Encoding of multivariate stimuli with MIMO neural circuits

We present a general MIMO neural circuit architecture for the encoding of multivariate stimuli in the time domain. The signals belong to the finite space of vector-valued trigonometric polynomials. They are filtered with a linear time-invariant kernel and then processed by a population of leaky integrate-and-fire neurons. We present formal, intuitive, necessary conditions for faithful encoding and provide a perfect recovery (decoding) algorithm. We extend these results to multivariate product spaces and apply them to video encoding with MIMO neural circuits. We demonstrate that our encoding circuits can serve as measurement devices for compressed sensing of frequency sparse signals. Finally, we provide necessary spike density conditions for the decoding of infinite-dimensional vector valued bandlimited functions encoded with MIMO neural circuits.