functional identification methodology can be effectively and intuitively performed in the stimulus space. In this space, a signal reconstructed from spike trains generated by the identified neural circuit can be compared to the original stimulus.